The 100 most-cited articles in Physical review. B./Physical review. B, 2018

Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward a different ordering unique to non-Hermitian lattices whereby a pristine system becomes devoid of extended states, a property which turns out to be robust to disorder. This is enabled by a peculiar type of non-Hermitian degeneracy where a macroscopic fraction of the states coalesce at a single point with a geometrical multiplicity of 1.

We introduce and explore a one-dimensional ``hybrid'' quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a ``quantum Zeno phase'' where strong measurements suppress the entanglement growth to saturate in an area law. Extensive numerical simulations of the quantum trajectories of the many-particle wave functions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable ``weak measurement phase'' that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a continuous quantum dynamical phase transition between the ``weak measurement phase'' and the ``quantum Zeno phase,'' driven by a competition between the entangling…

Recent observation of intrinsic ferromagnetism in two-dimensional (2D) ${\mathrm{CrI}}_{3}$ is associated with the large magnetic anisotropy due to strong spin-orbit coupling of I. Magnetic anisotropy energy (MAE) defines the stability of magnetization in a specific direction with respect to the crystal lattice and is an important parameter for nanoscale applications. In this work we apply the density functional theory to study the strain dependence of MAE in 2D monolayer chromium trihalides $\mathrm{Cr}{X}_{3}$ (with $X$ = Cl, Br, and I). Detailed calculations of their energetics, atomic structures, and electronic structures under the influence of a biaxial strain $\ensuremath{\varepsilon}$ have been carried out. It is found that all three compounds exhibit ferromagnetic ordering at the ground state (with $\ensuremath{\varepsilon}=0$), and upon applying a compressive strain, phase transition to the antiferromagnetic state occurs. Unlike in ${\mathrm{CrCl}}_{3}$ and ${\mathrm{CrBr}}_{3}$, the electronic band gap in ${\mathrm{CrI}}_{3}$ increases when a tensile strain is applied. The…

Here, higher-order topological insulators and superconductors protected by inversion symmetry are investigated. These phases are characterized by gapped bulk and surface with gapless modes confined to hinges or corners of the sample. Such surface states can be understood as topological defects that are globally stabilized by inversion. They can be built using a layer construction that embeds a standard topological insulator/superconductor into a higher dimension by symmetrically adding to it copies of itself. Using this procedure, a complete classification of such states in any dimension is obtained and several examples for possible physical realizations are provided.

We address the conditions required for a $\mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally symmetric SSH model will possess a ``conjugated-pseudo-Hermiticity'' which we show is responsible for a quantized ``complex'' Berry phase. Consequently, we provide an example where the complex Berry phase of a band is used as a quantized invariant to predict the existence of gapless edge modes in a non-Hermitian model. The chirally broken, $PT$-symmetric model is studied; we suggest an explanation for why the topological invariant is a global property of the Hamiltonian. A geometrical picture is provided by examining eigenvector evolution on the Bloch sphere. We justify our analysis numerically and discuss relevant applications.

Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not yet been found in photonic crystals. Here, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically nontrivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily fabricated structure of the photonic crystals, different topological phases can be realized straightforwardly. Our study can be generalized to higher dimensions and provides a platform for higher-order photonic topological insulators and semimetals.

Recent experiments on Rydberg-atom quantum simulators have observed surprising signatures of nonergodic quantum dynamics, which has been attributed to the emergence of ``many-body quantum scars.'' Here, the authors present a detailed study of the eigenstate properties of strongly interacting Rydberg-atom chains, identifying distinct families of quantum scarred states that are responsible for the revivals in the quench dynamics. The results show that quantum scarred states have distinct features, such as subthermal entanglement and anomalous expectation values of local observables. The presence of scarred eigenstates leaves an imprint on the rest of the many-body spectrum, leading to a weak breakdown of ergodicity.

Transition-metal dichalcogenides (TMDs) monolayers have been considered as important two-dimensional semiconductor materials for the study of fundamental physics in the field of spintronics. However, the out-of-plane mirror symmetry in TMDs may constrain electrons' degrees of freedom and it may limit spin-related applications. Recently, a newly synthesized Janus TMDs MoSSe was found to intrinsically possess both the in-plane inversion and the out-of-plane mirror-symmetry breaking. Here we performed first-principles calculations in order to systematically investigate the electronic band structures of a series of Janus monolayer TMDs with chemical formula $MXY\phantom{\rule{0.16em}{0ex}}(M=\mathrm{Mo},\phantom{\rule{0.16em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{and}\phantom{\rule{0.16em}{0ex}}X,Y=\mathrm{S},\phantom{\rule{0.16em}{0ex}}\mathrm{Se},\phantom{\rule{0.16em}{0ex}}\mathrm{Te})$. It is found that they possess robust electronic properties like their parent phases. We explored also the effect of perpendicular external electric field and in-plane biaxial strain on…

While topological insulators have a gapped bulk band structure, they have gapless surface states. Recently, it was shown that the presence of additional crystalline symmetries can lead to topological phases that combine a gapped bulk spectrum with gapless states on edges or corners of the crystal. Such topological phases have been called ``higher-order topological phases''. This article presents a complete classification of second-order topological insulators and superconductors with mirror, twofold-rotation, or inversion symmetry. The authors show that crystals with a mirror symmetry and a nontrivial bulk band structure either have gapless surfaces or gapless edges. On the other hand, there are crystals with twofold rotation or inversion symmetry with a nontrivial bulk topology but without surface or edge states.

We present a transparent and computationally efficient approach for the first-principles calculation of Hubbard parameters from linear-response theory. This approach is based on density-functional perturbation theory and the use of monochromatic perturbations. In addition to delivering much improved efficiency, the present approach makes it straightforward to calculate automatically these Hubbard parameters for any given system, with tight numerical control on convergence and precision. The effectiveness of the method is showcased in three case studies---${\mathrm{Cu}}_{2}\mathrm{O}$, NiO, and ${\mathrm{LiCoO}}_{2}$---and by the direct comparison with finite differences in supercell calculations.

Due to mirror symmetry breaking, two-dimensional Janus transition metal dichalcogenides $MXY$ ($M=\text{Mo,W}$; $X,Y=\text{S,Se,Te}$) present charming electronic properties. However, there have not been many related studies as of yet, and the intrinsic physical pictures are unclear. Here, we use first-principles calculations to explore the universality of electronic characteristics and photocatalyst applications of Janus $MXY$, finding that the induced dipole moment, vibrational frequency, Rashba parameters, and direct-indirect band transition of monolayer $MXY$ are deeply associated with the atomic radius and electronegativity differences of chalcogen $X$ and $Y$ elements. The internal electric field renders Janus $MXY$ the ideal photocatalysts. Moreover, the stacking-dependent on/off switch of the dipole moment further confirms that asymmetric Janus $MXY$ serves as a promising candidate for highly efficient photocatalysts within a broad range from infrared, visible, to ultraviolet light.

Here, the authors develop a general formalism to analytically compute the entanglement spectra of exact excited states and use it to obtain the entanglement spectra of the infinite tower of states of the spin-$S$ AKLT models, which are the first analytical examples of what are now called quantum many-body scars. Located in the bulk of the spectrum, these states have a subthermal entanglement entropy, showing for the first time the violation of the strong eigenstate thermalization hypothesis (ETH) in a well-known translation-invariant nonintegrable model.

Hexagonal boron nitride ($h$-BN) is a technologically important electronic and dielectric material. Recently, research into this material has intensified due to the discovery of bright single-photon-emitting color centers in the form of point defects, with potential applications in advanced quantum technologies. Despite this technological promise, the defect physics of this material is still largely unexplored. Here, the authors have performed detailed first-principles investigations of the defect properties of $h$-BN, finding that the defect physics of this material is dictated by impurities, in particular carbon, oxygen, and hydrogen. They show how the defect properties of this material can be selectively engineered by growth or processing conditions. These insights will be fundamental to controlled generation of single-photon emitters and for general defect engineering of this material.

We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence bands cross on closed nodal surfaces in the Brillouin zone. We propose different classes of nodal surfaces, both in the absence and in the presence of spin-orbit coupling (SOC). In the absence of SOC, a class of nodal surfaces can be protected by space-time inversion symmetry and sublattice symmetry and characterized by a ${\mathbb{Z}}_{2}$ index, while another class of nodal surfaces are guaranteed by a combination of nonsymmorphic twofold screw-rotational symmetry and time-reversal symmetry. We show that the inclusion of SOC will destroy the former class of nodal surfaces but may preserve the latter provided that the inversion symmetry is broken. We further generalize the result to magnetically ordered systems and show that protected nodal surfaces can also exist in magnetic materials without and with SOC, given that certain magnetic group…

Motivated by the exciting discovery of correlated insulating behavior and superconductivity in magic-angle bilayer graphene, the authors discuss here the salient features of the band structure of this system. A remarkable feature is the appearance of isolated, nearly flat bands around the magic angles. The authors discuss the importance of emergent symmetries of this system and clarify some potential confusion regarding commensurate structures of twisted bilayer graphene. Furthermore, they discuss the band topology, which leads to obstructions to constructing well-localized Wannier functions of the nearly flat bands, and give directions towards overcoming the difficulties.

We probe the accuracy limit of ab initio calculations of carrier mobilities in semiconductors, within the framework of the Boltzmann transport equation. By focusing on the paradigmatic case of silicon, we show that fully predictive calculations of electron and hole mobilities require many-body quasiparticle corrections to band structures and electron-phonon matrix elements, the inclusion of spin-orbit coupling, and an extremely fine sampling of inelastic scattering processes in momentum space. By considering all these factors we obtain excellent agreement with experiment, and we identify the band effective masses as the most critical parameters to achieve predictive accuracy. Our findings set a blueprint for future calculations of carrier mobilities, and pave the way to engineering transport properties in semiconductors by design.

We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moir\'e pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moir\'e Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the exciton moir\'e potential energy restores circular optical selection rules by coupling excitons with different center of mass momenta. A variety of interlayer excitons with both senses of circular optical activity, and energies that are tunable by twist angle, are present at each valley. The lowest energy exciton states are generally localized near the exciton potential energy minima. We discuss the possibility of using the moir\'e pattern to achieve scalable two-dimensional arrays of nearly…

In bilayer graphene with a small twist angle, the moir\'e pattern creates a superlattice with over 10000 atoms per supercell and complex minibands with a small bandwidth. The low-energy narrow bands host correlated insulating and unconventional superconducting phases discovered recently. Here, the authors introduce a two-orbital tight-binding and Hubbard model on a honeycomb lattice to capture the physics of these narrow bands. This model provides a starting point for studying the metal-insulator transition, Landau level degeneracy lifting, and superconductivity in twisted bilayer graphene.

We introduce configuration space as a natural representation for calculating the mechanical relaxation patterns of incommensurate two-dimensional (2D) bilayers. The approach can be applied to a wide variety of 2D materials through the use of a continuum model in combination with a generalized stacking fault energy for interlayer interactions. We present computational results for small-angle twisted bilayer graphene and molybdenum disulfide (${\mathrm{MoS}}_{2}$), a representative material of the transition-metal dichalcogenide family of 2D semiconductors. We calculate accurate relaxations for ${\mathrm{MoS}}_{2}$ even at small twist-angle values, enabled by the fact that our approach does not rely on empirical atomistic potentials for interlayer coupling. The results demonstrate the efficiency of the configuration space method by computing relaxations with minimal computational cost. We also outline a general explanation of domain formation in 2D bilayers with nearly aligned lattices, taking advantage of the relationship between real space and configuration space. The configuration…

We discuss a method of numerically identifying exact energy eigenstates for a finite system, whose form can then be obtained analytically. We demonstrate our method by identifying and deriving exact analytic expressions for several excited states, including an infinite tower, of the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) model, a celebrated nonintegrable model. The states thus obtained for the AKLT model can be interpreted as from one to an extensive number of quasiparticles on the ground state or on the highest excited state when written in terms of dimers. Included in these exact states is a tower of states spanning energies from the ground state to the highest excited state. Some of the states of the tower appear to be in the bulk of the energy spectrum, allowing us to make conjectures on the strong eigenstate thermalization hypothesis. We also generalize these exact states including the tower of states to the generalized integer spin AKLT models. Furthermore, we establish a correspondence between some of our states and those of the Majumdar-Ghosh model, yet…

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in nonintegrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse-grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the ``Floquet-Fredrickson-Andersen'' model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive…

A recent paper [D. Go et al., Phys. Rev. Lett. 121, 086602 (2018)] proposed that the intrinsic orbital Hall effect (OHE) can emerge from momentum-space orbital texture in centrosymmetric materials. In searching for real materials with strong OHE, we investigate the intrinsic OHE in metals with small spin-orbit coupling (SOC) in face-centered cubic and body-centered cubic structures (Li, Al, V, Cr, Mn, Ni, and Cu). We find that orbital Hall conductivities (OHCs) in these materials are gigantic $\ensuremath{\sim}{10}^{3}\ensuremath{-}{10}^{4}\phantom{\rule{4pt}{0ex}}(\ensuremath{\hbar}/e){(\mathrm{\ensuremath{\Omega}}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{cm})}^{\ensuremath{-}1}$, which are comparable or larger than spin Hall conductivity (SHC) of Pt. Although SHCs in these materials are smaller than OHCs due to small SOC, we found that SHCs are still sizable and the spin Hall angles may be of the order of 0.1. We discuss implications on recent spin-charge interconversion experiments on materials having small SOC.

The anomalous nature of spin transport in the XXZ quantum spin chain has been a topic of theoretical interest for some time. Here, the integrability of the underlying dynamics leads to a ballistic component of the spin current, characterized by a spin Drude weight, which measures the degree of divergence of the zero-frequency spin conductivity. However, this quantity had previously proven to be beyond the reach of standard Bethe ansatz techniques. Here, the authors show that a recently developed hydrodynamic formalism for quantum integrable models may be used to compute the spin Drude weight. They also propose a numerical scheme to obtain hydrodynamic predictions for finite-time energy transport. This suggests that the hydrodynamic approach captures completely the ballistic component that dominates transport at long times and distances in the gapless regime of the XXZ model.

Here, the authors tune the color of light emitted by single-atom imperfections (silicon vacancy color centers) inside a diamond. Such tunable imperfections can be networked together to build a quantum internet, where information can be securely exchanged using the laws of quantum physics. One problem is that all the centers need to emit at precisely the same color or wavelength. The authors overcome this challenge by placing color centers inside a diamond nanostring. By adjusting the tension in the string, atoms are stretched inside the crystal and tune the center to emit photons of a desired wavelength. The tuning method involves bending the string with a force controlled handily with an electrical voltage. A symphony of such tunable diamond strings could serve as the backbone of a future quantum internet.

The current efforts to find the materials hosting Kitaev model physics have been focused on Mott insulators of ${d}^{5}$ pseudospin-1/2 ions ${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ru}}^{3+}$ with ${t}_{2g}^{5}(S=1/2,L=1)$ electronic configuration. Here we propose that the Kitaev model can be realized in materials based on ${d}^{7}$ ions with ${t}_{2g}^{5}{e}_{g}^{2}(S=3/2,L=1)$ configuration such as ${\mathrm{Co}}^{2+}$, which also host the pseudospin-1/2 magnetism. Considering possible exchange processes, we have derived the ${d}^{7}$ pseudospin-1/2 interactions in ${90}^{\ensuremath{\circ}}$ bonding geometry. The obtained Hamiltonian comprises the bond-directional Kitaev $K$ and isotropic Heisenberg $J$ interactions as in the case of ${d}^{5}$ ions. However, we find that the presence of additional spin-active ${e}_{g}$ electrons radically changes the balance between Kitaev and Heisenberg couplings. Most remarkably, we show that the exchange processes involving ${e}_{g}$ spins are highly sensitive to whether the system is in Mott ($U<\mathrm{\ensuremath{\Delta}}$) or charge-transfer…

We analyze a two-dimensional Kondo lattice model with special emphasis on non-Hermitian properties of the single-particle spectrum, following a recent proposal by Kozii and Fu. Our analysis based on the dynamical mean-field theory elucidates that the single-particle spectral weight shows the exceptional points (EPs). Correspondingly, the spectral weight exhibits the band touching, resulting in a structure similar to the Fermi arc. Furthermore, we find an intriguing phenomenon arising from the periodicity of the lattice. The EPs generated by two distinct Dirac points merge and change into a hybrid point, which vanishes as the exchange interaction is increased. Accordingly, the paramagnetic phase in the low-temperature region shows a significant difference from noninteracting fermions: the imaginary part of the self-energy yields the Fermi loop without any defective points.

The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time reversal in his theory of ``elementary'' band representations. In a recent paper [Bradlyn et al., Nature (London) 547, 298 (2017)] we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups.…

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

The specificity of modal-expansion formalisms is their capabilities to model the physical properties in the natural resonance-state basis of the system in question, leading to a transparent interpretation of the numerical results. In electromagnetism, modal-expansion formalisms are routinely used for optical waveguides. In contrast, they are much less mature for analyzing open non-Hermitian systems, such as micro- and nanoresonators. Here, by accounting for material dispersion with auxiliary fields, we considerably extend the capabilities of these formalisms, in terms of computational effectiveness, number of states handled, and range of validity. We implement an efficient finite-element solver to compute the resonance states, and derive closed-form expressions of the modal excitation coefficients for reconstructing the scattered fields. Together, these two achievements allow us to perform rigorous modal analysis of complicated plasmonic resonators, being not limited to a few resonance states, with straightforward physical interpretations and remarkable computation speeds. We…

Toroidal multipole moments are usually underestimated as they are quite weak in most cases of light-matter interaction. Herein, we reveal a strong link between the toroidal dipole resonance and the bound state in the continuum in the context of all-dielectric metasurfaces. We introduce the concept of toroidal dipole bound states in the continuum, in which two eigenmodes of the silicon metasurface exhibit an intrinsic toroidal dipolar character and have an infinite lifetime. They can be classified as transverse (trivial) and longitudinal (nontrivial) toroidal dipole modes, which correspond to symmetry unprotected and protected bound states in the continuum, respectively. We demonstrate that such toroidal bound states in the continuum supported by the symmetry metasurface can be turned into ultrahigh-$Q$ resonances with a dominant toroidal dipole excitation, which validates their physical origin associated with the ultrahigh-$Q$ toroidal dipole leaky resonances. A full multipole decomposition with dispersive, lossy, and substrate effects further validates that the proposed concept is…

We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two-level systems and quantum harmonic oscillators. In particular, we study energy-transfer processes from a given quantum system, termed a ``charger,'' to another one, i.e., the proper ``battery.'' In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by properly accounting for them in the global energy balance of the model.

In the present work, the electronic and vibrational properties of both pristine ${\mathrm{V}}_{2}\mathrm{C}$ and fully terminated ${\mathrm{V}}_{2}\mathrm{C}{T}_{2}$ (where $T=\mathrm{F},$ O, OH) two-dimensional monolayers are investigated using density functional theory. First, the atomic structures of ${\mathrm{V}}_{2}\mathrm{C}$-based MXene phases are optimized, and their respective dynamical stabilities are discussed. Second, electronic band structures are computed indicating that ${\mathrm{V}}_{2}\mathrm{C}$ is metallic as well as all the corresponding functionalized systems. Third, the vibrational properties (phonon frequencies and spectra) of ${\mathrm{V}}_{2}\mathrm{C}$-based MXenes are computed with the density functional perturbation theory and reported. Both Raman-active (${E}_{g}$, ${A}_{1g}$) and infrared-active (${E}_{u}$, ${A}_{2u}$) vibrational modes are predicted ab initio with the aim to correlate the experimental Raman peaks with the calculated vibrational modes and to assign them to specific atomic motions. The effect of the terminal groups on the vibrational…

The concept of multipoles has attracted growing interest in condensed matter physics, since it is widely utilized to characterize electronic states microscopically in a unified manner. Here, the authors theoretically construct a general formalism of multipole description by considering four independent types of multipoles: electric, magnetic, electric toroidal, and magnetic toroidal. The authors systematically derive microscopic expressions of multipoles in both real and momentum spaces, and clarify how multipoles determine the structure of electronic band and linear response tensors with or without space-time parity conversion. The complete tables to summarize the active multipoles under 32 crystallographic point groups will give a comprehensive and systematic understanding of a wide variety of physical phenomena at the microscopic level.

The nonlocal character of Majorana zero modes is a key feature for topological protection of Majorana qubits, and distinguishes separated Majorana bound states from localized Andreev modes. Applying recent theoretical results on the coupling of quantum dots at the wire ends to the zero-energy mode in the wire, the authors provide a first quantitative measure of the nonlocality of Majorana modes in semiconductor-superconductor hybrid nanowires. The spin character of the Majorana mode is revealed by analyzing its coupling to two consecutive quantum dot resonances. Cases of zero modes with moderate and high degrees of nonlocality are compared.

The restricted Boltzmann machine is a fundamental building block of deep learning. The authors demonstrate its equivalence with tensor network states with explicit mappings, thus drawing a constructive connection between deep learning and quantum physics. On one side, deep learning approaches can be used to study novel states of matter. In return, investigations of tensor network states and their expressibility can be adapted to guide neural network architecture design.

We have developed a formalism of the exact solution to linearized phonon Boltzmann transport equation (BTE) for thermal conductivity calculation including three- and four-phonon scattering. We find strikingly high four-phonon scattering rates in single-layer graphene (SLG) based on the optimized Tersoff potential. The reflection symmetry in graphene, which forbids the three-ZA (out-of-plane acoustic) scattering, allows the four-ZA processes $\mathrm{ZA}+\mathrm{ZA}\ensuremath{\rightleftharpoons}\mathrm{ZA}+\mathrm{ZA}$ and $\mathrm{ZA}\ensuremath{\rightleftharpoons}\mathrm{ZA}+\mathrm{ZA}$ + ZA. As a result, the large phonon population of the low-energy ZA branch originated from the quadratic phonon dispersion leads to high four-phonon scattering rates, even much higher than the three-phonon scattering rates at room temperature. These four-phonon processes are dominated by the normal processes, which lead to a failure of the single mode relaxation time approximation. Therefore, we have solved the exact phonon BTE using an iterative scheme and then calculated the length- and…

Noncentrosymmetric metals are anticipated to exhibit a dc photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing these nonlinear effects because they carry a large Berry curvature concentrated in small regions, i.e., near the Weyl points. We have implemented the semiclassical Berry curvature dipole formalism into an ab initio scheme and investigated the second-order nonlinear response for two representative groups of materials: the TaAs-family type-I WSMs and the ${\mathrm{MoTe}}_{2}$-family type-II WSMs. Both types of WSMs exhibited a Berry curvature dipole in which type-II Weyl points are usually superior to the type-I WSM because of the strong tilt. Corresponding nonlinear susceptibilities in several materials promise a nonlinear Hall effect in the dc field limit, which is within the experimentally detectable range.

Recent measurements in magic-angle twisted bilayer graphene find a correlated insulator flanked by superconducting domes upon tuning the gate voltage. These results have prompted an analogy with the high-${T}_{c}$ cuprates and the physics of doped Mott insulators. Here, the authors instead propose an analogy with alkali-doped C${}_{60}$ and a violation of Hund's first rule, whereby the resultant attractive interactions, as opposed to a large repulsive Hubbard $U$, are responsible for superconductivity. A two-band phenomenological model for twisted bilayer graphene is studied, which includes nematic orbital ferromagnet and orbital-triplet spin-singlet superconducting broken-symmetry phases.

We demonstrate a classical analog of electromagnetically induced transparency (EIT) in a highly flexible planar terahertz metamaterial (MM) comprised of three-gap split-ring resonators. The keys to achieve EIT in this system are the frequency detuning and hybridization processes between two bright modes coexisting in the same unit cell as opposed to bright-dark modes. We present experimental verification of two bright modes coupling for a terahertz EIT-MM in the context of numerical results and theoretical analysis based on a coupled Lorentz oscillator model. In addition, a hybrid variation of the EIT-MM is proposed and implemented numerically to dynamically tune the EIT window by incorporating photosensitive silicon pads in the split gap region of the resonators. As a result, this hybrid MM enables the active optical control of a transition from the on state (EIT mode) to the off state (dipole mode).

Recently, the experimental realization of flat bands in twisted bilayer graphene has attracted much attention as in these systems the kinetic energy is almost fully quenched, giving rise to prominent interaction effects. Indeed, experimental indications for correlation-induced insulating as well as superconducting phases show a striking similarity to the physics of unconventional high-${T}_{c}$ superconductors. Here, the authors employ an unbiased functional renormalization group scheme to connect to these findings from a theoretical side. A topological $d$-wave superconducting state as well as insulating behavior are found, depending on the parameters of the model.

Very recently, the half-metallic compound ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ was proposed to be a magnetic Weyl semimetal (WSM) with Weyl points only 60 meV above the Fermi level ${E}_{F}$. Owing to the low charge carrier density and large Berry curvature induced, ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ possesses both a large anomalous Hall conductivity and a large anomalous Hall angle, which provide strong evidence for the existence of Weyl points in ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$. In this work, we theoretically study the surface topological feature of ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ and its counterpart ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{Se}}_{2}$. By cleaving the sample at the weak Sn-S/Se bonds, one can achieve two different surfaces terminated with Sn and S/Se atoms, respectively. The resulting Fermi-arc-related states can range from the energy of the Weyl points to ${E}_{F}\ensuremath{-}0.1$ eV in the Sn-terminated surface. Therefore, it should be possible to observe the Fermi arcs in…

We show that a pair of overlapping Majorana bound states (MBSs) forming a partially separated Andreev bound state (ps-ABS) represents a generic low-energy feature in spin-orbit-coupled semiconductor-superconductor (SM-SC) hybrid nanowire in the presence of a Zeeman field. The ps-ABS interpolates continuously between the ``garden variety'' ABS, which consists of two MBSs sitting on top of each other, and the topologically protected Majorana zero modes (MZMs), which are separated by a distance given by the length of the wire. The really problematic ps-ABSs consist of component MBSs separated by a distance of the order of the characteristic Majorana decay length $\ensuremath{\xi}$, and have nearly zero energy in a significant range of control parameters, such as the Zeeman field and chemical potential, within the topologically trivial phase. Despite being topologically trivial, such ps-ABSs can generate signatures identical to MZMs in local charge tunneling experiments. In particular, the height of the zero-bias conductance peak (ZBCP) generated by ps-ABSs has the quantized value…

A powerful mechanism for constructing gauge theories is to start from a theory with a global symmetry, then apply the ``gauge principle,'' which demands that this symmetry hold locally. For example, the global phase rotation of a system of conserved charges can be promoted to a local phase rotation by coupling to an ordinary $U(1)$ vector gauge field. More recently, a class of particles has been studied featuring not only charge conservation, but also conservation of higher moments, such as dipole moment, which leads to severe restrictions on the mobility of charges. These particles, called fractons, are known to be intimately connected to symmetric tensor gauge fields. In this work, we show how to derive such tensor gauge theories by applying the gauge principle to a theory of ungauged fractons. We begin by formulating a field theory for ungauged fractons exhibiting global conservation of charge and dipole moment. We show that such fracton field theories have a characteristic non-Gaussian form, reflecting the fact that fractons intrinsically interact with each other even in the…

The authors investigate the influence of strain on the electronic properties of monolayer WSe${}_{2}$ using optical absorption and photoluminescence spectroscopy. The linewidth of the $A$ exciton exhibits a significant and unexpected decrease, from 42 to 24 meV at room temperature. A slightly different behavior is observed for WS${}_{2}$; its linewidth decreases from 30 to 24 meV. They provide a model that explains both the decrease in linewidth and differences in the magnitude of the effect in these two similar material systems. Their findings reveal the utility of strain tuning for probing subtle aspects of 2D materials.

In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high precision the ground states of some notable quantum many-body systems. We consider the one-dimensional free bosons and fermions, spinless fermions on a square lattice away from half-filling, as well as frustrated quantum magnetism with a rapidly oscillating ground-state characteristic function. In the latter case, an ANN with a standard architecture fails, while that with a slightly modified one successfully learns the frustration-induced complex sign rule in the ground state and approximates the ground states with high precisions. As an example of practical use of our method, we also perform the variational method to explore the ground state of an antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model.

We present an accurate interatomic potential for graphene, constructed using the Gaussian approximation potential (GAP) machine learning methodology. This GAP model obtains a faithful representation of a density functional theory (DFT) potential energy surface, facilitating highly accurate (approaching the accuracy of ab initio methods) molecular dynamics simulations. This is achieved at a computational cost which is orders of magnitude lower than that of comparable calculations which directly invoke electronic structure methods. We evaluate the accuracy of our machine learning model alongside that of a number of popular empirical and bond-order potentials, using both experimental and ab initio data as references. We find that whilst significant discrepancies exist between the empirical interatomic potentials and the reference data---and amongst the empirical potentials themselves---the machine learning model introduced here provides exemplary performance in all of the tested areas. The calculated properties include: graphene phonon dispersion curves at 0 K (which we predict with…

In the search for quantum spin liquids, candidate materials for the Kitaev model and its extensions have been intensively explored during the past decade, as the models realize the exact quantum spin liquids in the ground state. Thus far, insulating magnets in the low-spin ${d}^{5}$ electron configuration under the strong spin-orbit coupling have been studied for realizing the Kitaev-type bond-dependent anisotropic interactions between the spin-orbital entangled Kramers doublets. To extend the candidates, here we investigate the systems in a high-spin ${d}^{7}$ electron configuration, whose ground state is described by the spin-orbital entangled Kramers doublet. By the second-order perturbation in terms of the ${t}_{2g}\ensuremath{-}{t}_{2g}$ and ${t}_{2g}\ensuremath{-}{e}_{g}$ hoppings, we show that the effective spin model possesses the anisotropic Kitaev interactions as well as the isotropic Heisenberg ones. While the Kitaev interaction is always ferromagnetic, the Heisenberg interaction can become either ferromagnetic or antiferromagnetic depending on the Coulomb interactions…

A method is introduced to stochastically generate crystal structures with defined structural characteristics. Reasonable quotient graphs for symmetric crystals are constructed using a random strategy combined with space group and graph theory. Our algorithm enables the search for large-size and complex crystal structures with a specified connectivity, such as threefold ${\mathrm{sp}}^{2}$ carbons, fourfold ${\mathrm{sp}}^{3}$ carbons, as well as mixed ${\mathrm{sp}}^{2}\text{\ensuremath{-}}{\mathrm{sp}}^{3}$ carbons. To demonstrate the method, we randomly construct initial structures adhering to space groups from 75 to 230 and a range of lattice constants, and we identify 281 new ${\mathrm{sp}}^{3}$ carbon crystals. First-principles optimization of these structures show that most of them are dynamically and mechanically stable and are energetically comparable to those previously proposed. Some of the new structures can be considered as candidates to explain the experimental cold compression of graphite.

Multifold fermions are generalizations of twofold degenerate Weyl fermions with three-, four-, six-, or eightfold degeneracies protected by crystal symmetries, of which only the last type is necessarily nonchiral. Their low-energy degrees of freedom can be described as emergent relativistic particles not present in the standard model of particle physics. We propose a range of experimental probes for multifold fermions in chiral symmetry groups based on the gyrotropic magnetic effect (GME) and the circular photogalvanic effect (CPGE). We find that, in contrast to Weyl fermions, multifold fermions can have zero Berry curvature yet a finite GME, leading to an enhanced response. The CPGE is quantized and independent of frequency provided that the frequency region at which it is probed defines closed optically activated momentum surfaces. We confirm the above properties by calculations in symmetry-restricted tight-binding models with realistic density functional theory parameters. We identify a range of previously unidentified ternary compounds able to exhibit chiral multifold fermions…

The recently demonstrated unconventional superconductivity [Cao et al., Nature (London) 556, 43 (2018)] in twisted bilayer graphene (tBLG) opens the possibility for interesting applications of two-dimensional layers that involve correlated electron states. Here we explore the possibility of modifying electronic correlations by the application of uniaxial pressure on the weakly interacting layers, which results in increased interlayer coupling and a modification of the magic angle value and associated density of states. Our findings are based on first-principles calculations that accurately describe the height-dependent interlayer coupling through the combined use of density functional theory and maximally localized Wannier functions. We obtain the relationship between twist angle and external pressure for the magic angle flat bands of tBLG. This may provide a convenient method to tune electron correlations by controlling the length scale of the superlattice.

Conventional topological superconductors are fully gapped in the bulk but host gapless Majorana modes on their boundaries. We instead focus on a new class of superconductors, second-order topological superconductors, that have gapped, topological surfaces and gapless Majorana modes instead on lower-dimensional boundaries, i.e., corners of a two-dimensional system or hinges for a three-dimensional system. Here, we propose two general scenarios in which second-order topological superconductivity can be realized spontaneously with weak-pairing instabilities. First, we show that $({p}_{x}+i{p}_{y})$-wave pairing in a (doped) Dirac semimetal in two dimensions with four mirror-symmetric Dirac nodes realizes second-order topological superconductivity. Second, we show that $p+id$ pairing on an ordinary spin-degenerate Fermi surface realizes second-order topological superconductivity as well. In the latter case, we find that the topological invariants describing the system can be written using simple formulas involving only the low-energy properties of the Fermi surfaces and superconducting…

Weyl semimetals are novel topological conductors that host Weyl fermions as emergent quasiparticles. In this Rapid Communication, we propose a new type of Weyl semimetal state that breaks both time-reversal symmetry and inversion symmetry in the $R\mathrm{AlGe}$ ($R=\mathrm{rare}\ensuremath{-}\mathrm{earth}$) family. Compared to previous predictions of magnetic Weyl semimetal candidates, the prediction of Weyl nodes in $R\mathrm{AlGe}$ is more robust and less dependent on the details of the magnetism because the Weyl nodes are generated already by the inversion breaking and the ferromagnetism acts as a simple Zeeman coupling that shifts the Weyl nodes in $k$ space. Moreover, $R\mathrm{AlGe}$ offers remarkable tunability, which covers all varieties of Weyl semimetals including type I, type II, inversion breaking, and time-reversal breaking, depending on a suitable choice of the rare-earth elements. Furthermore, the unique noncentrosymmetric and ferromagnetic Weyl semimetal state in $R\mathrm{AlGe}$ enables the generation of spin currents.

Ab initio calculation of intrinsic spin Hall conductivity (SHC) generally requires a strict convergence criterion and a dense $k$-point mesh to sample the Brillouin zone, making its convergence challenging and time consuming. Here we present a scheme for efficiently and accurately calculating SHC based on the maximally localized Wannier function (MLWF). The quantities needed by the Kubo formula of SHC are derived in the space of the MLWF and it is shown that only the Hamiltonian, the overlap, and the spin operator matrices are required from the initial ab initio calculation. The computation of these matrices and the interpolation of the Kubo formula on a dense $k$-point mesh can be easily achieved. We validate our results by prototypical calculations on fcc Pt and GaAs, which demonstrate that the Wannier interpolation approach is of high accuracy and efficiency. Calculations of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ta}$ and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ta}$ show that SHC of $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ta}$ is 2.7 times that of…

Recent observations of robust zero-bias quantized conductance plateaus of height $2{e}^{2}/h$ in quantum dot-semiconductor-superconductor nanowire heterostructures have been interpreted as clear evidence for the presence of non-Abelian topologically protected Majorana zero modes (MZMs), since other sources of low-energy conductance are believed to be unable to produce such quantized plateaus. Based on extensive numerical calculations, we show that, in fact, quantized conductance plateaus of height $2{e}^{2}/h$ can also arise as a result of partially separated Andreev bound states (ps-ABSs), in which the component Majorana bound states are somewhat shifted in space without being topological MZMs. As ps-ABSs can form rather generically in the topologically trivial phase, even in the absence of disorder, our results conclusively establish that the observation of quantized conductance plateaus of height $2{e}^{2}/h$ does not represent sufficient evidence for the existence of topologically protected MZMs localized at the opposite ends of a wire.

We provide the bulk topological invariant for chiral higher-order topological insulators in (i) fourfold rotoinversion invariant bulk crystals, and (ii) inversion-symmetric systems with or without an additional threefold rotation symmetry. These states of matter are characterized by a nontrivial ${\mathbb{Z}}_{2}$ index, which we define in terms of symmetric hybrid Wannier functions of the filled bands, and can be readily calculated from the knowledge of the crystalline symmetry labels of the bulk band structure. The topological invariant determines the generic presence or absence of protected chiral gapless one-dimensional modes localized at the hinges between conventional gapped surfaces.

We consider the out-of-equilibrium dynamics generated by joining two domains with arbitrary opposite magnetizations. We study the stationary state which emerges by the unitary evolution via the spin-1/2 $XXZ$ Hamiltonian, in the gapless regime, where the system develops a stationary spin current. Using the generalized hydrodynamic approach, we present a simple formula for the space-time profile of the spin current and the magnetization exact in the limit of long times. As a remarkable effect, we show that the stationary state has a strongly discontinuous dependence on the strength of interaction as confirmed by the exact analytic expression of the Drude weight that we compute. These features allow us to give a qualitative estimation for the transient behavior of the current which is in good agreement with numerical simulations. Moreover, we analyze the behavior around the edge of the magnetization profile, and we argue that, unlike the $XX$ free-fermionic point, interactions always prevent the emergence of a Tracy-Widom scaling.

We describe and implement a first-principles algorithm based on maximally localized Wannier functions for calculating the shift-current response of piezoelectric crystals in the independent-particle approximation. The proposed algorithm presents several advantages over existing ones, including full gauge invariance, low computational cost, and a correct treatment of the optical matrix elements with nonlocal pseudopotentials. Band-truncation errors are avoided by a careful formulation of $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ perturbation theory within the subspace of wannierized bands. The needed ingredients are the matrix elements of the Hamiltonian and of the position operator in the Wannier basis, which are readily available at the end of the wannierization step. If the off-diagonal matrix elements of the position operator are discarded, our expressions reduce to the ones that have been used in recent tight-binding calculations of the shift current. We find that this ``diagonal'' approximation can introduce sizable errors, highlighting the importance of carefully…

We investigate the spin Hall magnetoresistance in thin-film bilayer heterostructures of the heavy metal Pt and the antiferromagnetic insulator NiO. While rotating an external magnetic field in the easy plane of NiO, we record the longitudinal and the transverse resistivity of the Pt layer and observe an amplitude modulation consistent with the spin Hall magnetoresistance. In comparison to Pt on collinear ferrimagnets, the modulation is phase shifted by ${90}^{\ensuremath{\circ}}$ and its amplitude strongly increases with the magnitude of the magnetic field. We explain the observed magnetic field dependence of the spin Hall magnetoresistance in a comprehensive model taking into account magnetic-field-induced modifications of the domain structure in antiferromagnets. With this generic model, we are further able to estimate the strength of the magnetoelastic coupling in antiferromagnets. Our detailed study shows that the spin Hall magnetoresistance is a versatile tool to investigate the magnetic spin structure as well as magnetoelastic effects, even in antiferromagnetic multidomain…

We study scrambling in connection with multipartite entanglement dynamics in regular and chaotic long-range spin chains, characterized by a well-defined semi-classical limit. For regular dynamics, scrambling and entanglement dynamics are found to be very different: up to the Ehrenfest time, they rise side by side, departing only afterward. Entanglement saturates and becomes extensively multipartite, while scrambling, characterized by the dynamic of the square commutator of initially commuting variables, continues its growth up to the recurrence time. Remarkably, the exponential growth of the latter emerges not only in the chaotic case but also in the regular one, when the dynamics occurs at a dynamical critical point.

Recent experiments show how a bilayer graphene twisted around a certain magic angle becomes superconducting as it is doped into a region with approximate flat bands. We investigate the mean-field $s$-wave superconducting state in such a system and show how the state evolves as the twist angle is tuned, and as a function of the doping level. We argue that part of the experimental findings could well be understood to result from an attractive electron-electron interaction mediated by electron-phonon coupling, but the flat-band nature of the excitation spectrum also makes the superconductivity quite unusual. For example, as the flat-band states are highly localized around certain spots in the structure, also the superconducting order parameter becomes strongly inhomogeneous.

Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a ``shell-like'' structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a ${t}^{\ensuremath{-}1}$ power law at long time $t$. On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a ``ball-like'' structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law ${t}^{\ensuremath{-}1/4}$ for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not…

Platelike high-quality ${\mathrm{NaYbS}}_{2}$ rhombohedral single crystals with lateral dimensions of a few mm have been grown and investigated in great detail by bulk methods such as magnetization and specific heat, but also by local probes such as nuclear magnetic resonance (NMR), electron-spin resonance (ESR), muon-spin relaxation ($\ensuremath{\mu}\mathrm{SR}$), and inelastic neutron scattering over a wide field and temperature range. Our single-crystal studies clearly evidence a strongly anisotropic quasi-two-dimensional magnetism and an emerging spin-orbit entangled ${J}_{\mathrm{eff}}=\frac{1}{2}$ state of Yb towards low temperatures together with an absence of long-range magnetic order down to 260 mK. In particular, the clear and narrow Yb ESR lines together with narrow $^{23}\mathrm{Na}$ NMR lines evidence an absence of inherent structural distortions in the system, which is in strong contrast to the related spin-liquid candidate ${\mathrm{YbMgGaO}}_{4}$ falling within the same space group $R\overline{3}m$. This identifies ${\mathrm{NaYbS}}_{2}$ as a rather pure…

In this work, we introduce a new type of topological order that is protected by subsystem symmetries that act on lower-dimensional subsets of lattice many-body system, e.g., along lines or planes in a three-dimensional system. The symmetry groups for such systems exhibit a macroscopic number of generators in the infinite-volume limit. We construct a set of exactly solvable models in $2D$ and $3D$, which exhibit such subsystem SPT (SSPT) phases with one-dimensional subsystem symmetries. These phases exhibit analogs of phenomena seen in SPTs protected by global symmetries: gapless edge modes, projective realizations of the symmetries at the edge, and nonlocal order parameters. Such SSPT phases are proximate, in theory space, to previously studied phases that break the subsystem symmetries and phases with fracton order, which result upon gauging them.

Graphene-based heterostructures are a promising material system for designing the topologically nontrivial Chern insulating devices. Recently, a two-dimensional monolayer ferromagnetic insulator ${\mathrm{CrI}}_{3}$ was successfully synthesized in experiments [B. Huang et al., Nature (London) 546, 270 (2017)]. Here, these two interesting materials are proposed to build a heterostructure $(\mathrm{Gr}\text{/}{\mathrm{CrI}}_{3})$. Our first-principles calculations show that the system forms a van der Waals (vdW) heterostructure, which is relatively facilely fabricated in experiments. A Chern insulating state is acquired in the $\mathrm{Gr}\text{/}{\mathrm{CrI}}_{3}$ heterostructure if the vdW gap is compressed to a distance between about 3.3 and 2.4 \AA{}, corresponding to a required external pressure between about 1.4 and 18.3 GPa. Amazingly, very strong magnetization (about 150 meV) is found in graphene, induced by the substrate ${\mathrm{CrI}}_{3}$, despite the vdW interactions between them. A low-energy effective model is employed to understand the mechanism. The work functions,…

The recent discovery of Weyl and Dirac semimetals is one of the most important progresses in condensed matter physics. Among the very few available tools to characterize Weyl semimetals through electrical transport, negative magnetoresistance is most commonly used. Considering the shortcomings of this method, new tools to characterize the chiral anomaly in Weyl semimetals are desirable. We employ the planar Hall effect (PHE) as an effective technique in the half Heusler Weyl semimetal GdPtBi to study the chiral anomaly. This compound exhibits a large value of 1.5 $\mathrm{m}\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ planar Hall resistivity at 2 K and in 9 T. Our analysis reveals that the observed amplitude is dominated by Berry curvature and chiral anomaly contributions. Through angle-dependent transport studies we establish that GdPtBi with relatively small orbital magnetoresistance is an ideal candidate to observe the large PHE.

Topological phases of matter that have an insulating bulk and robust gapless boundary states can exist both in static materials and when system parameters are changed periodically in time. In the latter case, the periodic driving can lead to so called ``anomalous'' topological phases. Here, the authors show that, in the newly introduced higher-order topological insulators, anomalous phases can exist even if the system is static, and provide an example of such behavior using a two-dimensional model with topological corner charges. This work opens up the possibility of studying anomalous phases without the inherent difficulties associated with time-periodic changes of a material, such as the risk that it will ``heat up'' due to the driving field and lose its topological features.

We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to $L=100$ spins, i.e., much larger than $L\ensuremath{\simeq}20$ that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent $\ensuremath{\beta}$ which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent ${\ensuremath{\beta}}_{\mathrm{\ensuremath{\Lambda}}}$ which characterizes the decay of a Schmidt gap in the entanglement spectrum; and (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder ${W}_{c}$ that…

Conventional topological semimetals are characterized by the energy momentum separation of the bulk nodes in the energy spectrum. Here, the authors demonstrate a few types of topological semimetals that are gapped in the bulk, but host one or a half of a Dirac semimetal on multiple surfaces. They show that these semimetals can be characterized by the bulk nodes in the hybrid Wannier spectrum, rather than the energy spectrum. This works points to a new direction in studying the higher order topology in semimetallic systems.

The authors present a derivation of finite-size corrections to entanglement entropies that possess an internal symmetry. They show that entanglement entropy is equally distributed among the different sectors of that internal symmetry. Its value is given by the standard area-law-violating logarithmic term, which depends on the central charge $c$, minus a double logarithmic correction related to the zero-temperature susceptibility. They present a very efficient way to determine the central charge and the Luttinger parameter. This opens the possibility that the measurement of these quantities can be successfully pursued in an optical lattice. The analytical predictions are verified against numerical results obtained by DMRG.

$\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$, a candidate material for power electronics and UV optoelectronics, shows strong room-temperature photoluminescence (PL). In addition to the three well-known bands of as-grown samples in the UV, blue, and green, also red PL was observed upon nitrogen doping. This raises the possibility of applying $\ensuremath{\beta}\ensuremath{-}\mathrm{G}{\mathrm{a}}_{2}{\mathrm{O}}_{3}$ nanostructures as white phosphors. Using an optimized, Koopmans-compliant hybrid functional, we show that most intrinsic point defects, as well as substitutional nitrogen, act as deep acceptors, and each of the observed PL bands can be explained by electron recombination with a hole trapped in one of them. We suggest this mechanism to be general in wide-band-gap semiconductors which can only be doped $n$-type. Calculations on the nitrogen acceptor reproduce the observed red luminescence accurately. Earlier we have shown that not only the energy, but the polarization properties of the UV band can be explained by self-trapped hole states.…

By performing first-principles calculations, we propose a stable direct band gap semiconductor Janus single-layer structure, ${\mathrm{In}}_{2}\mathrm{SSe}$. The binary analogs of the Janus structure, InS and InSe single layers are reviewed to evince the structural and electronic relation with ${\mathrm{In}}_{2}\mathrm{SSe}$. The structural optimization calculations reveal that a Janus ${\mathrm{In}}_{2}\mathrm{SSe}$ single layer has hexagonal geometry like the InS and InSe single layers, which are also its structural analogs. The Janus single layer is dynamically stable, as indicated by the phonon spectrum. The electronic band diagram of the Janus structure shows that an ${\mathrm{In}}_{2}\mathrm{SSe}$ single layer is a direct band gap semiconductor, in contrast to its analogs, InS and InSe single layers, which are indirect band gap semiconductors. Nevertheless, it is found that the strain effect on electronic properties of the InS and InSe single layers designates the electronic structure of the Janus single layer. A rough model for the construction of the electronic band diagram…

We study the quantum nonlinear Hall effect in two-dimensional (2D) materials with time-reversal symmetry. When only one mirror line exists, a transverse charge current occurs in the second-order response to an external electric field, as a result of the Berry curvature dipole in momentum space. Candidate 2D materials to observe this effect are two-dimensional transition metal dichalcogenides (TMDCs). First, we use an ab initio based tight-binding approach to demonstrate that monolayer ${T}_{d}$-structure TMDCs exhibit a finite Berry curvature dipole. In the $1H$ and $1{T}^{\ensuremath{'}}$ phase of TMDCs, we show the emergence of a finite Berry curvature dipole with the application of strain and an electrical displacement field, respectively.

A non-Hermitian extension of a Chern insulator and its bulk-boundary correspondence are investigated. It is shown that in addition to the robust chiral edge states that reflect the nontrivial topology of the bulk (nonzero Chern number), anomalous helical edge states localized only at one edge can appear, which are unique to the non-Hermitian Chern insulator.

Lifting the valley degeneracy is an efficient way to achieve valley polarization for further valleytronics operations. In this Rapid Communication, we demonstrate that a large valley splitting can be obtained in monolayer transition metal dichalcogenides by magnetic proximity coupling to an insulating antiferromagnetic substrate. As an example, we perform first-principles calculations to investigate the electronic structures of monolayer ${\mathrm{WS}}_{2}$ on the MnO(111) surface. Our calculation results suggest that a large valley splitting of 214 meV, which corresponds to a Zeeman magnetic field of 1516 T, is induced in the valence band of monolayer ${\mathrm{WS}}_{2}$. The magnitude of valley splitting relies on the strength of interfacial orbital hybridization and can be tuned continually by applying an external out-of-plane pressure and in-plane strain. More interestingly, we find that both spin and valley index will flip when the magnetic ordering of MnO is reversed. Besides, owing to the sizable Berry curvature and time-reversal symmetry breaking in the…

A higher-order topological insulator (HOTI) is an extended notion of the conventional topological insulator. It belongs to a special class of topological insulators to which the conventional bulk-boundary correspondence is not applicable. Provided the mirror symmetries are present, the bulk topological number is described by the quantized Wannier center located at a high-symmetry point of the crystal. The emergence of corner states is a manifestation of nontrivial topology in the bulk. In this paper we propose minimal models for the Wannier-type second-order topological insulator in two dimensions and the third-order topological insulator in three dimensions. They are anisotropic chiral-symmetric two-band models. It is explicitly shown that the Wannier center is identical to the winding number in the present model, demonstrating that it is indeed a topological quantum number. Finally we point out that the essential physics of phosphorene near the Fermi energy is described by making a perturbation of the Wannier-type HOTI. We predict that these corner states will be observed in the…

Huygens' metasurfaces are electrically thin devices which allow arbitrary field transformations. Beam refraction is among the first demonstrations of realized metasurfaces. As previously shown for extreme-angle refraction, control over only the electric impedance and magnetic admittance of the Huygens' metasurface proved insufficient to produce the desired reflectionless field transformation. To maintain zero reflections for wide refraction angles, magnetoelectric coupling between the electric and magnetic response of the metasurface, leading to bianisotropy, can be introduced. In this paper, we report the theory, design, and experimental characterization of a reflectionless bianisotropic metasurface for extreme-angle refraction of a normally incident plane wave towards $71.{8}^{\ensuremath{\circ}}$ at 20 GHz. The theory and design of three-layer asymmetric bianisotropic unit cells are discussed. The realized printed circuit board structure was tested via full-wave simulations as well as experimental characterization. To experimentally verify the prototype, two setups were used. A…

Key properties of nine possible defect sites in hexagonal boron nitride (h-BN), ${V}_{\mathrm{N}},{{V}_{\mathrm{N}}}^{\ensuremath{-}1},{\mathrm{C}}_{\mathrm{N}},{V}_{\mathrm{N}}{\mathrm{O}}_{2\mathrm{B}},{V}_{\mathrm{N}}{\mathrm{N}}_{\mathrm{B}},{V}_{\mathrm{N}}{\mathrm{C}}_{\mathrm{B}},{V}_{\mathrm{B}}{C}_{\mathrm{N}},{V}_{\mathrm{B}}{\mathrm{C}}_{\mathrm{N}}\mathrm{S}{\mathrm{i}}_{\mathrm{N}}$, and ${V}_{\mathrm{N}}{\mathrm{C}}_{\mathrm{B}}\mathrm{S}{\mathrm{i}}_{\mathrm{B}}$, are predicted using density-functional theory and are corrected by applying results from high-level ab initio calculations. Observed h-BN electron-paramagnetic resonance signals at 22.4, 20.83, and 352.70 MHz are assigned to ${V}_{\mathrm{N}},{\mathrm{C}}_{\mathrm{N}}$, and ${V}_{\mathrm{N}}{\mathrm{O}}_{2\mathrm{B}}$, respectively, while the observed photoemission at 1.95 eV is assigned to ${V}_{\mathrm{N}}{\mathrm{C}}_{\mathrm{B}}$. Detailed consideration of the available excited states, allowed spin-orbit couplings, zero-field splitting, and optical transitions is made for the two related defects…

We study the interplay of disorder and band-structure topology in a Weyl semimetal with a tilted conical spectrum around the Weyl points. The spectrum of particles is given by the eigenvalues of a non-Hermitian matrix, which contains contributions from a Weyl Hamiltonian and complex self-energy due to electron elastic scattering on disorder. We find that the tilt-induced matrix structure of the self-energy gives rise to either a flat band or a nodal line segment at the interface of the electron and hole pockets in the bulk band structure of type-II Weyl semimetals depending on the Weyl cone inclination. For the tilt in a single direction in momentum space, each Weyl point expands into a flat band lying on the plane, which is transverse to the direction of the tilt. The spectrum of the flat band is fully imaginary and is separated from the in-plane dispersive part of the spectrum by the ``exceptional nodal ring'' where the matrix of the Green's function in momentum-frequency space is defective. The tilt in two directions might shrink a flat band into a nodal line segment with…

Atomically thin ferromagnetic (FM) films were recently prepared by mechanical exfoliation of bulk FM semiconductor ${\mathrm{Cr}}_{2}{\mathrm{Ge}}_{2}{\mathrm{Te}}_{6}$. They provide a platform to explore novel two-dimensional (2D) magnetic phenomena, and they offer exciting prospects for new technologies. By performing systematic ab initio density functional calculations, here we study two relativity-induced properties of these 2D materials (monolayer, bilayer, and trilayer as well as bulk), namely magnetic anisotropy energy (MAE) and magneto-optical (MO) effects. Competing contributions of both magnetocrystalline anisotropy energy (C-MAE) and magnetic dipolar anisotropy energy (D-MAE) to the MAE are computed. The calculated MAEs of these materials are large, being on the order of $\ensuremath{\sim}0.1$ meV/Cr. Interestingly, we find that out-of-plane magnetic anisotropy is preferred in all the systems except the monolayer, where in-plane magnetization is favored because here the D-MAE is larger than the C-MAE. Crucially, this explains why long-range FM order was observed in all…

Axion insulators are magnetic topological insulators in which the nontrivial ${\mathbb{Z}}_{2}$ index is protected by inversion symmetry instead of time-reversal symmetry. The naturally gapped surfaces of axion insulators give rise to a half-quantized surface anomalous Hall conductivity (AHC), but the sign of the surface AHC cannot be determined from topological arguments. In this paper, we consider topological phenomena at the surface of an axion insulator. To be explicit, we construct a minimal tight-binding model on the pyrochlore lattice and investigate the all-in-all-out (AIAO) and ferromagnetic (FM) spin configurations. We also implement a recently proposed approach for calculating the surface AHC directly, which allows us to explore how the interplay between surface termination and magnetic ordering determines the sign of the half-quantized surface AHC. In the case of AIAO ordering, we show that it is possible to construct a topological state with no protected metallic states on boundaries of any dimension (surfaces, hinges, or corners), although chiral hinge modes do occur…

We report the structural, static, and dynamic properties of ${\mathrm{Cr}}_{0.5}{\mathrm{Fe}}_{0.5}\mathrm{Ga}$ by means of powder x-ray diffraction, dc magnetization, heat capacity, ac susceptibility, magnetic relaxation, and magnetic memory effect measurements. The dc magnetization and ac susceptibility studies reveal a spin-glass transition at around ${T}_{\mathrm{f}}\ensuremath{\simeq}22$ K. An intermediate value of the relative shift in freezing temperature $\ensuremath{\delta}{T}_{\mathrm{f}}\ensuremath{\simeq}0.017$, obtained from the ac susceptibility data reflects the formation of cluster spin-glass states. The frequency dependence of ${T}_{\mathrm{f}}$ is also analyzed within the framework of dynamic scaling laws such as power law and Vogel-Fulcher law. The analysis using power law yields a characteristic time constant for a single spin flip $\ensuremath{\tau}*\ensuremath{\simeq}1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ s and critical exponent $z{\ensuremath{\nu}}^{\ensuremath{'}}=4.2\ifmmode\pm\else\textpm\fi{}0.2$. On the other hand, the Vogel-Fulcher…

Starting from a minimal model of a time-reversal-invariant topological superconductor in two dimensions, the author shows that an in-plane magnetic field could drive the superconductor into a second-order topological phase, which features Majorana zero modes, bound at two of the four corners of the system. These Majorana corner states occur where edges with distinct topology intersect. Hence, the corner states are topologically protected. With variation of magnetic-field orientation, the nontrivial corner states would move along the boundary and reside on different corners.

Nonequilibrium open systems effectively described by non-Hermitian Hamiltonians with parity-time ($P\phantom{\rule{0}{0ex}}T$) symmetry have recently attracted considerable attention due to their properties with no Hermitian counterparts. In particular, there exists a growing interest in non-Hermitian topological phases of matter. Here, the authors show that a $P\phantom{\rule{0}{0ex}}T$-symmetric topological superconducting wire possesses two distinct types of unconventional edge modes, those with complex energies and with nonorthogonal Majorana zero modes. The latter induce anomalous particle transport with nonlocal currents present only at the edges. This work explores a unique nonequilibrium topological phenomenon that results from the interplay between $P\phantom{\rule{0}{0ex}}T$ symmetry and topological superconductivity.

We present a combined ab initio study of several gyrotropic effects in $p$-doped trigonal tellurium (effects that reverse direction with the handedness of the spiral chains in the atomic structure). The key ingredients in our study are the $k$-space Berry curvature and intrinsic orbital magnetic moment imparted on the Bloch states by the chirality of the crystal structure. We show that the observed sign reversal with temperature of the circular photogalvanic effect can be explained by the presence of Weyl points near the bottom of the conduction band acting as sources and sinks of Berry curvature. The passage of a current along the trigonal axis induces a rather small parallel magnetization, which can nevertheless be detected by optical means (Faraday rotation of transmitted light) due to the high transparency of the sample. In agreement with experiment, we find that when infrared light propagates antiparallel to the current at low doping the current-induced optical rotation enhances the natural optical rotation. According to our calculations the plane of polarization rotates in the…

Nonsymmorphic space group symmetries can generate exotic band crossings in topological metals and semimetals. Here, based on symmetry analysis and first-principles calculations, we reveal rich band-crossing features in the existing layered compounds ${\mathrm{Ta}}_{3}{\mathrm{SiTe}}_{6}$ and ${\mathrm{Nb}}_{3}{\mathrm{SiTe}}_{6}$, enabled by nonsymmorphic symmetries. We show that in the absence of spin-orbit coupling (SOC), these three-dimensional (3D) bulk materials possess accidental Dirac loops and essential fourfold nodal lines. In the presence of SOC, there emerges an hourglass Dirac loop---a fourfold degenerate nodal loop, on which each point is a neck point of an hourglass-type dispersion. We show that this interesting type of band crossing is protected and dictated by the nonsymmorphic space group symmetries and it gives rise to drumheadlike surface states. Furthermore, we also investigate these materials in the monolayer form. We show that these two-dimensional (2D) monolayers host nodal lines in the absence of SOC and the nodal lines transform to essential spin-orbit Dirac…

Inspired by the quantum spin Hall effect shown by topological insulators, we propose a plate structure that can be used to demonstrate the pseudospin Hall effect for flexural waves. The system consists of a thin plate with periodically arranged resonators mounted on its top surface. We extend a technique based on the plane-wave expansion method to identify a double Dirac cone emerging due to the zone-folding in frequency band structures. This particular design allows us to move the double Dirac cone to a lower frequency than the resonating frequency of local resonators. We then manipulate the pattern of local resonators to open subwavelength Bragg band gaps that are topologically distinct. Building on this method, we verify numerically that a waveguide at an interface between two topologically distinct resonating plate structures can be used for guiding low-frequency, spin-dependent one-way flexural waves along a desired path with bends.

It has been a long-standing challenge to expand the notion of exponential sensitivity to small perturbations in the initial conditions from the realm of classical chaos to that of many-body quantum systems. Recently, exponential growth in a measure known as the out-of-time-order commutator (OTOC) has been proposed as a diagnostic of chaos in the setting of many-body quantum systems. The authors examine the behavior of the OTOC along rays of different velocities for a variety of spatially local extended many-body quantum systems, both integrable and nonintegrable. They find that the velocity-dependent Lyapunov exponents are negative for velocities greater than a characteristic ``butterfly speed'', which defines the light cone for the spreading of operators. It is demonstrated that a regime with well-defined positive Lyapunov exponents inside the light-cone may only exist for classical, semiclassical, weakly interacting, or large-$N$ systems, but not for fully quantum systems with strong short-range interactions and local Hilbert space dimensions of order one.

Conventional $n$-dimensional topological superconductors (TSCs) have protected gapless $(n\ensuremath{-}1)$-dimensional boundary states. In contrast to this, second-order TSCs are characterized by topologically protected gapless $(n\ensuremath{-}2)$-dimensional states with the usual gapped $(n\ensuremath{-}1)$ boundaries. Here, we study a second-order TSC with a two-dimensional (2D) magnetic topological insulator proximity coupled to a high-temperature superconductor, where Majorana bound states (MBSs) are localized at the corners of a square sample with gapped edge modes. Due to the mirror symmetry of the hybrid system considered here, there are two MBSs at each corner for both cases: $d$-wave and ${s}_{\ifmmode\pm\else\textpm\fi{}}$-wave superconducting pairing. We present the corresponding topological phase diagrams related to the role of the magnetic exchange interaction and the pairing amplitude. A detailed analysis, based on edge theory, reveals the origin of the existence of MBSs at the corners of the 2D sample, which results from the sign change of the Dirac mass emerging at…

We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state remains pinned near zero energy for Zeeman energies that exceed the characteristic spacing between Andreev bound state levels but that are smaller than the spin-orbit energy of the quantum dot. Importantly, as the pinning of the Andreev bound state depends only on properties of the quantum dot, we conclude that this behavior is unrelated to topological superconductivity. To support our analytical model, we also perform a numerical simulation of a hybrid system while explicitly incorporating a…

The authors extend the recent successful application of neural networks fordistinguishing phases of matter to the case of topologically driven phase transitions. They demonstrate that supervised networks correctly identify the Kosterlitz-Thouless transition in the two-dimensional classical XY model. However, their analysis suggests that a naive classification of phases is based on bulk features, rather than on detecting local topological defects. While they show that it is possible to fine-tune a network to recognize vortices, it generally remains a difficult task to detect topological defects without $a\phantom{\rule{0.333em}{0ex}}p\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i$ knowledge.

The pairing symmetry of the Hubbard Hamiltonian on a triangle lattice with a nearly flat low-energy band is studied with the determinant quantum Monte Carlo method (DQMC). We show that the low-temperature phase is insulating at half-filling, even for relatively weak interactions. The natures of the spin and pairing correlations upon doping are determined, and they exhibit an electron-hole asymmetry. Among the pairing symmetries allowed, we demonstrate that the dominating channels are $d$ wave, opening the possibility of condensation into an unconventional ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ phase, which is characterized by an integer topological invariant and gapless edge states. The results are closely related to the correlated insulating phase and unconventional superconductivity discovered recently in twisted bilayer graphene.

Electric circuits are known to realize topological quadrupole insulators. We explore electric circuits made of capacitors and inductors forming the breathing kagome and pyrochlore lattices. They are known to possess three phases (trivial insulator, higher-order topological insulator, and metallic phases) in the tight-binding model, where the topological phase is characterized by the emergence of zero-energy corner states. A topological phase transition is induced by tuning continuously the capacitance, which is possible by using variable capacitors. It is found that the two-point impedance yields huge resonance peaks when one node is taken at a corner in the topological phase. It is a good signal to detect a topological phase transition. We also show that the topological corner resonance is robust against the randomness of capacitance and inductance. Furthermore, the size of the electric circuits can be quite small to realize the topological phase together with topological phase transitions.

We investigate correlated insulating states in magic-angle twisted bilayer graphene (TBG) by the exact diagonalization method applied to the extended Hubbard model with interaction parameters recently evaluated in the realistic effective model. Our model can handle the competing interactions among Wannier orbitals owing to their significant overlap, which is a crucial but overlooked aspect of the magic-angle TBG. We propose two candidates for the correlated insulating states: spin- and valley-ferromagnetic band insulator and the Dirac semimetallic state for two flavors with peculiar renormalization, where a flavor denotes a combined degree of freedom with spin and valley. One of the important consequences for the latter candidate is that it allows van Hove singularity near half-filling of the whole band structure (i.e., near the Dirac points) to play some role in superconductivity. The consistency between the two flavor degrees of freedom for the Dirac semimetallic state and the twofold degeneracy of the Landau level observed in the experiment is also noteworthy.

Monolayer transition metal dichalcogenides (TMDs) exhibit high nonlinear optical (NLO) susceptibilities. Experiments on ${\mathrm{MoS}}_{2}$ have indeed revealed very large second-order (${\ensuremath{\chi}}^{(2)}$) and third-order (${\ensuremath{\chi}}^{(3)}$) optical susceptibilities. However, third-harmonic generation results of other layered TMDs have not been reported. Furthermore, the reported ${\ensuremath{\chi}}^{(2)}$ and ${\ensuremath{\chi}}^{(3)}$ of ${\mathrm{MoS}}_{2}$ vary by several orders of magnitude, and a reliable quantitative comparison of optical nonlinearities across different TMDs has remained elusive. Here, we investigate second- and third-harmonic generation, and three-photon photoluminescence in TMDs. Specifically, we present an experimental study of ${\ensuremath{\chi}}^{(2)}$ and ${\ensuremath{\chi}}^{(3)}$ of four common TMD materials (${\mathrm{MoS}}_{2}$, ${\mathrm{MoSe}}_{2}$, ${\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$) by placing different TMD flakes in close proximity to each other on a common substrate, allowing their NLO properties to be…

It is well known that theorems of Lieb-Schultz-Mattis type prohibit the existence of a trivial symmetric gapped ground state in certain systems possessing a combination of internal and lattice symmetries. In the continuum description of such systems, the Lieb-Schultz-Mattis theorem is manifested in the form of a quantum anomaly afflicting the symmetry. We demonstrate this phenomenon in the context of the deconfined critical point between a Neel state and a valence bond solid in an $S=1/2$ square lattice antiferromagnet and compare it to the case of $S=1/2$ honeycomb lattice where no anomaly is present. We also point out that new anomalies, unrelated to the microscopic Lieb-Schultz-Mattis theorem, can emerge, prohibiting the existence of a trivial gapped state in the immediate vicinity of critical points or phases. For instance, no translationally invariant weak perturbation of the $S=1/2$ gapless spin chain can open up a trivial gap even if the spin-rotation symmetry is explicitly broken. The same result holds for the $S=1/2$ deconfined critical point on a square lattice.

The propagation of light in Weyl semimetal films is analyzed. The magnetic family of these materials is known by anomalous Hall effect, which, being enhanced by the large Berry curvature, allows one to create strong gyrotropic and nonreciprocity effects without external magnetic field. The existence of nonreciprocal waveguide electromagnetic modes in ferromagnetic Weyl semimetal films in the Voigt configuration is predicted. Thanks to the strong dielectric response caused by the gapless Weyl spectrum and the large Berry curvature, ferromagnetic Weyl semimetals combine the best waveguide properties of magnetic dielectrics or semiconductors with strong anomalous Hall effect in ferromagnets. The magnitude of the nonreciprocity depends both on the internal Weyl semimetal properties, the separation of Weyl nodes, and the external factor, the optical contrast between the media surrounding the film. By tuning the Fermi level in Weyl semimetals, one can vary the operation frequencies of the waveguide modes in THz and mid-IR ranges. Our findings pave the way to the design of compact,…

Motivated by recent experimental findings of correlating insulator and superconductor behavior in twisted bilayer graphene, the authors study a cluster charge interaction model on a honeycomb lattice. The cluster charge is defined on the dual lattice of honeycomb to mimic charge centers forming a triangular lattice found in experiments. Based on unbiased sign-problem-free quantum Monte Carlo simulations, the authors determine the phase diagram for this model. It features a fermionic quantum critical point with chiral XY universality and a Kekul\'e valence bond solid phase at intermediate interaction, which may be related to the correlating insulator phase found in experiments. This is an example of the rich phases found in a simple model without artificial design.

The recent discovery of intrinsic ferromagnetism in two-dimensional (2D) van der Waals crystals down to the monolayer limit has sparked intense interest due to their potential applications in spintronics. Here, using first-principles calculations we predict that the 2D pristine ${\mathrm{MnX}}_{3}$ (X = F, Cl, Br, I) is a family of intrinsic Dirac half-metals characterized by a band structure with an unusually large gap in one spin channel and a Dirac cone in the other with carrier mobilities comparable to those in graphene. We demonstrate that the ${\mathrm{MnX}}_{3}$ are dynamically and thermodynamically stable up to high temperatures, and exhibit large magnetic moments of about $4\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{B}$ per ${\mathrm{Mn}}^{3+}$ ion, high Curie temperatures, and large in-plane magnetic anisotropy energy. In addition, the gap opening induced by the spin-orbit coupling drives the lighter systems into the quantum anomalous Hall state. The combination of these unique properties renders this class of 2D ferromagnets a promising platform for high efficiency…

The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small ``magic'' twist angles has been linked to the existence of nearly flat bands, which make TBG a fresh playground to investigate the interplay between correlations and superconductivity. The low-energy narrow bands were shown to be well described by an effective tight-binding model on the honeycomb lattice (the dual of the triangular Moir\'e superlattice) with a local orbital degree of freedom. In this paper, we perform a strong-coupling analysis of the proposed $\left({p}_{x},\phantom{\rule{0.16em}{0ex}}{p}_{y}\right)$ two-orbital extended Hubbard model on the honeycomb lattice. By decomposing the interacting terms in the particle-particle and particle-hole channels, we classify the different possible superconducting, magnetic, and charge instabilities of the system. In the pairing case, we pay particular attention to the two-component ($d\text{\ensuremath{-}}\mathrm{wave}$) pairing channels, which admit vestigial phases with nematic or chiral orders, and study…

Spin-orbit coupled honeycomb lattice magnets offer a route to novel states of matter through the presence of significant Kitaev exchange coupling. Here, the authors explored the spin-polarized paramagnetic regime in a very general model for such magnets, showing that the magnon band topology is nontrivial throughout the phase. This finding implies the presence a thermal Hall effect and, neglecting magnon interactions, topologically protected chiral magnon edge states. They further show that the edge states are robust to the presence of interactions, decisively showing that such exotic excitations are experimentally robust quasiparticles.