The 100 most-cited articles in Physical review. B./Physical review. B, 2021

We develop a neuroevolution-potential (NEP) framework for generating neural network-based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A descriptor of the atomic environment is constructed based on Chebyshev and Legendre polynomials. The method is implemented in graphic processing units within the open-source gpumd package, which can attain a computational speed over ${10}^{7}$ atom-step per second using one Nvidia Tesla V100. Furthermore, per-atom heat current is available in NEP, which paves the way for efficient and accurate MD simulations of heat transport in materials with strong phonon anharmonicity or spatial disorder, which usually cannot be accurately treated either with traditional empirical potentials or with perturbative methods.

As one of the most fundamental physical phenomena, the anomalous Hall effect (AHE) typically occurs in ferromagnetic materials but is not expected in conventional superconductors. Here, the authors find a giant AHE in the kagome superconductor CsV${}_{3}$Sb${}_{5}$. Strikingly, the AHE develops spontaneously with the occurrence of a charge density wave (CDW), indicating a strong correlation between the CDW state and AHE. These discoveries make CsV${}_{3}$Sb${}_{5}$ an ideal platform to study the interplay among nontrivial band topology, CDW, and unconventional superconductivity

The newly discovered family of kagome metals $A$V${}_{3}$Sb${}_{5}$ ($A$=K,Cs,Rb) has recently gained wide attention. Here, the authors study these materials using a general continuum model and utilize renormalization group and mean field theory methods to identify mechanisms that can lead to the experimentally observed charge density wave ordering. The authors find that the charge density wave is the primary density wave instability in certain cases but could also be induced by a leading orbital current or spin density wave order.

Recent years have witnessed major progress in the understanding of monitored quantum dynamics, an open quantum setting where the environment is a measurement apparatus that probes the system locally. For the resulting quantum trajectory, unitary evolution and local measurements have competing tendencies in the building of quantum correlations: while the coherent interactions in the former increase the entanglement, the resolving nature of the local measurement collapses the state of the system. Here, the authors study the interplay of monitoring and system dynamics by focusing on the monitored quantum Ising chain as the measurement strength is varied, going from the regime of weak detection, corresponding to the limit of infinite small jumps, to the case of post-selected no-jump case. A sharp transition is found between a logarithmic law phase to an area law phase for the entanglement entropy, which occurs at the same value of the measurement rate in the two limiting situations.

The recent discovery of topological charge density waves in the superconducting kagome metals $A$V${}_{3}$Sb${}_{5}$ ($A$=K, Rb, Cs) has attracted enormous attention. Motivated by the experiments, the authors analyze here the interplay of real and imaginary charge density waves at the Van Hove singularity, but in a broader scope of general hexagonal lattices. Phenomenological analysis uncovers a rich Haldane-model phase diagram. The theoretical model sheds light on the experimental observations in these kagome metals and future experiments of hexagonal lattice materials.

Materials that integrate magnetism, miniaturization, and valley properties hold potential for spintronic and valleytronic nanodevices. Recently, ferromagnetism was reported to be able to exist in the $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ monolayer which is half-metallic and belongs to a new kind of two-dimensional material [Hong et al., Science 369, 670 (2020)]. Using first-principles calculations and model analysis, we find that $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ is a ferromagnetic semiconductor harboring valley-contrasting physics and a magnetic critical temperature over room temperature. By tuning magnetization orientation from in plane to out of plane, valley polarization can be generated, resulting in the anomalous valley Hall effect in $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$. Furthermore, we obtain the formula for energy splitting of valleys and adopt a tight-binding model for $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$, which elucidates the physical mechanism of spin-valley coupling. More interestingly, under 4% tensile strain, the intrinsic…

The self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently introduced approach based on density-functional perturbation theory (DFPT) for the calculation of the onsite Hubbard $U$ to also compute the intersite Hubbard $V$. DFPT allows us to reduce significantly computational costs, improve numerical accuracy, and fully automate the calculation of the Hubbard parameters by recasting the linear response of a localized perturbation into an array of monochromatic perturbations that can be calculated in the primitive cell. In addition, here we generalize the entire formalism from norm-conserving to ultrasoft and projector-augmented wave formulations, and to metallic ground states. After benchmarking DFPT against the conventional real-space Hubbard linear response in a supercell, we demonstrate the effectiveness of the present extended Hubbard formulation in determining the equilibrium crystal structure of…

We derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4)$\ifmmode\times\else\texttimes\fi{}\mathrm{U}$(4) symmetry, and we find that the exact ground states at integer filling $\ensuremath{-}4\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}4$ relative to charge neutrality are Chern insulators of Chern numbers ${\ensuremath{\nu}}_{C}=4\ensuremath{-}|\ensuremath{\nu}|,2\ensuremath{-}|\ensuremath{\nu}|,\ensuremath{\cdots},|\ensuremath{\nu}|\ensuremath{-}4$, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $\ensuremath{\nu}=0,\ifmmode\pm\else\textpm\fi{}2$ has…

Transition-metal dichalcogenides (TMDs) are promising for two-dimensional (2D) semiconducting devices and novel phenomena. For 2D applications, their work function, ionization energy, and electron affinity are required as a function of thickness, but research on this is yet to cover the full family of compounds. Here, we present the work function, ionization energy, and electron affinity of few-layer and bulk $M{X}_{2}$ ($M=\text{Mo},$ W and $X=\text{S}$, Se, Te) in 2H phase obtained accurately by the density functional theory and GW calculations. For each compound, we consider one-, two-, three-, four-layer, and bulk geometry. In GW calculations, accurate results are obtained by nonuniform $q$ sampling for two-dimensional geometry. From band energies including the GW self-energy correction, we estimate the work function, band gap, ionization energy, and electron affinity as functions of the number of layers. We compare our results with available theoretical and experimental reports, and we discuss types of band alignments in in-plane and out-of-plane junctions of these few-layer…

CsV${}_{3}$Sb${}_{5}$ has been recently discovered to be a kagome superconductor. Here, the authors use scanning tunneling microscopy to study its charge order and superconductivity at the atomic scale. Through mapping the energy gap of the charge order, the authors identify its chiral electronic nature. They also elucidate the surface nature of the 1$\ifmmode\times\else\texttimes\fi{}$4 superlattice and superconducting excitations.

In the last five years a large number of new high-temperature superconductors have been predicted and experimentally discovered among hydrogen-rich crystals, at pressures, which are way too high to meet any practical application. In this paper, we report the computational prediction of a hydride superconductor, $\mathrm{La}{\mathrm{BH}}_{8}$, with a ${T}_{\text{c}}$ of 126 K at a pressure of 50 GPa, thermodynamically stable above 100 GPa, and dynamically stable down to 40 GPa, an unprecedentedly low pressure for high-${T}_{\text{c}}$ hydrides. $\mathrm{La}{\mathrm{BH}}_{8}$ can be seen as a ternary sodalite-like hydride, in which a metallic hydrogen sublattice is stabilized by the chemical pressure exerted by the La-B scaffolding, which achieves a more efficient packing of atoms than in binary sodalite hydrides thanks to the combination of elements with very different sizes. The proposed aufbau principle may be exploited to design high-${T}_{\text{c}}$ hydrides that survive at even lower pressure, through a careful choice of the elements.

There have been extensive efforts to engineer magnetic two-dimensional materials with a view to using them for spintronic applications, in conjunction with other materials from the two-dimensional family. Here, the authors reveal N\'eel-type chiral magnetic skyrmions and their lattice formation in the van der Waals ferromagnet Fe${}_{3}$GeTe${}_{2}$ (FGT). They demonstrate the capability to drive an individual skyrmion by current along this van der Waals heterostructure on $h$-BN. Utilizing $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations, the study proposes the presence of Dzyaloshinskii-Moriya interaction at FGT interfaces with oxidized layers.

Manipulation of the valley degree of freedom provides a novel paradigm in quantum information technology. In this work, through first principles calculations, we demonstrate that monolayer $\mathrm{Gd}{\mathrm{I}}_{2}$ is a promising candidate material for valleytronic applications. Monolayer $\mathrm{Gd}{\mathrm{I}}_{2}$ can be easily exfoliated from bulk, and it is spontaneously valley polarized with a giant splitting of 149 meV due to its intrinsic ferromagnetism and large spin orbital coupling. The anomalous valley Hall effect could be realized in monolayer $\mathrm{Gd}{\mathrm{I}}_{2}$ by an appropriate external electric field. Furthermore, the valley polarization feature is stable against the biaxial in-plane strain. Our findings provide an extraordinary and potential material platform for experimental studies and practical applications in the emergent field of valleytronics.

The quasi-two-dimensional kagome superconductors $A$V${}_{3}$Sb${}_{5}$ ($A$ $=$ K, Rb, and Cs) have attracted great interest due to various exotic quantum phenomena, such as topological charge density waves and the giant anomalous Hall effect. Here, the authors find two-dome unconventional superconductivity in CsV${}_{3}$Sb${}_{5}$ under high pressure. They also confirm the absence of a structural phase transition up to 43.1 GPa through high-pressure synchrotron x-ray diffraction measurements, suggesting that the novel reemergent superconductivity dome can be attributed to the Fermi surface reconstruction caused by the Lifshitz transition.

Random quantum dynamics generates quantum error correcting codes that are robust against observers and errors. Here, the authors describe a simple physical picture of such codes, mapping characteristic code properties to the statistical mechanics of fluctuating ``entanglement domain walls''. The error correcting criterion is understood as a decoupling condition of domain walls, which leads to a universal scaling law of the ``code distance''.

Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature ${T}_{c}$ up to 7 K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than ${T}_{c}$. In this work, we use scanning tunneling microscopy to study the charge order in kagome superconductor $\mathrm{Rb}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$. We observe both a $2\ifmmode\times\else\texttimes\fi{}2$ chiral charge order and nematic surface superlattices (predominantly $1\ifmmode\times\else\texttimes\fi{}4$). We find that the $2\ifmmode\times\else\texttimes\fi{}2$ charge order exhibits intrinsic chirality with magnetic field tunability. Defects can scatter electrons to introduce standing waves, which couple with the charge order to cause extrinsic effects. While the chiral charge order resembles that discovered in $\mathrm{K}{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$, it further interacts with the nematic surface superlattices that…

The kagome metal ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$ hosts charge order, topologically nontrivial Dirac band crossings, and a superconducting ground state with unconventional characteristics, providing an ideal platform to investigate the interplay between different electronic states on the kagome lattice. Here we study the evolution of charge order and superconductivity in ${\mathrm{KV}}_{3}{\mathrm{Sb}}_{5}$ under hydrostatic pressure using electrical resistivity measurements. With the application of pressure, the superconducting transition temperature ${T}_{\mathrm{c}}=0.9$ K under ambient pressure quickly increases to 3.1 K at $p=0.4$ GPa, as charge order progressively weakens. Upon further increasing pressure, signatures of charge order disappear at ${p}_{\mathrm{c}1}\ensuremath{\approx}0.5$ GPa and ${T}_{\mathrm{c}}$ is gradually suppressed, forming a superconducting dome that terminates at $p\ensuremath{\approx}10$ GPa. Beyond $p\ensuremath{\approx}10$ GPa, a second superconducting dome emerges with maximum ${T}_{\mathrm{c}}\ensuremath{\approx}1.0$ K at…

Quantum systems evolving under unitary dynamics with a low rate of projective measurements can realize a highly entangled steady state. However, the stability of this phase against the disentangling action of measurements has not been fully understood. Here, the authors quantify the ability of this highly entangled phase to hide local quantum information, thereby relating its stability to its behavior as an emergent quantum error-correcting code. The authors estimate the tolerable measurement rate, above which this quantum code becomes unstable.

We derive the explicit Hamiltonian of twisted bilayer graphene (TBG) with Coulomb interaction projected into the flat bands and study the symmetries of the Hamiltonian. First, we show that all projected TBG Hamiltonians can be written as positive semidefinite Hamiltonians, an example of which was found in work by Kang and Vafek [Phys. Rev. Lett. 122, 246401 (2019)]. We then prove that the interacting TBG Hamiltonian exhibits an exact U(4) symmetry in the exactly flat band (nonchiral-flat) limit. We further define, besides a first chiral limit where the AA stacking hopping is zero, a second chiral limit where the AB/BA stacking hopping is zero. In the first chiral-flat limit (or second chiral-flat limit) with exactly flat bands, the TBG is enhanced to have an exact U(4)$\ifmmode\times\else\texttimes\fi{}$U(4) symmetry, whose generators are different between the two chiral limits. While in the first chiral limit and in the nonchiral case these symmetries have been found in work by Bultinck et al. [Phys. Rev. X 10, 031034 (2020)], for the eight lowest bands, we here prove that they are…

Based on an all-band moir\'e Hartree-Fock variational method, the authors study theoretically the correlated and topological states in magic-angle twisted bilayer graphene. They construct phase diagrams at various integer fillings. In particular, a so far unknown quantum state of matter, the moir\'e orbital antiferromagnetic state, is identified as the possible ground state at some fillings.

The kagome metals $A$V${}_{3}$Sb${}_{5}$ ($A$=K, Rb, Cs) feature a three-dimensional charge density wave of a presently unknown character and origin. In this work, the authors use group-representation theory to construct a Landau free energy and demonstrate how the interplay between in- and out-of-plane ordering tendencies can stabilize nematic phases. The phases uncovered exhibit many features consistent with experimental observations.

Kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, and Cs) exhibit superconductivity at 0.9--2.5 K and charge-density wave (CDW) at 78--103 K. Key electronic states associated with the CDW and superconductivity remain elusive. Here, we investigate low-energy excitations of ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ by angle-resolved photoemission spectroscopy. We found an energy gap of 50--70 meV at the Dirac-crossing points of linearly dispersive bands, pointing to an importance of spin-orbit coupling. We also found a signature of strongly Fermi-surface and momentum-dependent CDW gap characterized by the larger energy gap of maximally 70 meV for a band forming a saddle point around the $M$ point, the smaller (0--18 meV) gap for a band forming massive Dirac cones and a zero gap at the $\mathrm{\ensuremath{\Gamma}}/A$-centered electron pocket. The observed highly anisotropic CDW gap which is enhanced around the $M$ point signifies an importance of scattering channel connecting the saddle points, laying foundation for understanding the nature of CDW and…

The study of superconductivity in compressed hydrides is of great interest due to measurements of high critical temperatures $({T}_{c})$ in the vicinity of room temperature, beginning with the observations of ${\mathrm{LaH}}_{10}$ at 170--190 GPa. However, the pressures required for synthesis of these high-${T}_{c}$ superconducting hydrides currently remain extremely high. Here we show the investigation of crystal structures and superconductivity in the La-B-H system under pressure with particle-swarm intelligence structure-searches methods in combination with first-principles calculations. Structures with seven stoichiometries, LaBH, ${\mathrm{LaBH}}_{4}, {\mathrm{LaBH}}_{6}, {\mathrm{LaBH}}_{7}, {\mathrm{LaBH}}_{8}$, La(${\mathrm{BH})}_{3}$, and $\mathrm{La}{({\mathrm{BH}}_{4})}_{3}$ were predicted to become stable under pressure. Remarkably, the hydrogen atoms in ${\mathrm{LaBH}}_{8}$ were found to bond with B atoms in a manner that is similar to that in ${\mathrm{H}}_{3}\mathrm{S}$. Lattice dynamics calculations indicate that ${\mathrm{LaBH}}_{7}$ and ${\mathrm{LaBH}}_{8}$…

Focusing specifically on the recently retracted work by Zhang et al. [H. Zhang et al., Nature (London) 556, 74 (2018); Retraction, Nature (London) 591, E30 (2021)] and the related recently available correctly analyzed data from this Delft experiment (H. Zhang et al., arXiv:2101.11456), we discuss the general problem of confirmation bias in experiments verifying various theoretical topological quantization predictions. We show that the Delft Majorana experiment is most likely dominated by disorder, which produces trivial (but quite sharp and large) zero-bias Andreev tunneling peaks with large conductance $\ensuremath{\sim}2{e}^{2}/h$ in the theory, closely mimicking the data. Thus, although the corrected Delft data are by far the best tunnel spectroscopy results available in the literature, manifesting large and sharp zero-bias peaks rising above the background with an impressive hard superconducting gap, our theory shows that the most natural explanation for these zero-bias peaks is that they are disorder induced and not topological Majorana modes. It is possible to misinterpret…

Efficient electrical generation of torque is desired to develop innovative magnetic nanodevices. The torque can be generated by charge to spin conversion of heavy-metal layers through their strong spin-orbit interaction followed by the injection of the converted spin into adjacent ferromagnetic layers. However heavy atomic elements indispensable for this torque generation scheme are often incompatible with device mass production processes. Here we demonstrate efficient torque generation without heavy elements in ferromagnetic metal/$\mathrm{Cu}/{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ trilayers. Despite the absence of heavy elements, their effective spin Hall conductivity can be one order of magnitude larger than those of heavy-metal based multilayers. Properties of the measured torque deviate from those of the spin-injection induced torque and are consistent instead with a recently proposed torque mechanism based on orbital angular momentum injection. Our results demonstrate a direction for magnetic nanodevices based on the orbital angular momentum injection.

We investigate relations between topology and the quantum metric of two-dimensional Chern insulators. The quantum metric is the Riemannian metric defined on a parameter space induced from quantum states. Similar to the Berry curvature, the quantum metric provides a geometrical structure associated to quantum states. We consider the volume of the parameter space measured with the quantum metric, which we call the quantum volume of the parameter space. We establish an inequality between the quantum volume of the Brillouin zone and that of the twist-angle space. Exploiting this inequality and the inequality between the Chern number and the quantum volume, we investigate how the quantum volume can be used as a good measure to infer the Chern number. The inequalities are found to be saturated for fermions filling Landau levels. Through various concrete models, we elucidate conditions when the quantum volume gives a good estimate of the topology of the system.

The breaking of the vertical symmetry in Janus monochalcogenides gave rise to many properties that were not present in the original monochalcogenide monolayers. However, recent papers have often focused only on Janus monochalcogenides containing S, Se, and Te elements despite that O is also one of the group VI chalcogen elements. In this paper, we systematically investigate the electronic, transport, optical, and thermoelectric properties of Janus monolayers ${\mathrm{In}}_{2}X\mathrm{O}$ ($X=\mathrm{S},\mathrm{Se},\mathrm{Te}$) using first-principles calculations. Based on phonon spectrum analysis and ab initio molecular dynamics simulations at room temperature, ${\mathrm{In}}_{2}X\mathrm{O}$ monolayers were reported to be stable. Our calculations reveal that, while ${\mathrm{In}}_{2}\mathrm{SO}$ is an indirect semiconductor, ${\mathrm{In}}_{2}\mathrm{SeO}$ exhibits a direct semiconducting characteristic, and biaxial strain can lead to the semiconductor-metal phase transition in ${\mathrm{In}}_{2}\mathrm{SeO}$. Monolayer ${\mathrm{In}}_{2}\mathrm{TeO}$ is metal at equilibrium, and…

We find exact analytic expressions for the energies and wave functions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of projected Coulomb Hamiltonians in twisted bilayer graphene. Our exact expressions are valid for any form of the Coulomb interaction and any form of $AA$ and $AB/BA$ tunneling. The single charge excitation energy is a convolution of the Coulomb potential with a quantum geometric tensor of the TBG bands. The neutral excitations are (high-symmetry group) magnons, and their dispersion is analytically calculated in terms of the form factors of the active bands in TBG. The two-charge excitation energy and wave functions are also obtained, and a sufficient condition on the graphene eigenstates for obtaining a Cooper pair from Coulomb interactions is obtained. For the actual TBG bands at the first magic angle, we can analytically show that the Cooper pair binding energy is zero in all such projected Coulomb models, implying that either phonons and/or nonzero kinetic energy are needed for superconductivity. Since…

Geometric frustration in the kagome lattice makes it a great host for the flat electronic band, nontrivial topological properties, and novel magnetism. Here, we use magnetotransport measurements to map out the field-temperature phase diagram of the centrosymmetric $\mathrm{Y}{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$ with a Mn kagome lattice and show that the system exhibits the topological Hall effect (THE) with an in-plane applied magnetic field around 240 K. In addition, our neutron diffraction results demonstrate that the observed THE cannot arise from a magnetic skyrmion lattice, but instead from an in-plane field-induced double-fan spin structure with $c$-axis components. This paper provides a platform to understand the influence of a field-induced novel magnetic structure on magnetoelectric response in topological kagome metals.

The recently discovered kagome metals $A$V${}_{3}$Sb${}_{5}$ ($A$=K, Rb or Cs) have generated great interest as they exhibit an unconventional charge density wave (CDW), superconductivity, and nontrivial band topology. Here, the authors combine infrared spectroscopy and first-principles calculations to shed light on the origin of the CDW. They find that below the CDW transition the optical conductivity component associated with the saddle points is significantly suppressed, while that arising from the light-electron and Dirac bands is not affected. These observations attest to the importance of saddle point nesting in driving the CDW instability in CsV${}_{3}$Sb${}_{5}$.

The authors show that the valley Hall effect in gapped graphene can be understood as a manifestation of the orbital Hall effect, in which electrons in states of opposite orbital magnetic moment flow in opposite directions, generating an orbital magnetization current. Replacing the ambiguous valley indices by a physical quantity -- the orbital magnetic moment -- this reformulation provides a convincing explanation of optical rotation measurements in gapped graphene.

We show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous and hence incompatible with lattice models. Previous works [e.g., Z. Song, Z. Wang, W. Shi, G. Li, C. Fang, and B. A. Bernevig, Phys. Rev. Lett. 123, 036401 (2019); J. Ahn, S. Park, and B.-J. Yang, Phys. Rev. X 9, 021013 (2019); H. C. Po, L. Zou, T. Senthil, and A. Vishwanath, Phys. Rev. B 99, 195455 (2019); J. Kang and O. Vafek, Phys. Rev. X 8, 031088 (2018); M. Koshino, N. F. Q. Yuan, T. Koretsune, M. Ochi, K. Kuroki, and L. Fu, Phys. Rev. X 8, 031087 (2018); J. Liu, J. Liu, and X. Dai, Phys. Rev. B 99, 155415 (2019); L. Zou, H. C. Po, A. Vishwanath, and T. Senthil, Phys. Rev. B 98, 085435 (2018)] found that the two flatbands in TBG possess a fragile topology protected by the ${C}_{2z}T$ symmetry. Song et al. [Z. Song, Z. Wang, W. Shi, G. Li, C. Fang, and B. A. Bernevig, Phys. Rev. Lett. 123, 036401 (2019)] also pointed out an approximate particle-hole symmetry ($\mathcal{P}$) in the continuous model of TBG. In this paper, we…

Unlike their Hermitian counterparts, non-Hermitian (NH) systems may display an exponential sensitivity to boundary conditions and an extensive number of edge-localized states in systems with open boundaries, a phenomena dubbed the ``non-Hermitian skin effect.'' The NH skin effect is one of the primary challenges to defining a topological theory of NH Hamiltonians, as the sensitivity to boundary conditions invalidates the traditional bulk-boundary correspondence. The NH skin effect has recently been connected to the winding number, a topological invariant unique to NH systems. In this paper we extend the definition of the winding number to disordered NH systems by generalizing established results on disordered Hermitian topological insulators. Our real-space winding number is self-averaging, continuous as a function of the parameters in the problem, and remains quantized even in the presence of strong disorder. We verify that our real-space formula still predicts the NH skin effect, allowing for the possibility of predicting and observing the NH skin effect in strongly disordered NH…

For a long time, two-dimensional (2D) hexagonal ${\mathrm{MoS}}_{2}$ was proposed as a promising material for the valleytronic system. However, the limited size of growth and low carrier mobility in ${\mathrm{MoS}}_{2}$ restrict its further application. Very recently, a new kind of hexagonal 2D MXene, $\mathrm{Mo}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$, was successfully synthesized with large size, excellent ambient stability, and considerable hole mobility. In this paper, based on first-principles calculations, we predict that the valley-contrasting properties can be realized in monolayer $\mathrm{Mo}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$ and its derivative $\mathrm{Mo}{\mathrm{Si}}_{2}{\mathrm{As}}_{4}$. Beyond the traditional two-level valleys, the valleys in monolayer $\mathrm{Mo}{\mathrm{Si}}_{2}{\mathrm{As}}_{4}$ are multiple folded, implying another valley dimension. Such multiple-folded valleys can be described by a three-band low-power Hamiltonian. This study presents the theoretical advance and the potential applications of monolayer $\mathrm{Mo}{\mathrm{Si}}_{2}{\mathrm{N}}_{4}$…

Two-dimensional ferromagnets have recently drawn extensive attention, and here we study the electronic structure and magnetic properties of the bulk and monolayer of CrSBr using first-principles calculations and Monte Carlo simulations. Our results show that bulk CrSBr is a magnetic semiconductor and has the easy magnetization $b$ axis, hard $c$ axis, and intermediate $a$ axis. Thus the experimental triaxial magnetic anisotropy (MA) is well reproduced here, and it is identified to be the joint effects of spin-orbit coupling and magnetic dipole-dipole interaction. We find that bulk CrSBr has a strong ferromagnetic (FM) intralayer coupling but a marginal interlayer one. We also study the CrSBr monolayer in detail and find that the intralayer FM exchange persists and the shape anisotropy has a more pronounced contribution to the MA. Using the parameters of the FM exchange and the triaxial MA, our Monte Carlo simulations show that the CrSBr monolayer has Curie temperature ${T}_{\mathrm{C}}=175$ K. Moreover, we find that a uniaxial tensile (compressive) strain along the $a$ $(b)$ axis…

Local measurements in random quantum circuits lead to a new class of ``entanglement phase transitions''. Through extensive calculations at the critical point of ``stabilizer'' circuits --- organized by a mapping from the finite rectangular geometry to the semi-infinite plane --- the authors find here an emergent conformal field theory description of the entanglement dynamics, whose critical exponents are beyond any known theory. As we show, conformal symmetry implies a measurement-induced Bell-like nonlocality, where distant qubits become entangled with an infinite speed.

Most topological properties of quantum systems, such as the braiding of anyons or protected edge modes, are easiest to define in systems with an energy gap. While some topological phenomena persist in the presence of gapless modes, this paper explores such properties that are only possible without a gap. These systems are here dubbed intrinsically gapless topological phases. The authors study a simple model -- a hole-doped one-dimensional antiferromagnet -- and describe a mechanism based on anomalies that applies in all dimensions.

We have recently shown that the logarithmic growth of the entanglement entropy following a quantum quench in a many-body localized phase is accompanied by a slow growth of the number entropy ${S}_{N}\ensuremath{\sim}ln\phantom{\rule{0.16em}{0ex}}ln\phantom{\rule{0.16em}{0ex}}t$. Here we provide an in-depth numerical study of ${S}_{N}(t)$ for the disordered Heisenberg chain and show that this behavior is not transient and persists even for very strong disorder. Calculating the truncated R\'enyi number entropy ${S}_{N}^{(\ensuremath{\alpha})}(t)={(1\ensuremath{-}\ensuremath{\alpha})}^{\ensuremath{-}1}ln{\ensuremath{\sum}}_{n}{p}^{\ensuremath{\alpha}}(n)$ for $\ensuremath{\alpha}\ensuremath{\ll}1$ and $p(n)>{p}_{c}$---which is sensitive to large number fluctuations occurring with low probability---we demonstrate that the particle number distribution $p(n)$ in one half of the system has a continuously growing tail. This indicates a slow but steady increase in the number of particles crossing between the partitions in the interacting case and is in sharp contrast to Anderson localization…

We propose a general analytic method to study the localization transition in one-dimensional quasicrystals with parity-time ($\mathcal{PT}$) symmetry, described by complex quasiperiodic mosaic lattice models. By applying Avila's global theory of quasiperiodic Schr\"odinger operators, we obtain exact mobility edges and prove that the mobility edge is identical to the boundary of $\mathcal{PT}$-symmetry breaking, which also proves the existence of correspondence between extended (localized) states and $\mathcal{PT}$-symmetry ($\mathcal{PT}$-symmetry-broken) states. Furthermore, we generalize the models to more general cases with nonreciprocal hopping, which breaks $\mathcal{PT}$ symmetry and generally induces skin effect, and obtain a general and analytical expression of mobility edges. While the localized states are not sensitive to the boundary conditions, the extended states become skin states when the periodic boundary condition is changed to open boundary condition. This indicates that the skin states and localized states can coexist with their boundary determined by the mobility…

By analyzing the Lyapunov exponent, the authors develop here a general scheme for the study of one-dimensional non-Hermitian quasicrystals. Based on Avila's global theory, they establish a correspondence between a series of non-Hermitian quasicrystals and their corresponding Hermitian models, which allows them to obtain the phase transition properties of non-Hermitian systems just by studying the corresponding Hermitian cases. They also unveil an intriguing feature in the robust spectrum and the intrinsic relation between the winding number and slope of the Lyapunov exponent.

Structural symmetry breaking in two-dimensional materials can lead to superior physical properties and introduce an additional degree of piezoelectricity. In the present paper, we propose three structural phases ($1H, 1T$, and $1{T}^{\ensuremath{'}}$) of Janus $\mathrm{W}X\mathrm{O}$ ($X=\mathrm{S}$, Se, and Te) monolayers and investigate their vibrational, thermal, elastic, piezoelectric, and electronic properties by using first-principles methods. Phonon spectra analysis reveals that while the $1H$ phase is dynamically stable, the $1T$ phase exhibits imaginary frequencies and transforms to the distorted $1{T}^{\ensuremath{'}}$ phase. Ab initio molecular dynamics simulations confirm that $1H$- and $1{T}^{\ensuremath{'}}\text{\ensuremath{-}}\mathrm{W}X\mathrm{O}$ monolayers are thermally stable even at high temperatures without any significant structural deformations. Different from binary systems, additional Raman active modes appear upon the formation of Janus monolayers. Although the mechanical properties of $1H\text{\ensuremath{-}}\mathrm{W}X\mathrm{O}$ are found to be…

Recent experimental observation of an unexpectedly large current-induced spin-orbit torque in surface oxidized Cu on top of a ferromagnet pointed to a possibly prominent role of the orbital Rashba effect (ORE) in this system. Here, we use first principles methods to investigate the ORE in a system of oxygen monolayer deposited on top of a Cu(111) film. We show that surface oxidization of the Cu film leads to a gigantic enhancement of the ORE near the Fermi energy. The resulting chiral orbital texture in the momentum space is exceptionally strong, reaching as much as $\ensuremath{\sim}0.5\ensuremath{\hbar}$ in magnitude. We find that resonant hybridization between O $p$ states and Cu $d$ states is responsible for the emergence of the ORE at the interface. We also present a minimal model that captures the emergence of the ORE through the $pd$ hybridization mechanism. We demonstrate that an application of an external electric field to the system generates colossal orbital Hall currents which are an order of magnitude larger than the spin Hall currents found in heavy metals. This…

Two-dimensional materials with valley-related multiple Hall effect are both fundamentally intriguing and practically appealing for exploring novel phenomena and applications, but have been largely overlooked to date. Here, using first-principles calculations, we show that the valley-related multiple Hall effect can exist in single-layer $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$. We identify single-layer $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$ as a ferromagnetic semiconductor with out of plane magnetization and valley physics. Arising from the joint effect of inversion symmetry breaking and time-reversal symmetry breaking, the exotic spontaneous valley polarization occurs in single-layer $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$, thus facilitating the observation of anomalous valley Hall effect. Moreover, under external strain, band inversion can occur at only one of the valleys of single-layer $\mathrm{V}{\mathrm{Si}}_{2}{\mathrm{P}}_{4}$, enabling the long-sought valley-polarized quantum anomalous Hall effect, and meanwhile the anomalous valley Hall effect is well…

We theoretically show that materials with perovskite-type crystal structures provide a platform for spin current generation. Its mechanism is based on spin-split band structures in certain kinds of collinear antiferromagnetic states, requiring neither spin-orbit coupling nor a ferromagnetic moment. By investigating a multiband Hubbard model for transition-metal compounds by means of the Hartree-Fock approximation and the Boltzmann transport theory, we find that a pure spin current is induced by an electric field applied to a $C$-type antiferromagnetic metallic phase. The spin current generation originates from a cooperative effect of spatially anisotropic electron transfer integrals owing to the ${\mathrm{GdFeO}}_{3}$-type lattice distortion, which is ubiquitous in many perovskites, and the collinear spin configuration. We discuss our finding from the symmetry point of view, in comparison with other spin current generator candidates with collinear antiferromagnetism. We also propose several ways to detect the phenomenon in candidate perovskite materials.

The recent experimental confirmation of a transformation between meron and skyrmion topological spin textures in the chiral magnet ${\mathrm{Co}}_{8}{\mathrm{Zn}}_{9}{\mathrm{Mn}}_{3}$ [S.-Z. Lin et al., Phys. Rev. B 91, 224407 (2015); X. Z. Yu et al., Nature 564, 95 (2018)] confirms that the skyrmion crystals discovered in 2009 [S. M\"uhlbauer et al., Science 323, 915 (2009)] are just the tip of the iceberg. Crystals of topological textures, including skyrmions, merons, vortices, and monopoles, can be stabilized by combining simple physical ingredients, such as lattice symmetry, frustration, and spin anisotropy. The current challenge is to find the combinations of these ingredients that produce specific topological spin textures. Here we report a simple mechanism for the stabilization of meron, skyrmion, and vortex crystals in centrosymmetric tetragonal magnets. In particular, the meron/skyrmion crystals can form even in absence of magnetic field. The application of magnetic field leads to a rich variety of topological spin textures that survive in the long wavelength limit of the…

Non-Hermitian systems show a non-Hermitian skin effect, where the bulk states are localized at a boundary of the systems with open boundary conditions. In this paper, we study the dependence of the localization length of the eigenstates on a system size in a specific non-Hermitian model with a critical non-Hermitian skin effect, where the energy spectrum undergoes discontinuous transition in the thermodynamic limit. We analytically show that the eigenstates exhibit remarkable localization, known as scale-free localization, where the localization length is proportional to a system size. Our result gives theoretical support for the scale-free localization, which has been proposed only numerically in previous works.

Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to finding the roots of a simple algebraic equation. As an application, our formulation provides the desirable formulas for the defining quantities, the gain and directionality, of directional amplification. Thus our formulas provide an efficient guide for designing directional amplifiers.

Janus transition metal dichalcogenides (TMDs) lose the horizontal mirror symmetry of ordinary TMDs, leading to the emergence of additional features, such as native piezoelectricity, Rashba effect, and enhanced catalytic activity. While Raman spectroscopy is an essential nondestructive, phase- and composition-sensitive tool to monitor the synthesis of materials, a comprehensive study of the Raman spectrum of Janus monolayers is still missing. Here, we discuss the Raman spectra of WSSe and MoSSe measured at room and cryogenic temperatures, near and off resonance. By combining polarization-resolved Raman data with calculations of the phonon dispersion and using symmetry considerations, we identify the four first-order Raman modes and higher-order two-phonon modes. Moreover, we observe defect-activated phonon processes, which provide a route toward a quantitative assessment of the defect concentration and, thus, the crystal quality of the materials. Our work establishes a solid background for future research on material synthesis, study, and application of Janus TMD monolayers.

Lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ is one of the key parameters involved in the design of microelectronics and energy-conversion devices. In determining the ${\ensuremath{\kappa}}_{\mathrm{L}}$, similar to the well-known cubic anharmonic effect, quartic anharmonicity is ubiquitous and also plays a crucial role in the final heat conduction of some compounds. In this paper, we use a high-throughput first-principles calculation method that combines self-consistent phonon (SCP) theory, compressive sensing techniques, and Boltzmann transport equation (BTE) to investigate the lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ with the inclusion of cubic and quartic anharmonicity in 16 cubic oxide and fluoride perovskites. The BTE is solved on top of SCP theory for complete treatment of the quartic anharmonic effect that comprises four-phonon scattering and temperature-driven phonon frequency shift. In particular, only the ${\ensuremath{\kappa}}_{\mathrm{L}}$ within SCP theory is numerically valid for six of the 16 candidate perovskites, since…

The authors use Hartree-Fock methods to provide a comprehensive understanding of the moir\'e Hubbard model, believed to describe the low-energy physics of the twisted bilayer dichalcogenide material WSe${}_{2}$. They present a comprehensive phase diagram, reveal a previously unnoticed gauge symmetry, demonstrate a region of a reentrant metal-insulator transition, and elucidate the roles of fermiology and commensurability in the transitions. Comparison to experimental data locates the currently studied systems in the intermediate coupling region of the phase diagram.

The Aubry-Andr\'e-Harper model provides a paradigmatic example of aperiodic order in a one-dimensional lattice displaying a delocalization-localization phase transition at a finite critical value ${V}_{c}$ of the quasiperiodic potential amplitude $V$. In terms of the dynamical behavior of the system, the phase transition is discontinuous when one measures the quantum diffusion exponent $\ensuremath{\delta}$ of wave-packet spreading, with $\ensuremath{\delta}=1$ in the delocalized phase $V<{V}_{c}$ (ballistic transport), $\ensuremath{\delta}\ensuremath{\simeq}1/2$ at the critical point $V={V}_{c}$ (diffusive transport), and $\ensuremath{\delta}=0$ in the localized phase $V>{V}_{c}$ (dynamical localization). However, the phase transition turns out to be smooth when one measures, as a dynamical variable, the speed $v(V)$ of excitation transport in the lattice, which is a continuous function of potential amplitude $V$ and vanishes as the localized phase is approached. Here we consider a non-Hermitian extension of the Aubry-Andr\'e-Harper model, in which hopping along the lattice is…

The time evolution of the entanglement entropy is a key concept to understand the structure of a nonequilibrium quantum state. In a large class of models, such evolution can be understood in terms of a semiclassical picture of moving quasiparticles spreading the entanglement throughout the system. However, it is not yet known how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. Here, guided by the examples of conformal field theories and free-fermion chains, we show that the quasiparticle picture can be adapted to this goal, leading to a general conjecture for the charged entropies whose Fourier transform gives the desired symmetry-resolved entanglement ${S}_{n}(q)$. We point out two physically relevant effects that should be easily observed in atomic experiments: a delay time for the onset of ${S}_{n}(q)$ which grows linearly with $|\mathrm{\ensuremath{\Delta}}q|$ (the difference between the charge $q$ and its mean value) and an effective equipartition when $|\mathrm{\ensuremath{\Delta}}q|$ is much smaller than the subsystem…

The discovery of high-temperature superconductivity in hydrogen-rich compounds has fueled the enthusiasm for finding materials with more promising superconducting properties among hydrides. However, the ultrahigh pressure needed to synthesize and maintain high-temperature hydrogen-rich superconductors hinders the experimental investigation of these materials. For practical applications, it is also highly desired to find more hydrogen-rich materials that superconduct at high temperatures but under relatively lower pressures. Based on first-principles density functional theory, we calculate the electronic and phonon band structures for a ternary borohydride formed by intercalating ${\mathrm{BH}}_{4}$ tetrahedrons into a fcc potassium lattice, ${\mathrm{KB}}_{2}{\mathrm{H}}_{8}$. Remarkably, we find that this material is dynamically stable and one of its $s{p}^{3}$-hybridized $\ensuremath{\sigma}$-bonding bands is metallized (i.e., partially filled) above a moderate high pressure. This metallized $\ensuremath{\sigma}$-bonding band couples strongly with phonons, giving rise to a strong…

Density functional theory calculations and crystal structure predictions using the particle swarm optimization method have been combined to determine stable hydrides of lead under pressure. In contrast to other group-IVa hydrides, the stoichiometry ${\mathrm{PbH}}_{6}$ is the first hydride to become stable, at just under 1 Mbar. For two previously studied stoichiometries, ${\mathrm{PbH}}_{4}$ and ${\mathrm{PbH}}_{8}$, energetically more favorable phases were identified to become stable around 2 Mbar. In all structures, the hydrogenic sublattices comprise negatively charged ${{\mathrm{H}}_{2}}^{\ensuremath{\delta}\ensuremath{-}}$ molecules. Competitive ${\mathrm{PbH}}_{4}$ and ${\mathrm{PbH}}_{6}$ structures are layered. ${\mathrm{PbH}}_{6}$ features ${\mathrm{H}}_{2}$ molecules intercalated between hcp Pb layers, the stable phase of dense pure lead, thus offering a potentially straightforward route towards synthesis. In ${\mathrm{PbH}}_{8}$, the Pb lattice adapts a $\ensuremath{\beta}$-Sn structure, and hydrogen atoms form quasi-one-dimensional-chains. All structures were found to…

The target of valleytronics developments is to manipulate the valley degree of freedom and utilize it in microelectronics as charge and spin degrees of freedom. Based on first-principles calculations, we demonstrate that $M{\mathrm{Br}}_{2}$ $(M=\mathrm{Ru},\phantom{\rule{4pt}{0ex}}\mathrm{Os})$ monolayers are intrinsically ferrovalley materials with large valley polarization up to 530 meV. Compressive strain can induce phase transitions in the materials from ferrovalley insulators to complete valley-polarized metals, called half-valley metals, in analogy to the concept of half metals in spintronics. With the increase of the strain, the materials become Chern insulators, whose edge states are chiral-spin-valley locking. The phase transition is caused by sequent band inversions of the ${d}_{xy}/{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals at $K\ensuremath{-}$ and $K+$ valleys, analyzed based on a strained $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ model. Our work provides a pathway for carrying out low-dissipation electronics devices with…

Using exact diagonalization, we study the projected Hamiltonian with the Coulomb interaction in the eight flat bands of first magic angle twisted bilayer graphene. Employing the U(4) [$\mathrm{U}(4)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(4)$] symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent that allows for study around $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}3,\ifmmode\pm\else\textpm\fi{}2,\ifmmode\pm\else\textpm\fi{}1$ fillings. In the first chiral limit ${w}_{0}/{w}_{1}=0$, where ${w}_{0}$ (${w}_{1}$) is the $AA$ ($AB$) stacking hopping, we find that the ground states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge $\ifmmode\pm\else\textpm\fi{}1$ excitations found in Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] are the lowest charge excitations up to system sizes $8\ifmmode\times\else\texttimes\fi{}8$ (for restricted Hilbert space) in the chiral-flat limit. We also find that the flat metric condition (FMC) used by Bernevig et al. [Phys.…

The Raman exponent of single molecular magnetic relaxation may take various unexpected values because of rich phonon spectra and spin-phonon coupling of molecular crystals. We systematically examine the origins of different abnormalities and clarify misunderstandings of the past, particularly the appropriateness of the fitting procedures for the exponents. We find that exponential laws raised by optical phonons can yield spurious power laws with low exponents. This observation indicates long-standing misunderstandings of the origins of low Raman exponents in a large bulk of single molecule magnets. Resulting from spin-lattice coupling with optical modes, the presence of these exponents suggests the importance of the local dynamical environment for the magnetic relaxation in this regime.

The skin effect and topological edge states in non-Hermitian systems have been well studied, and the second-order skin effect and corner modes have also been proposed in non-Hermitian systems recently. In this paper, we construct the nested tight-binding formalism to research the second-order corner modes analytically, which is a direct description of the generic non-Hermitian tight-binding model without other assumptions. Within this formalism, we obtain the exact solutions of second-order topological zero-energy corner modes for the non-Hermitian four-band model. We validate the nested tight-binding formalism in the hybrid skin-topological corner modes for the four-band model and a non-Hermitian two-dimensional (2D) extrinsic model. In addition, we exactly illustrate the corner modes induced by second-order skin effect for a simplest 2D non-Hermitian model by the nested tight-binding formalism.

Classical meta-absorber designs usually have a tradeoff between bandwidth, efficiency, and thickness. Here, we introduce the concept of a nonlocal acoustic metasurface absorber by using a bridge structure connecting resonating unit cells to improve the performances of the meta-absorber. By utilizing the coupling effect between the adjacent unit cells, ultrabroadband sound absorption is achieved with deep-wavelength thickness. The physical mechanism of the nonlocal acoustic metasurface absorber is investigated and uncovered by developing analytical models. We theoretically and numerically study the nonlocal metasurface with a connecting bridge and the traditional metasurface without a bridge. The nonlocality can introduce three specific effects: the optimization of effective acoustic impedances, the shift of Fabry-Perot resonant frequencies, and the enhancement of the coupling effects between adjacent unit cells. These effects contribute to improve the bandwidth and the efficiency of the acoustic meta-absorber. We numerically and experimentally achieve an average absorption…

We theoretically investigate the origin of the square-type skyrmion crystal in centrosymmetric itinerant magnets, motivated by the recent experimental findings in ${\mathrm{GdRu}}_{2}{\mathrm{Si}}_{2}$ [N. D. Khanh et al., Nat. Nanotech. 15, 444 (2020)]. By simulated annealing for an effective spin model derived from the Kondo lattice model on a square lattice, we find that a square skyrmion crystal composed of a superposition of two spin helices is stabilized in a magnetic field by synergy between the positive biquadratic, bond-dependent anisotropic, and easy-axis anisotropic interactions. This is in stark contrast to triangular skyrmion crystals, which are stabilized by only one of the three, suggesting that the square skyrmion crystal is characteristic of itinerant magnets with magnetic anisotropy. We also show that a variety of noncollinear and noncoplanar spin textures appear, depending on the model parameters as well as the applied magnetic field. The present systematic study will be useful not only for identifying the key ingredients in ${\mathrm{GdRu}}_{2}{\mathrm{Si}}_{2}$…

The synthesis and characterization of vanadium-based kagome metals ${\mathrm{YV}}_{6}{\mathrm{Sn}}_{6}$ and ${\mathrm{GdV}}_{6}{\mathrm{Sn}}_{6}$ are presented. X-ray diffraction, magnetization, magnetotransport, and heat capacity measurements reveal an ideal kagome network of V ions coordinated by Sn and separated by triangular lattice planes of rare-earth ions. The onset of low-temperature magnetic order of Gd spins is detected in ${\mathrm{GdV}}_{6}{\mathrm{Sn}}_{6}$ and is suggested to be noncollinear, while V ions in both compounds remain nonmagnetic. Density functional theory calculations are presented modeling the band structures of both compounds, which can be classified as ${\mathbb{Z}}_{2}$ topological metals in the paramagnetic state. Both compounds exhibit high mobility, multiband transport and present an interesting platform for controlling the interplay between magnetic order associated with the $R$-site sublattice and nontrivial band topology associated with the V-based kagome network. Our results invite future exploration of other $R{\mathrm{V}}_{6}{\mathrm{Sn}}_{6}$…

Mutual interplay between the electronic degrees of freedom in solids, such as charge, spin, orbital, sublattice, and bond degrees of freedom, is a source of cross-correlated phenomena with unconventional electronic ordered states. Such degrees of freedom can be described by four types of multipoles (electric, magnetic, magnetic toroidal, and electric toroidal) in a unified way, which enable us to tightly connect the microscopic degrees of freedom with macroscopic physical responses in a transparent manner. We complete a classification of the multipoles in all 122 magnetic point groups based on group theory. The classification is useful to identify potentially active multipoles, not only in ordinary ferromagnetic and antiferromagnetic orderings but also in exotic orderings breaking time-reversal symmetry, e.g., a loop-current state. Moreover, the classification gives an insight into the microscopic origin of the multiferroic responses and quantum transports. By analyzing response functions up to the second order, we summarize the indispensable multipole moments for various responses,…

Very recently, a new type of two-dimensional layered material, ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$, was fabricated that is semiconducting with weak interlayer interaction, high strength, and excellent stability. We systematically investigate the effect of vertical strain on the electronic structure of ${MA}_{2}{Z}_{4}$ ($M=\text{Ti/Cr/Mo}, A=\mathrm{Si}, Z=\text{N/P}$) bilayers. Taking bilayer ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$ as an example, our first-principles calculations show that its indirect band gap decreases monotonically as the vertical compressive strain increases. Under a critical strain around 22%, it undergoes a transition from semiconductor to metal. We attribute this to the opposite energy shift of states in different layers, which originates from the built-in electric field induced by the asymmetric charge transfer between two inner sublayers near the interface. Similar semiconductor to metal transitions are observed in other strained ${MA}_{2}{Z}_{4}$ bilayers, and the estimated critical pressures to realize such transitions are within the same order as…

Moir\'e superlattices of transition metal dichalcogenide (TMD) bilayers have been shown to host correlated electronic states, which arise from the interplay of long wavelength moir\'e potential and long-range Coulomb interaction. Here, we theoretically investigate structural relaxation and single-particle electronic structure of twisted TMD homobilayer. From the large-scale density functional theory calculation and continuum model with layer degrees of freedom, we find that the out-of-plane gating field creates a tunable charge transfer gap at the Dirac point between the first and second moir\'e valence bands. We further study the charge orders at the fractional band fillings. In the flat band limit, we find from Monte Carlo simulations a series of charge-ordered insulating states at various fillings $n=\frac{1}{4},\frac{1}{3},\frac{1}{2},\frac{2}{3},1$. We predict that gating field induces a phase transition between different electron crystals at fixed filling $n=\frac{1}{2}$ or $\frac{2}{3}$. At half-filling $n=1$, the ground state is a Mott insulator with electronically driven…

Two-dimensional (2D) ferrovalley materials, displaying coexistence of spontaneous spin and valley polarizations, have recently attracted significant attention due to their potential for applications in the fields of spintronics and valleytronics. However, unfortunately, to date only a few 2D ferrovalley materials exist. Here, first-principles calculations predict a 2D Janus ferrovalley material lanthanum bromiodide (LaBrI). It is found that LaBrI is a stable ferromagnetic electride, whose magnetic moment originates mainly from the interstitial anionic electrons. The magnetic transition temperature of LaBrI monolayers is estimated to be far beyond room temperature, and a sizable magnetic anisotropy with easy in-plane magnetization is also present. Most importantly, LaBrI monolayers exhibit a large valley polarization due to the concurrent broken space- and time-reversal symmetries, with the calculated valley polarization reaching up to 59 meV. This value is comparable to that of the ferrovalley materials reported to date. Intriguingly, the inequivalent Berry curvature at the two…

We propose an anti-parity-time (anti-$\mathcal{PT}$) symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model, where the large non-Hermiticity constructively creates nontrivial topology and greatly expands the topological phase. In the anti-$\mathcal{PT}$-symmetric SSH model, the gain and loss are alternatively arranged in pairs under the inversion symmetry. The appearance of the degenerate point at the center of the Brillouin zone determines the topological phase transition, whereas the exceptional points unaffect the band topology. The large non-Hermiticity leads to unbalanced wave-function distribution in the broken anti-$\mathcal{PT}$-symmetric phase and induces the nontrivial topology. Our findings can be verified through introducing dissipations in every other two sites of the standard SSH model even in its trivial phase where the nontrivial topology is solely induced by the dissipations.

We theoretically investigate the properties of holes in a ${\mathrm{Si}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}/\mathrm{Ge}/{\mathrm{Si}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}$ quantum well in a perpendicular magnetic field that make them advantageous as qubits, including a large ($>100$ meV) intrinsic splitting between the light and heavy hole bands, a very light ($\ensuremath{\sim}0.05\phantom{\rule{4pt}{0ex}}{m}_{0}$) in-plane effective mass, consistent with higher mobilities and tunnel rates, and larger dot sizes that could ameliorate constraints on device fabrication. Compared to electrons in quantum dots, hole qubits do not suffer from the presence of nearby quantum levels (e.g., valley states) that can compete with spins as qubits. The strong spin-orbit coupling in Ge quantum wells may be harnessed to implement electric-dipole spin resonance, leading to gate times of several nanoseconds for single-qubit rotations. The microscopic mechanism of this spin-orbit coupling is discussed, along with its implications for quantum gates based on electric-dipole spin resonance, stressing the…

The discovery of ferroelectric ${\mathrm{HfO}}_{2}$ in thin films and more recently in bulk is an important breakthrough because of its silicon compatibility and unexpectedly persistent polarization at low dimensions, but the origin of its ferroelectricity is still under debate. The stabilization of the metastable polar orthorhombic phase was often considered as the cumulative result of various extrinsic factors such as stress, grain boundary, and oxygen vacancies as well as phase transition kinetics during the annealing process. We propose a mechanism to stabilize the polar orthorhombic phase over the nonpolar monoclinic phase that is the bulk ground state. Our first-principles calculations demonstrate that the doubly positively charged oxygen vacancy, an overlooked defect but commonly presenting in binary oxides, is critical for the stabilization of the ferroelectric phase. The charge state of the oxygen vacancy serves as a degree of freedom to control the thermodynamic stability of competing phases of wide band gap oxides.

By using density functional theory and ab initio quantum-transport simulation, we study the Schottky barrier and the rectifying behavior of diodes consisting of the two-dimensional metal phase $1T\text{\ensuremath{-}}{\mathrm{MoS}}_{2}$ and semiconductor phase 2H-${\mathrm{MoS}}_{2}$. The results show that the Schottky barrier of the out-of-plane (OP) contacted ${\mathrm{MoS}}_{2}$ heterostructure diode is a little different from that of the in-plane (IP) contacted ${\mathrm{MoS}}_{2}$ heterostructure diode. The current-voltage characteristics show that the OP diode has the better rectifying behavior compared to the IP diode under the zero gate voltage. The corresponding maximum rectifier ratio of the OP Schottky barrier diode is close to ${10}^{7}$ at 0.9 V bias voltage. More interestingly, we find that the gate voltage can be used to effectively control the rectifying behavior of the two diodes. The positive gate voltages can increase the current value of two Schottky barrier diodes, but weaken their rectification ratios. The negative gate voltages can reverse the rectifying…

The heterojunction between different materials often exhibits a rectifying effect; e.g., pn junction is used for diode. On the other hand, the Josephson junction between two different superconductors is assumed to show symmetric response between two directions of the current, i.e., the voltage drop $V$ is antisymmetric with respect to the sign change of the current $I$. However, there should be an asymmetry between the states of charge accumulation on the right and left sides of the Josephson junction, which can lead to the nonreciprocal responses. Here we demonstrate theoretically that nonreciprocal $I\text{\ensuremath{-}}V$ characteristic appears due to this charging energy difference both in the classical and quantum regimes.

The physics of twisted bilayer graphene (TBG) is a complicated m\'elange of topology and interactions. A unified understanding of the correlated insulators in TBG emerges in this series of six papers (TBG1--TBG6). Starting from the physics of single-particle bands, TBG1 simplifies the physics of the infinite dimensional Bistritzer-Macdonald Hamiltonian to that of a 12-site model. TBG2 challenges the well-accepted thought that the active bands in TBG are fragile topological, and proves their stable topology. TBG3 and TBG4 analytically obtain the many-body interacting Hamiltonian, its symmetries, and the exact correlated insulator ground states at integer filling. TBG5 then obtains charge 0,+- 1,+-2 exact excitations above these ground states and their Goldstone modes, and proves the impossibility of pairing with repulsive projected interactions. Finally, TBG6 performs large-scale exact diagonalization studies, confirming the validity of the analytic results.

A relation between the local integrals of motions and the Hilbert-space structure of eigenstates is found across the many-body localization transition. Absence of self-averaging of wave function spread in the Hilbert space at the transition is related to the jump in the fractal dimensions and the localization length.

Paramagnetic substitutional carbon (${\mathrm{C}}_{\text{B}},{\mathrm{C}}_{\text{N}}$) defects in hexagonal boron nitride are discussed as candidates for quantum bits. Their identification and suitability are approached by means of photoluminescence (PL), charge transitions, electron paramagnetic resonance, and optically detected magnetic resonance (ODMR) spectra. Several clear trends in these are revealed by means of an efficient plane wave periodic supercell ab initio density functional theory approach. In particular, this yields insight into the role of the separation between ${\mathrm{C}}_{\text{B}}$ and ${\mathrm{C}}_{\text{N}}$. In most of the cases, the charge transition between the neutral and a singly charged ground state of a defect is predicted to be experimentally accessible, since the charge transition level position lies within the band gap. A posteriori charge corrections are also discussed. A near-identification of an experimentally isolated single spin center as the neutral ${\mathrm{C}}_{\text{B}}$ point defect was found via comparison of results to recently…

The spin chirality, created by magnetic atoms, has been comprehensively understood to generate and control the magneto-optical effects. In comparison, the role of the crystal chirality that relates to nonmagnetic atoms has received much less attention. Here, we theoretically discover the crystal chirality magneto-optical (CCMO) effects, which depend on the chirality of crystal structures that originates from the rearrangement of nonmagnetic atoms. We show that the CCMO effects exist in many collinear antiferromagnets, such as ${\mathrm{RuO}}_{2}$ and ${\mathrm{CoNb}}_{3}{\mathrm{S}}_{6}$, which has a local and global crystal chirality, respectively. The key character of the CCMO effects is the sign change if the crystal chirality reverses. The magnitudes of the CCMO spectra can be effectively manipulated by reorienting the N\'eel vector with the help of an external electric field, and the spectral integrals are strongly correlated to magnetocrystalline anisotropy energy bridging by orbital magnetic moments.

Critical Fermi surfaces appear in many physical systems, including the half-filled Landau level, and certain spin liquids. Many theories have studied the nonquasiparticle excitations near the Fermi surface, and possible instabilities to pairing or density wave orders, but without a fully systematic method. Here, the authors study an ensemble of self-averaging theories with random coupling constants, and obtain a controlled large-$N$ expansion.

Large-scale exact diagonalization reveals the competition between fractional Chern insulator and charge density wave states in a realistic spin- and valley-polarized single-band model for twisted bilayer graphene aligned with its hexagonal boron nitride substrate. While charge-ordered ground states are found across a whole range of filling fractions, consistent with experimental results in related moir\'e heterostructures, the interplay of the Berry curvature with the nontrivial single-particle dispersions may lead to the formation of topologically nontrivial correlated states at $\ensuremath{\nu}=1/3$ as well as $\ensuremath{\nu}=2/5$.

Exploration of new superconductors still relies on the experience and intuition of experts, and is largely a process of experimental trial and error. In one study, only 3% of the candidate materials showed superconductivity [Hosono et al., Sci. Technol. Adv. Mater. 16, (2015)]. Here, we report a deep learning model for finding new superconductors. We introduced the method named ``reading periodic table'' that represented the periodic table in a way that allows deep learning to learn to read the periodic table and to learn the law of elements for the purpose of discovering novel superconductors which are outside the training data. It is recognized that it is difficult for deep learning to predict something outside the training data. Although we used only the chemical composition of materials as information, we obtained an ${R}^{2}$ value of 0.92 for predicting ${T}_{\text{c}}$ for materials in a database of superconductors. We also introduced the method named ``garbage-in'' to create synthetic data of nonsuperconductors that do not exist. Nonsuperconductors are not reported, but the…

We study the electroacoustic properties of aluminum scandium nitride crystals ${\mathrm{Al}}_{1\ensuremath{-}x}{\mathrm{Sc}}_{x}\mathrm{N}$ with the metastable wurtzite structure by means of first-principles calculations based on density functional theory. We extract the material property data relevant for electroacoustic device design, namely, the full tensors of elastic and piezoelectric constants. Atomistic models were constructed and analyzed for a variety of Sc concentrations $0\ensuremath{\le}x\ensuremath{\le}50$%. The functional dependence of the material properties on the scandium concentration was extracted by fitting the data obtained from an averaging procedure for different disordered atomic configurations. We give an explanation of the observed elastic softening and the extraordinary increase in piezoelectric response as a function of Sc content in terms of an element-specific analysis of bond lengths and bond angles.

The spreading of information forms the basis of several quantum nonequilibrium phenomena, such as seen in the emergence of thermodynamics and statistical physics. Recently, much progress has been made in understanding the dynamics of information in isolated integrable systems after a quantum quench, by using a quasiparticle picture predicting ballistic spreading of quantum correlations. This paper shows how to apply these ideas to describe the dissipative dynamics of correlations and of entanglement in open quantum many-body systems.

Electronic correlations could have significant impact on the material properties. They are typically pronounced for localized orbitals and enhanced in low-dimensional systems, so two-dimensional (2D) transition metal compounds could be a good platform to study their effects. Recently, a new class of 2D transition metal compounds, the ${\mathrm{MoSi}}_{2}{\mathrm{N}}_{4}$-family materials, has been discovered, and some of them exhibit intrinsic magnetism. Here, taking monolayer ${\mathrm{VSi}}_{2}{\mathrm{P}}_{4}$ as an example from the family, we investigate the impact of correlation effects on its physical properties, based on the first-principles calculations with the $\mathrm{DFT}+U$ approach. We find that different correlation strengths can drive the system into a variety of interesting ground states, with rich magnetic, topological, and valley features. With increasing correlation strength, while the system favors a ferromagnetic semiconductor state for most cases, the magnetic anisotropy and the band gap type undergo multiple transitions, and in the process, the band edges can…

Light absorption plays a vital role in governing the performance of optoelectronic devices, such as solar cells and photodetectors. However, it is quite challenging to realize perfect absorption for materials with low intrinsic dissipative losses and requires the careful design of nanoscale structures. This study theoretically proposes a polarization-independent germanium (Ge) metasurface absorber at the telecommunication C band by exploring the quasibound state in the continuum (QBIC). Such a QBIC is excited by breaking the in-plane symmetry of the Ge metasurface in which each unit cell is made of four subwavelength Ge nanodisks. The Q factor of QBIC is mainly governed by the asymmetry parameter, providing a straightforward way of optimizing the light absorption by the critical coupling. We demonstrate two designs that boost the absorption up to 50% in the transmission and up to 100% in the reflection modes.

The Fermi surface plays a crucial rule in understanding the fundamental physics of crystals, such as superconductivity, the charge/spin density wave, and anomalous transport. Here, the authors discover the type-III Weyl semimetal, whose novel Fermi surface consists of two electron or hole pockets touching at the double Weyl points in Ta${}_{2}$Se${}_{8}$I, supporting the axionic charge density wave phase at low temperature. A unified and transparent picture to classify all of type-I, type-II, and type-III Weyl fermions based on the general tilting mechanism is also found.

Mappings between fermions and qubits are valuable constructions in physics. To date only a handful exist. In addition to revealing dualities between fermionic and spin systems, such mappings are indispensable in any quantum simulation of fermionic physics on quantum computers. The number of qubits required per fermionic mode, and the locality of mapped fermionic operators strongly impact the cost of such simulations. We present a fermion to qubit mapping that outperforms all previous local mappings in both the qubit to mode ratio and the locality of mapped operators. In addition to these practically useful features, the mapping bears an elegant relationship to the toric code, which we discuss. Finally, we consider the error mitigating properties of the mapping---which encodes fermionic states into the code space of a stabilizer code. Although there is an implicit tradeoff between low weight representations of local fermionic operators, and high distance code spaces, we argue that fermionic encodings with low-weight representations of local fermionic operators can still exhibit error…

Solutions of the Peierls-Boltzmann transport equation using inputs from density functional theory calculations have been successful in predicting the thermal conductivity in a wide range of materials. In the case of two-dimensional (2D) materials, the accuracy of this method can depend highly on the shape of the dispersion curve for flexural phonon (ZA). As a universal feature, very recent theoretical studies have shown that the ZA branch of 2D materials is quadratic. However, many prior thermal conductivity studies and conclusions are based on a ZA branch with linear components. In this paper, we systematically study the impact of the long-wavelength dispersion of the ZA branch in graphene, silicene, and $\ensuremath{\alpha}$-nitrophosphorene to highlight its role on thermal conductivity predictions. Our results show that the predicted $\ensuremath{\kappa}$ value, its convergence and anisotropy, as well as phonon lifetimes and mean free path can change substantially even with small linear to pure quadratic corrections to the shape of the long-wavelength ZA branch. Also, having a…

Recently, the concept of ferrovalley materials has been proposed. These systems, in which ferromagnetism or ferroelectricity triggers spontaneous valley polarization, can be applied to nonvolatile valleytronic devices. In addition, a fabricated Janus transition metal dichalcogenide has been attracting immense attention due to its intrinsic valley properties and piezoelectricity. Inspired by these works, we predict a ferrovalley material, Janus VClBr monolayer, by performing first-principles calculations. The Janus VClBr monolayer possesses a large valley polarization due to the spin-orbit coupling coexisting with the intrinsic exchange interaction of vanadium $3d$ electrons, which can be illustrated by a $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model. Combining the valley band structures with group theory analysis, we also find the chirality-dependent optical band gap that could be used to detect the valley state of the system. An anomalous valley Hall effect is confirmed by calculating the Berry curvatures in such a material system. Meanwhile, mirror…

Can the Brewster angle have a temporal equivalent? Here, the authors exploit time-dependent metamaterials to propose the idea of such a temporal analog. When the permittivity of the medium rapidly changes in time from an isotropic to anisotropic value, the backward wave may be absent for such an angle of incidence. A closed-form mathematical expression, along with numerical simulations, for this temporal analog of the Brewster angle is provided.

We study Chern insulators from the point of view of K\"ahler geometry, i.e., the geometry of smooth manifolds equipped with a compatible triple consisting of a symplectic form, an integrable almost complex structure, and a Riemannian metric. The Fermi projector, i.e., the projector onto the occupied bands, provides a map to a K\"ahler manifold. The quantum metric and Berry curvature of the occupied bands are then related to the Riemannian metric and symplectic form, respectively, on the target space of quantum states. We find that the minimal volume of a parameter space with respect to the quantum metric is $\ensuremath{\pi}|\mathcal{C}|$, where $\mathcal{C}$ is the first Chern number. We determine the conditions under which the minimal volume is achieved both for the Brillouin zone and the twist-angle space. The minimal volume of the Brillouin zone, provided the quantum metric is everywhere nondegenerate, is achieved when the latter is endowed with the structure of a K\"ahler manifold inherited from the one of the space of quantum states. If the quantum volume of the twist-angle…

Kagome magnets are believed to have numerous exotic physical properties due to the possible interplay between lattice geometry, electron correlation and band topology. Here, we report the large anomalous Hall effect in the kagome ferromagnet ${\mathrm{LiMn}}_{6}{\mathrm{Sn}}_{6}$, which has a Curie temperature of 382 K and easy plane along with the kagome lattice. At low temperatures, unsaturated positive magnetoresistance and opposite signs of ordinary Hall coefficient for ${\ensuremath{\rho}}_{xz}$ and ${\ensuremath{\rho}}_{yx}$ indicate the coexistence of electrons and holes in the system. A large intrinsic anomalous Hall conductivity of $380\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, or $0.44\phantom{\rule{0.16em}{0ex}}{e}^{2}/h$ per Mn layer, is observed in ${\ensuremath{\sigma}}_{xy}^{A}$. This value is significantly larger than those in other $R{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$ ($R$ = rare earth elements) kagome compounds. Band structure calculations show several band crossings,…

Motivated by recent experimental results for ${\mathrm{GdRu}}_{2}{\mathrm{Si}}_{2}$ [Khanh et al., Nat. Nanotechnol. 15, 444 (2020)], in which a nanometric square skyrmion lattice was observed, we propose a simple analytical mean-field description of the high-temperature part of the phase diagram of centrosymmetric tetragonal frustrated antiferromagnets with dipolar interaction in the external magnetic field. Dipolar forces provide momentum-dependent biaxial anisotropy in reciprocal space. It is shown that in a tetragonal lattice, in the large part of the Brillouin zone, for mutually perpendicular modulation vectors in the $ab$ plane this anisotropy has mutually perpendicular easy axes and collinear middle axes, which leads to double-$Q$ modulated spin structure stabilization. In the large part of its stability region, the latter turns out to be a square skyrmion lattice with a topological charge of $\ifmmode\pm\else\textpm\fi{}1$ per magnetic unit cell, which is determined by the frustrated exchange coupling and thus nanometer sized. Easy and middle axes can be swapped in the…

We consider a central-spin battery where ${N}_{b}$ central spins serve as battery cells and ${N}_{c}$ bath spins serve as charging units. It is shown that the energy stored in the battery that can be extractable is quantified by the ergotropy, and that battery-charger entanglement is quantified via the Von Neumann entropy. By using an exact approach to a one-cell and two-cell battery, our analytical results suggest that, during the charging process, the extractable work slowly increases before the battery-charger entanglement reaches its maximum and then it will rapidly increase when the entanglement begins to decrease. In particular, we rigorously show that there is an inverse relationship between the extractable work and the entanglement at the end of the charging process. Moreover, we investigate different approaches to realize optimal work extraction without wasted energy. Among them a central-spin battery with an unpolarized Dicke state as the charger possesses a universal charging time $\ensuremath{\propto}1/{N}_{c}$, large extractable work and $\sqrt{{N}_{c}}$-improvement of…

The discovery of superconductivity in infinite-layer nickelate thin films has produced fervent theoretical research about the doping evolution of their electronic structure. Here, by means of x-ray spectroscopy and atomic multiplet calculations, the authors show that doped holes are mainly introduced in Ni sites in a spin-singlet configuration. The dominant role of the Ni 3${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ band implies that infinite-layer nickelates are likely a strongly correlated electronic system, reminiscent of their cuprate siblings.

MnBi${}_{2}$Te${}_{4}$ and MnSb${}_{2}$Te${}_{4}$ are the first examples of antiferromagnetic topological insulators. However, the presence of magnetic defects in the form of antisite mixing between Mn and Bi or Sb introduces defect-driven ferrimagnetism. The application of a large magnetic field of ~50 Tesla aligns the magnetic defects with the main Mn layer, allowing for estimates of the defect concentration and the strength of the antiferromagnetic coupling (${J}^{\ensuremath{'}}$) between Mn defects and the main layer, which is by far the largest magnetic coupling in the system.

We investigate the proximity-induced spin-orbit coupling in heterostructures of twisted graphene and monolayers of transition metal dichalcogenides (TMDCs) ${\mathrm{MoS}}_{2}, {\mathrm{WS}}_{2}, {\mathrm{MoSe}}_{2}$, and ${\mathrm{WSe}}_{2}$ from first principles. We identify strain, which is necessary to define commensurate supercells, as the key factor affecting the band offsets and thus magnitudes of the proximity couplings. We establish that for biaxially strained graphene the band offsets between the Dirac point and conduction (valence) TMDC bands vary linearly with strain, regardless of the twist angle. This relation allows us to identify the apparent zero-strain band offsets and find a compensating transverse electric field correcting for the strain. The resulting corrected band structure is then fitted around the Dirac point to an established spin-orbit Hamiltonian. This procedure yields the dominant, valley-Zeeman, and Rashba spin-orbit couplings. The magnitudes of these couplings do not vary much with the twist angle, although the valley-Zeeman coupling vanishes for…

We study disorder effects in a two-dimensional system with chiral symmetry and find that disorder can induce a quadrupole topological insulating phase (a higher-order topological phase with quadrupole moments) from a topologically trivial phase. Their topological properties manifest in a topological invariant defined based on effective boundary Hamiltonians, the quadrupole moment, and zero-energy corner modes. We find gapped and gapless topological phases and a Griffiths regime. In the gapless topological phase, all the states are localized, while in the Griffiths regime, the states at zero energy become multifractal. We further apply the self-consistent Born approximation to show that the induced topological phase arises from disorder renormalized masses. We finally introduce a practical experimental scheme with topoelectrical circuits where the predicted topological phenomena can be observed by impedance measurements. Our work opens the door to studying higher-order topological Anderson insulators and their localization properties.

Due to a strong Coulomb interaction, excitons dominate the excitation kinetics in two-dimensional (2D) materials. While Coulomb scattering between electrons has been well studied, the interaction of excitons is more challenging and remains to be explored. As neutral composite bosons consisting of electrons and holes, excitons show nontrivial scattering dynamics. Here, we study exciton-exciton interaction in transition-metal dichalcogenides and related van der Waals heterostructures on microscopic footing. We demonstrate that the crucial criterion for efficient scattering is a large electron/hole mass asymmetry, giving rise to internal charge inhomogeneities of excitons and emphasizing their cobosonic substructure. Furthermore, both exchange and direct exciton-exciton interactions are boosted by enhanced exciton Bohr radii. We also predict an unexpected temperature dependence that is usually associated with phonon-driven scattering, and we reveal an orders of magnitude stronger interaction of interlayer excitons due to their permanent dipole moment. The developed approach can be…

We report the observation of anomalous Hall resistivity in single crystals of ${\mathrm{EuAl}}_{4}$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at ${T}_{\mathrm{N}}\ensuremath{\sim}15.6\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{CDW}}\ensuremath{\sim}140\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, ${\mathrm{EuAl}}_{4}$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear humplike anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering different scenarios, we conclude that such a humplike feature is most likely a manifestation of the topological Hall effect, normally occurring in noncentrosymmetric materials known to host nontrivial topological spin textures. In view of this, ${\mathrm{EuAl}}_{4}$ would represent a rare case where the topological Hall effect not only arises in a centrosymmetric…

The connection of novel electromagnetic responses to Weyl nodes in topological semimetals is intriguing but difficult to establish in experiments. Here, the authors discover CeAlSi to be a new ferromagnetic Weyl semimetal by combining first-principles calculations with various experimental techniques. These reveal a new loop Hall effect that is induced purely by the proximity of the material's Fermi level to its Weyl nodes. The loop Hall effect can potentially result from topological Fermi arcs located on magnetic domain walls.

We theoretically investigate multiple-$Q$ spin textures, which are composed of superpositions of spin density waves with different wave numbers, for an effective spin model of centrosymmetric itinerant magnets. Our focus is on the interplay between biquadratic interactions arising from the spin-charge coupling and magnetic anisotropy caused by the spin-orbit coupling. Taking into account two types of the magnetic anisotropy, single-ion anisotropy and bond-dependent anisotropy, we elucidate magnetic phase diagrams for an archetypal triangular-lattice system in the absence and presence of an external magnetic field. In the case of the single-ion anisotropy, we find a plethora of multiple-$Q$ instabilities depending on the strength and the sign of the anisotropy (easy plane or easy axis), including a noncoplanar triple-$Q$ state regarded as a skyrmion crystal with topological number of two, and coplanar and noncoplanar double-$Q$ states. In an external magnetic field, we find that another noncoplanar triple-$Q$ state, a skyrmion crystal with topological number of one, is stabilized by…

We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of two-dimensional topologically ordered phases of matter. The ground states of these models can be thought of as superpositions of different ``string-net configurations,'' where each string-net configuration is a trivalent graph with labeled edges, drawn in the $xy$ plane. What makes this construction more general than the original string-net construction is that, unlike the original construction, tetrahedral reflection symmetry is not assumed, nor is it assumed that the ground-state wave function $\mathrm{\ensuremath{\Phi}}$ is ``isotropic'': i.e., in the generalized setup, two string-net configurations ${X}_{1},{X}_{2}$ that can be continuously deformed into one another can have different ground-state amplitudes $\mathrm{\ensuremath{\Phi}}({X}_{1})\ensuremath{\ne}\mathrm{\ensuremath{\Phi}}({X}_{2})$. As a result, generalized string-net models can realize topological phases that are inaccessible to the original construction. In this paper, we provide a…

``Magic'' is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the ${\mathbb{Z}}_{3}$ Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the $q=3$ ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the three-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer and constrain tensor network models of AdS-CFT.