Usually, robust invariants in physics take discrete values for the reason of topology, such as integers or fractions in the integer or fractional quantum Hall effect. Here, we show theoretically that the valley Chern number can be responsible for continuous invariants which are insensitive to most parameters, but continuously tunable by a critical parameter. We numerically calculate the ac charge current generated by a periodically varying strain in the $\alpha \text{−}{T}_3$ lattice where the valley Chern number is continuously tunable by $\alpha$. The periodically varying strain induces a valley-opposite ac pseudoelectric field which leads to a pure valley current in the longitudinal direction, and a charge current in the transverse direction via the topological valley Hall effect. The corresponding Hall pseudoconductance at the low-frequency limit equals the valley Chern number in gapped $\alpha \text{−}{T}_3$ lattices and is robust against long-range disorders. This finding advances the understanding of the relation between invariants and topology, and also provides a scheme to test the quantum valley Hall effect.

We theoretically investigate the dynamics of wave packets in a generic, non-Hermitian, optically anisotropic exciton-polariton system that exhibits degeneracies of its complex-valued eigenenergies in the form of pairs of exceptional points in momentum space. We observe the self-acceleration and reshaping of the wave packets governed by their eigenenergies. We further find that the exciton-polariton wave packets tend to evolve into the eigenstate with the smaller decay rate, then propagate towards the minima of the decay rates in momentum space, resulting in directional transport in real space. We also describe the formation of pseudospin topological defects on the imaginary Fermi arc, where the decay rates of the two eigenstates coincide in momentum space. These effects of non-Hermiticity on the dynamics of exciton polaritons can be observed experimentally in a microcavity with optically anisotropic cavity spacer or exciton-hosting materials. This rich non-Hermitian dynamics can also be observed in other two-dimensional, two-band systems with similar complex band structures such as purely photonic planar microcavities, liquid crystal cavities, and non-Hermitian photonic lattices.

Two-dimensional second-order topological insulators are characterized by the presence of topologically protected zero-energy bound states localized at the corners of a flake. In this paper we theoretically study the occurrence and features of such corner states inside flakes in the shape of a convex polygon. We consider two different models, both in Cartan class IIIA—the first obeying inversion symmetry and the other obeying a combined $\pi /4$ rotation symmetry and time-reversal symmetry (${\widehat{C}}_4^z\widehat{T}$). By using an analytical effective model of an edge corresponding to a massive Dirac fermion, we determine the presence of a corner state between two given edges by studying the sign of their induced masses and derive general rules for flakes in the shape of a convex polygon. In particular, we find that the number of corner states in a flake is always two in the first model, while in the second model there are either 0, 2, or 4. To corroborate our findings, we focus on flakes of specific shapes (a triangle and a square) and use a numerical finite-difference approach to determine the features of the corner states in terms of their probability density. In the case of a triangular flake, we can change the position of corner states by rotating the flake in the first model, while in the second model we can also change their number. Remarkably, when the induced mass of an edge is zero the corresponding corner state becomes delocalized along the edge. In the case of a square flake and the model with ${\widehat{C}}_4^z\widehat{T}$ symmetry, there is an orientation of the flake with respect to the crystal axes, for which the corner states extend along the whole perimeter of the square.

Herein, we investigate the impact of all electron and phonon scattering mechanisms on the electrical and thermal transport properties of the monolayer and bilayer transition-metal dichalcogenide ${\mathrm{WS}}_2$. We used the Boltzmann transport equation under the relaxation-time approximation to calculate both the electron and phonon transport properties. Due to multiple valleys near the Fermi energy level, intervalley scattering is seen as the prominent scattering mechanism that critically impacts the electrical transport properties in both of these materials. The power factor reduces by $93\%$ and $83\%$ for monolayer and bilayer ${\mathrm{WS}}_2$, respectively, due to intervalley scattering leading to almost equal values for both materials at room temperature. Earlier theoretical reports on monolayer ${\mathrm{WS}}_2$ overestimated the experimentally observed lattice thermal conductivity values. Experimental observations suggest that when monolayer and bilayer ${\mathrm{WS}}_2$ is formed, defects might be present in these systems, affecting phonon transport. We found that defect scattering significantly contributes to phonon scattering when the relative sulfur vacancy concentration exceeds 0.01 for both monolayer and bilayer ${\mathrm{WS}}_2$, resulting in a remarkable $99\%$ agreement with experimental values. A high $ZT\sim 3$ is attained for monolayer ${\mathrm{WS}}_2$ as compared to $ZT\sim 2$ for bilayer ${\mathrm{WS}}_2$ at 800 K because of the higher thermal conductivity of the bilayer due to elevated group velocities of its optical-phonon modes. This work presents a deep insight into the scattering mechanisms controlling the thermoelectric performance of monolayer and bilayer ${\mathrm{WS}}_2$.

The coupling of the lattice, charge, spin, and valley degrees of freedom is a fundamental scientific issue in spintronics and valleytronics. The nonvolatile electric field control of the spin and valley polarization has important potential applications for the development of next-generation ultrahigh speed processors and memories. However, the efficient electrical control of spin and valley degrees of freedom remains a challenge due to the weak coupling between them and external electric fields. Here we report the strong coupling between the spin, valley, and electric polarization in a two- dimensional multiferroic material ${\mathrm{Nb}}_3{\mathrm{I}}_8$ with a breathing Kagome lattice. The ferroelectric transition controls the local sublattice symmetry in the ferroelectric monolayer ${\mathrm{Nb}}_3{\mathrm{I}}_8$ and thus results in the sublattice-dependent Berry curvature switching in the momentum space, where the sign reversal of the Berry curvature can be controlled by reversing the ferroelectric polarization. More importantly, for the ferroelectric bilayer ${\mathrm{Nb}}_3{\mathrm{I}}_8$ with A-type antiferromagnetic coupling, the spin-valley-layer polarized anomalous Hall effect can be realized by coupling the electric polarization to spin, valley and layer degrees of freedom. So, the electrically driven the ferroelectric transition in a ${\mathrm{Nb}}_3{\mathrm{I}}_8$ bilayer can be applied to design nonvolatile memory and switch based on the spin, valley and layer dependent Berry curvature. Our findings open an avenue towards exploring the coupling between the ferroelectricity, ferromagnetism, and ferrovalley in the hidden local sublattice symmetry and demonstrate a nonvolatile electric-field controlled anomalous Hall effect in the atomically thin limit.

Using ab initio band structure and $\mathrm{DFT}+\mathrm{dynamical}$ mean-field theory methods we examine the effects of electron-electron interactions on the normal state electronic structure, Fermi surface, and magnetic correlations of the recently discovered double-layer perovskite superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under pressure. Our results suggest the formation of a negative charge transfer mixed-valence state with the Ni valence close to $1.75+$. We find a remarkable orbital-selective renormalization of the Ni $3d$ bands, with $m^{*}/m\sim 3$ and 2.3 for the Ni $3z^2\text{−}{r}^2$ and $x^2\text{−}{y}^2$ orbitals, respectively, in agreement with experimental estimates. Our results for the $k$-dependent spectral functions and Fermi surfaces show significant incoherence of the Ni $3z^2\text{−}{r}^2$ states, implying the proximity of the Ni $3d$ states to orbital-dependent localization. Based on our analysis of the static magnetic susceptibility, we propose the possible formation of the spin and charge (or bond) density wave stripe states in high-pressure ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$.

Motivated by the recent studies of intrinsic local moments and Kondo-driven phases in magic-angle twisted bilayer graphene, we investigate the renormalization of Kondo coupling ($J_K$) and the competing Hund's rule interaction ($J$) in the low-energy limit. Specifically, we consider a surrogate single-impurity generalized Kondo model and employ the poor man's scaling approach. The scale dependent $J_K$ and $J$ are derived analytically within the one-loop poor man's scaling approach, and the Kondo temperature ($T_K$) and the characteristic Hund's rule coupling ($J^{*}$, defined by the renormalized value of $J$ at some small finite-energy scale) are estimated over a wide range of filling factors. We find that $T_K$ depends strongly on the filling factors as well as the value of $J_K$. Slightly doping away from integer fillings and/or increasing $J_K$ may substantially enhance $T_K$ in the parameter regime relevant to experiments. $J^{*}$ is always reduced from the bare value of $J$, but the filling-factor dependence is not as significant as it is for $T_K$. Our results suggest that it is essential to incorporate the renormalization of $J_K$ and $J$ in the many-body calculations, and Kondo screening should occur for a wide range of fractional fillings in magic-angle twisted bilayer graphene, implying the existence of Kondo-driven correlated metallic phases. We also point out that the observation of distinct phases at integer fillings in different samples may be due to the variation of $J_K$ in addition to disorder and strain in the experiments.

The $GW$ approximation is a well-established method for calculating ionization potentials and electron affinities in solids and molecules. For numerous years, obtaining self-consistent $GW$ total energies in solids has been a challenging objective that is not accomplished yet. However, it was shown recently that the linearized $GW$ density matrix permits a reliable prediction of the self-consistent $GW$ total energy for molecules [F. Bruneval, M. Rodríguez-Mayorga, P. Rinke, and M. Dvorak, J. Chem. Theory Comput. 17, 2126 (2021)] for which self-consistent $GW$ energies are available. Here we implement, test, and benchmark the linearized $GW$ density matrix for several solids. We focus on the total energy, lattice constant, and bulk modulus obtained from the $GW$ density matrix and compare our findings to more traditional results obtained within the random-phase approximation (RPA). We conclude on the improved stability of the total energy obtained from the linearized $GW$ density matrix with respect to the mean-field starting point. We bring compelling clues that the RPA and the $GW$ density matrix total energies are certainly close to the self-consistent $GW$ total energy in solids if we use hybrid functionals with enriched exchange as a starting point.

Realizing sizable Zeeman spin splittings (ZSSs) with persistent spin textures (PSTs) in semiconductors is promising for the design of high-performance spintronic devices. The ZSSs of this kind have long been known in ferromagnetic semiconductors, while whether antiferromagnetic semiconductors—much more plenteous than ferromagnetic semiconductors—can host an analogous effect remains elusive. Here, we show that such ZSSs can occur in antiferromagnetic semiconductors. By symmetry analysis, we find 12 magnetic point groups that can host ZSSs and PSTs, providing theoretical guidelines for screening the corresponding antiferromagnets. Our first-principles calculations further confirm ${\mathrm{CaTcO}}_3$ as an antiferromagnetic semiconductor showcasing ZSSs that are sizable (tens of meV), possibly controllable by a magnetic field, and accompanied with PSTs. Our work thus may open a route towards the application of antiferromagnetic semiconductors in spintronics.

Standard field theoretic formulations of composite fermion theories for the anomalous metals that form at or near even-denominator filling fractions of the lowest Landau level do not possess Galilean invariance. To restore Galilean symmetry, these theories must be supplemented by correction terms. We study the effect of the leading correction term, known as the dipole term, in the Dirac composite fermion theory (a theory that consists of a Dirac fermion coupled to an Abelian Chern-Simons gauge field) on quantum oscillations in the electrical resistivity due to a periodic scalar potential about even-denominator filling fractions. We find the dipole term to be insufficient to resolve the systematic discrepancy, discovered in Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)], between the locations of the oscillation minima predicted by Dirac composite fermion theory without Galilean invariance and those observed in experiment. Further, in contrast to Hossain et al., [Phys. Rev. B 100, 041112(R) (2019)], we find the quantum oscillations about the half-filled and quarter-filled lowest Landau level to have qualitatively similar behavior. This analysis uses a mean-field approximation, in which gauge field fluctuations are neglected. Based on this and previous analyses, we speculate that the discrepancy with experiment may be an indirect signature of the effect of gauge field fluctuations in composite fermion theory.

The Yb-terminated and Bi-terminated (111) surface electronic structure of topological Kondo semimetal YbPtBi is investigated using both density-functional-theory (DFT) -based calculations and angle-resolved photoemission spectroscopy (ARPES). The cleavage plane is found to be between Yb-layers and Bi-layers in both experiment and theory, and the broken inversion symmetry ensures the Yb-terminated surface does not mix with the Bi-terminated surface. The ARPES results at the Bi-terminated surface are similar to those reported for YPtBi or LuPtBi, and they can be well explained using DFT calculations assuming trivalent Yb atoms. In contrast, at the Yb-terminated surface, a trivalent to divalent transition and reduced hybridization with conduction electrons for the topmost Yb atoms are observed, as a result of reduced bonding with Bi-atoms. In addition, the Fermi arc features induced by the triply degenerate-points, which are missing at the Bi-terminated surface, can be identified at the Yb-terminated surface. Our study demonstrates unambiguously the reconstruction of surface electronic structure due to the valence transition of the lanthanide element in a Kondo lattice system.

The equilibrium atomic configuration and electronic structure of the (001) surface of the IV-VI semiconductors PbTe, PbSe, SnTe, and SnSe are studied using density functional theory methods. At the surfaces of all these compounds, the displacements of ions from their perfect lattice sites reveal two features characteristic of rocksalt crystals. First, the ionic displacements occur only along the direction perpendicular to the surface, and they exhibit a rumpling effect; that is, the vertical shifts of cations and anions differ. Second, the interlayer spacing of the first few monolayers at the surface oscillates. Our results are in good agreement with previous x-ray experimental data and theoretical results where available. They are also consistent with the presence of two {110} mirror planes at the (001) surface of the rocksalt. One the other hand, experiments preformed for the topological ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}$ alloy indicate breaking of the mirror symmetry due to a large 0.3 Å relative displacement of the cation and anion sublattices at the surface, which induces the opening of the gap of the Dirac cones. Our results for ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}$, including simulated scanning tunneling microscopy images, are in contradiction to these findings since surface reconstructions with broken symmetry are never ground state configurations. The impact of the theoretically determined surface configurations and of the chemical disorder on the surface states is analyzed.

Topological lattice systems combined with nonlinearity and non-Hermiticity can give rise to novel solitons, whose exceptional properties are demonstrated in both unique quench dynamics and topological boundary states. Especially, we focus on an Aubry-André-Harper-type lattice with nonlinear hopping and demonstrate its ability to host distinct topological soliton states in the short-run regime and intensity amplification in the long-run regime. Actually, these topological soliton states arise from the competition between nonreciprocal hopping and on-site modulation, resulting in an alternating dominance between the skin effect and Anderson localization. Notably, we find that the site intensities near the edge of the lattice are strongly enhanced in the long-run regime due to the combination of nonlinearity and the non-Hermitian skin effect, which distinguishes it from the previously studied nonlinear lattices. To reveal the intensity amplification effect in more detail, we explore a time-dependent intensification factor and find that the amplification effect is more pronounced in the long-run regime. Our results demonstrate the promising possibilities of combining nonlinearity and non-Hermiticity in topological lattice systems to develop novel solitons with exceptional properties.

The frozen-phonon method, used to calculate electron-phonon coupling effects, requires calculations of the investigated structure using atomic coordinates displaced according to certain phonon eigenmodes. The process of “freezing in” the specific phonon can bring electronic eigenstates that are energetically close in energy into an anticrossing. This electronic anticrossing effect is, however, unrelated to electron-phonon coupling and needs to be removed if the eigenvalues are used to obtain electron-phonon coupling. We present a procedure for how to deal with these problematic anticrossing situations and apply it to the band gap zero-point motion renormalization of 16 diamondoids and urotropine using different exchange correlation functionals. From the 17 structures, 5 require the correction presented here, leading to a modification of the zero-point renormalization between 4% and 185%. We find gap renormalizations in the range of $-150$ to $-370\mathrm{meV}$ for diamondoids but only around $-40\mathrm{meV}$ for urotropine.

Among the many two-dimensional materials, germanene and Janus MoSSe have received considerable attention due to their novel electrical and optical properties. We anticipate that the heterojunction formed by germanene and MoSSe will exhibit exceptional properties and immense potential for applications in optoelectronic devices. Here, germanene/MoSSe vertical heterojunctions (VHJs) have been constructed by stacking the twisted bilayers, and their electronic properties, structural stability, and interface characteristics are calculated by applying the density functional theory. Meanwhile, the ab initio molecular dynamics simulation shows that the germanene/MoSSe VHJs are thermodynamically stable, and the germanene/SeMoS (Ge/SeMoS) VHJ is more energetically stable than germanene/SMoSe (Ge/SMoSe) VHJ. The Schottky contact is formed in the germanene/MoSSe heterojunctions. In particular, the Schottky barrier of Ge/SeMoS VHJ can be modulated by the electric field, resulting in the change of Schottky contact from p-type to n-type, even to Ohmic contact. However, the change in interlayer distance also can lead to variation of the Schottky barrier, but the contact type is unchanged. In addition, the Ge/SeMoS VHJ exhibits an excellent light absorption performance. Therefore, the Ge/SeMoS VHJ is a potential material for the design and fabrication of optoelectronic devices.

Silicon/silicon-germanium heterostructures have many important advantages for hosting spin qubits. However, controlling the valley splitting (the energy splitting between the two low-lying conduction-band valleys) remains a critical challenge for ensuring qubit reliability. Broad distributions of valley splittings are commonplace, even among quantum dots formed on the same chip. In this work, we theoretically explore the interplay between quantum-well imperfections that suppress the valley splitting and cause variability, such as broadened interfaces and atomic steps at the interface, while self-consistently accounting for germanium concentration fluctuations. We consider both conventional and unconventional approaches for controlling the valley splitting and present concrete strategies for implementing them. Our results provide a clear path for achieving qubit uniformity in a scalable silicon quantum computer.

Lattice and electronic states of thin FeSe films on ${\mathrm{LaAlO}}_3$ substrates are investigated in the vicinity of the nematic phase transition. No evidence of a structural phase transition is found by x-ray diffraction below $T^{*}\sim 90$ K, while results obtained from a resistivity measurement and angle-resolved photoemission spectroscopy clearly show the appearance of a nematic state. These results indicate the formation of a pure nematic state in the iron-based superconductor and provide conclusive evidence that the nematic state originates from the electronic degrees of freedom. This pure nematicity in the thin film implies the difference in the electron-lattice interaction from bulk FeSe crystals. FeSe films provide valuable playgrounds for observing the pure response of “bare” electron systems free from the electron-lattice interaction, and should make an important contribution to investigate nematicity and its relationship with superconductivity.

Andreev reflection is widely used in practical applications, such as on chip coolers and thermometers at very low temperatures, as well as a powerful tool in experiments with superconductors and fermionic superfluid ${}^3\mathrm{He}\text{−}B$, where it has been used to study quantum turbulence. Although superfluid ${}^4\mathrm{He}$ is the bosonic superfluid, its dispersion relation displays features similar to that of ${}^3\mathrm{He}\text{−}B$, especially at high pressures approaching the solidification pressure, where the roton energy gap vanishes. We discuss an analog of Andreev reflection in superfluid ${}^4\mathrm{He}$ and suggest experiments of using it for detection of quantum turbulence.

The magnetic structure of ${\mathrm{RuO}}_2$ and the Ru atomic configuration are unknown. A magnetic structure is inferred by confronting measured and calculated Bragg diffraction patterns and adjusting the latter to achieve satisfactory agreement. An accepted pattern, a magnetic symmetry, includes symmetry of sites occupied by the magnetic ions. As a realistic starting point, we provide diffraction patterns for a magnetic symmetry of ${\mathrm{RuO}}_2$, a descendent of the tetragonal parent structure, which accommodates a departure of Ru axial dipoles from the crystal c axis. A chiral signal and piezomagnetic effect are permitted, and a linear magnetoelectric effect forbidden. Features of the neutron diffraction pattern test the nonrelativistic requirement of altermagnetism, and we scrutinize published room-temperature data. Specifically, one Bragg point is consistent with Ru orbital angular momentum and magnetic quadrupole both zero, and the latter result is not expected from nonrelativistic altermagnetism. Azimuthal angle scans in resonant x-ray diffraction are sensitive to the Ru site symmetry and the atomic configuration. Acid tests of the studied magnetic symmetry include a chiral signature and null intensity for unrotated photon polarization.