Weyl semimetals are promising quantum materials with gapless electronic excitations and distinctive topological properties. In this paper, we explore the high harmonic generation in three-dimensional Weyl semimetal ${\mathrm{WP}}_2$ based on semiconductor Bloch equations in the Wannier gauge. Selection rules and mechanisms for harmonic generation driven by a single pulse in different polarization state are discussed. We also find that the harmonic yield exhibits an oscillating increase with the laser intensity due to the quantum interference between long and short trajectories. Moreover, the results also reveal an anomalous ellipticity dependence, with the total harmonic yield first decreasing and then increasing. Our simulations capture the complex band structure and dipole moments, providing valuable insights for strong-field-driven electron dynamics in Weyl semimetals.

Quantum anomalous Hall effect (QAHE) is significant for future low-power electronics devices, where a main challenge is realizing QAHE at high temperatures. In this work, based on experimentally reported two-dimensional (2D) germanene and magnetic semiconductors ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ and ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$, and the first-principles calculations, germanene/magnetic semiconductor heterostructures are investigated. Topologically nontrivial edge states and quantized anomalous Hall conductance are demonstrated. It is shown that the QAHE temperature can be enhanced to approximately 62 K in germanene/monolayer (ML) ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ with 2.1% tensile strain, 64 K in germanene/bilayer (BL) ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ with 1.4% tensile strain, and 50 K in germanene/ML ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$ with 1.3% tensile strain. With increasing tensile strain of these heterostructures, the band gap decreases and the Curie temperature rises, and the highest temperature of QAHE is obtained. Since these 2D materials were discovered in recent experiments, our results provide promising materials for achieving high-temperature QAHE.

We derive asymptotically exact formulas for the equilibrium magnetic stripe period in ultrathin films with out-of-plane anisotropy that include the full domain wall magnetic dipolar energy. Starting with the reduced two-dimensional micromagnetic model valid for thin films, we obtain the leading-order approximation for the energy per unit volume in the vanishing film thickness limit in the case of Bloch and Néel wall rotations. Its minimization in the stripe period leads to an analytical expression for the equilibrium period with a prefactor proportional to the Bloch wall width. The constant in the prefactor, which is related to the long-range dipolar interactions, is carefully evaluated. This results in a remarkable agreement of the stripe domain energy density and stripe period predicted by our analytical formulas with micromagnetic simulations. Our formula can be used to accurately deduce magnetic parameters from the experimental measurements of the stripe period and to systematically predict the equilibrium stripe periods in ultrathin films.

The emergent inductor, which is a concept of an inductor employing quantum mechanics on helical magnets, has been studied actively from both theoretical and experimental aspects. Interestingly, finite inductance has been observed not only in spiral magnetic phases but also across various other magnetic phases, although the underlying mechanism behind emergent inductance in nonhelical magnets remains unresolved. In this paper, we broaden the concept of emergent inductance to encompass nonhelical magnets and establish a comprehensive formalism of the emergent inductance generated by magnetization dynamics. Using a diagrammatic approach, we derive the linear response of current density mediated by magnetization dynamics and formulate impedance and inductance for general magnetic materials. We reveal that the emergent inductance is composed of two distinct components, each contributing positively or negatively. Notably, the positive inductance arises from Ohmic dissipation including the effect of the emergent electric field (Berry phase in real space) while the negative inductance arises from the polarization of itinerant electrons (Berry curvature in $k-t$ space). We also apply the present method to quasi-1D models and show the numerical results of the inductance, the spin dynamics, the impedance, and the $Q$ value.

Doping nonmagnetic semiconductors with magnetic impurities is a feasible way to obtain diluted magnetic semiconductors (DMSs). It is generally accepted that for the most extensively studied DMS, (Ga, Mn)As, its highest Curie temperature ${\mathrm{T}}_{\text{C}}$ was achieved at 200 K with a Mn concentration of approximately 16% in experiments. A recent experiment reported record-breaking high electron and hole mobilities in the semiconductor BAs [Science 377, 437 (2022)]. Since BAs shares the same zinc-blende structure with GaAs, here we predict four DMSs (B, Mn)$X$ ($X=\mathrm{N}$, P, As, Sb) by density functional theory calculations. Using a rescaling method to diminish the overestimation of Curie temperature, our results indicate that a significantly higher ${\mathrm{T}}_{\text{C}}$ in the range of 467 to 485 K for (B, Mn)As with a Mn concentration of around 15.6% and even higher ${\mathrm{T}}_{\text{C}}$ values above the room temperature for (B, Mn)P with a Mn concentration exceeding 9.4%. Furthermore, using the method of ab initio scattering and transport (amset) with first-principles material parameters, we have predicted a hole mobility of 48.9 ${\mathrm{cm}}^{\text{2}}{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at 300 K for (B, Mn)As with the hole concentration of about $n_{\text{h}}=$ 4.2 $\times {10}^{\text{19}}{\mathrm{cm}}^{-3}$, which is about two times larger than the hole mobility at 300 K in the calculations for (Ga, Mn)As. The hole mobility of (B, Mn)As can be enhanced faster than that of (Ga, Mn)As when the hole concentration is decreased. Our findings predict the emergence of a new family of DMS, (B, Mn)$X$, and are expected to stimulate both experimental and theoretical studies of the DMS with possible high $T_{\text{C}}$.

The kagome metal $\mathrm{Sc}{\mathrm{V}}_6\mathrm{S}{\mathrm{n}}_6$ displays a variety of exotic electronic states, including charge density wave (CDW) order, nontrivial topological states, Van Hove singularity (VHS), and electronic nematic order, which strongly correlate with the V kagome lattice. We unveil herein that the partial substitution of V by Mn in the kagome lattice $\mathrm{Sc}{\mathrm{V}}_6\mathrm{S}{\mathrm{n}}_6$ results in multiple magnetic transitions including the long-range magnetic order above room temperature with the transition temperature of $\sim 320$ K. In addition, the Mn substitution suppresses the CDW order and the VHSs, while leading to unconventional anomalous and other anomalous Hall effects caused by both intrinsic Berry curvature and extrinsic skew scattering. Our work provides valuable insights into the correlation between magnetism and the electronic band structure of the kagome lattice, which is instructive for future research on this system.

We investigate the robustness of virtual topological states—topological phases away from the Fermi energy—against the electron-electron interaction and band filling. As a case study, we employ a realistic model to investigate the properties of vacancy-driven topological phases in transition metal dichalcogenides (TMDs) and establish a connection between the degree of localization of topological wave functions, the vacancy density, and the electron-electron interaction strength with the topological phase robustness. We demonstrate that electron-electron interactions play a crucial role in degrading topological phases thereby determining the validity of single-particle approximations for topological insulator phases. Our findings can be naturally extended to virtual topological phases of a wide range of materials.

Two-dimensional topological insulators (2D TIs) exhibit a characteristic Landau level spectrum in which a pair of zeroth Landau levels disperse oppositely as a result of band inversion. The two Landau levels cross at a critical magnetic field, marking the transition to a trivial phase. Experiments sometimes show an avoided crossing, signifying hybridization (mixing) of the zeroth Landau level wave functions. Here, we theoretically identify the essential symmetries that protect against zeroth Landau level mixing, using thin films of cadmium arsenide (${\mathrm{Cd}}_3{\mathrm{As}}_2$), a prototype 2D TI, as an example. We show that avoided crossings that result from zeroth Landau level mixing indicate the breaking of the four-fold rotational symmetry, inherent to bulk ${\mathrm{Cd}}_3{\mathrm{As}}_2$. We discuss potential reasons for the symmetry breaking, including the formation of novel correlated states, and the relevance of our results to other materials.

Rare-earth trihydride ($R{\mathrm{H}}_3$) compounds exhibit intriguing coupled electronic and structural properties as a function of doping, hydrogen vacancies, and thermodynamic conditions. Theoretical studies of these materials typically rely on density functional theory (DFT), including the use of small supercells that may underestimate strong correlation effects and structural distortions which in turn may influence their metallicity. Here, we elucidate the roles of lattice distortions and correlation effects on the electronic properties of pristine and doped $R{\mathrm{H}}_3$ compounds by adopting $\mathrm{DFT}+\mathrm{U}$ and quantum Monte Carlo (QMC) methods. Linear-response constrained DFT (LR-cDFT) methods find Hubbard U $\approx 2$ eV for $R_d$ orbitals and $\mathrm{U}\approx 6$ eV for ${\mathrm{H}}_s/{\mathrm{N}}_p/{\mathrm{O}}_p$ orbitals. The small U on ${\mathrm{Lu}}_d$ orbitals is consistent with QMC calculations on ${\mathrm{LuH}}_3$ and ${\mathrm{LuH}}_{2.875}{\mathrm{N}}_{0.125}$. In pure face-centered-cubic (FCC) $R{\mathrm{H}}_3$ ($R=\mathrm{Lu},\mathrm{Y}$) compounds, neither DFT nor $\mathrm{DFT}+\mathrm{U}$ with the self-consistently determined U is enough to create a band gap, however a supercell with hydrogen distortions creates a small gap whose magnitude increases when performing $\mathrm{DFT}+\mathrm{U}$ with self-consistently determined U values. Correlation effects, in turn, have a moderate influence on the coupled structural and electronic properties of doped $R{\mathrm{H}}_3$ compounds and may be important when considering the competition between structural distortions and superconductivity.

Symmetry protected topology has been studied extensively since the mid-2000s, but the topology protected by spin symmetry has just begun to be studied. In this work, based on spin-symmetry analysis, we propose that a class of Weyl nodal line metals is protected by the spin symmetry. Then, by the first-principles electronic structure calculations, we predict that both altermagnetic ${\mathrm{Nb}}_2{\mathrm{FeB}}_2$ and ${\mathrm{Ta}}_2{\mathrm{FeB}}_2$ are node-network metals protected by the spin symmetry. Moreover, both altermagnetic ${\mathrm{Nb}}_2{\mathrm{FeB}}_2$ and ${\mathrm{Ta}}_2{\mathrm{FeB}}_2$ have nodal rings protected by the mirror symmetry and Dirac points protected by nonsymmorphic spin symmetry. Furthermore, both altermagnetic ${\mathrm{Nb}}_2{\mathrm{FeB}}_2$ and ${\mathrm{Ta}}_2{\mathrm{FeB}}_2$ transform node-network metal phase into Weyl metal phase when considering spin-orbit coupling. Therefore, our work not only enriches the topological phases protected by spin symmetry but also provides an excellent material platform to investigate the exotic physical properties of multiple altermagnetic topological metal phases in experiment.

The Kohn-Sham density functional method for the fractional quantum Hall (FQH) effect has recently been developed by mapping the strongly interacting electrons into an auxiliary system of weakly interacting composite fermions (CFs) that experience a density-dependent effective magnetic field. This approach has been successfully applied to explore the edge reconstruction, fractional charge, and fractional braiding statistics of quasiparticle excitations. In this work, we investigate composite fermion excitons in the bulk of the disk geometry. By varying the separation of the quasiparticle-quasihole pairs and calculating their energy, we compare the dispersion of the exciton with results from other numerical methods, such as exact diagonalization (ED) and Monte Carlo (MC) simulation. Furthermore, from the spectral function calculation, we identify chiral “graviton” excitations: a spin $-2$ mode for the particle-like Laughlin state and a spin 2 mode for the hole-like Laughlin state. This method can be extended to construct neutral collective excitations for other fractional quantum Hall states in disk geometry.

We investigate the transport properties of the Holstein model using the numerically exact quantum typicality (QT) approach. Roughly speaking, QT exploits the fact that even a single, randomly chosen pure state can effectively represent the full statistical ensemble in a high-dimensional Hilbert space. This allows us to compute frequency-dependent mobilities, representative of the thermodynamic limit, that are well converged with respect to all numerical parameters. Our results are compared against other numerically exact methods, and used to analyze the contribution of vertex corrections to frequency-dependent mobility. The promising accuracy and efficiency of the QT approach suggest its applicability to a broader class of Hamiltonians.

The scattering of electrons with polar optical phonons (POP) is an important mechanism that limits electronic transport and determines electron mobility in polar materials. This is typically a stronger mechanism compared to nonpolar acoustic and optical phonon scattering and of similar strength to the Coulomb ionized impurity scattering. At high densities, on the other hand, the cloud of charge carriers screens the dipoles that are responsible for POP scattering and weakens the electron-POP scattering strength. However, in contrast to ionized impurity scattering, for which the well-known Brooks-Herring equation provides the scattering rates with the effect of screening included, for scattering with POP there is no such closed-form mathematical expression. In this work, we derive such an expression based on Fermi's golden rule, which would prove particularly useful in understanding electronic transport in complex crystal and complex band structure materials, in which electron-POP scattering could dominate electronic transport.

Based on the lattice Green's function technique, we theoretically investigate the topological charge pump driven by two time-dependent staggered potentials in graphene with Rashba spin-orbit coupling. A topological transition occurs with increasing Rashba strength, where the pumped charge in a period changes from 1 to 0 per spin. The transition is attributed to the change of Berry phase from $\pi$ to $2\pi$ when the Rashba spin-orbit coupling is turned on. In the gap opened by the staggered potential, the Berry phase becomes the valley Chern number and very sensitive to the Rashba strength. As a consequence, the pumped current undergoes an abrupt transition from 1 to 0 even in the presence of a weak Rashba coupling. This proposal provides a scheme to realize tunable topological transitions in quantized charge pumps.

In two dimensions, Hermitian lattices with nonzero Chern numbers and non-Hermitian lattices with a higher-order skin effect (HOSE) bypass the constraints of the Nielsen–Ninomiya “no-go” theorem at their one-dimensional boundaries. This allows the realization of topologically protected one-dimensional edges with nonreciprocal dynamics. However, unlike the edge states of Chern insulators, the nonreciprocal edges of HOSE phases exist only at certain edges of the two-dimensional lattice, not all, leading to corner-localized states. In this paper, we investigate the topological connections between these two systems and uncover novel non-Hermitian topological phases possessing “higher-order topological knots” (HOTKs). These phases arise from multiband topology protected by crystalline symmetries and host nonreciprocal edge states that circulate the entire boundary of the two-dimensional lattice. We show that phase transitions typically separate HOTK phases from “complex Chern insulator” phases—non-Hermitian lattices with nonzero Chern numbers protected by imaginary line gaps in the presence of time-reversal symmetry.

The sound propagation properties resulting from a dynamical axion insulator generated from a Weyl semimetal are explored. Axial electron-phonon coupling in Weyl semimetals hybridizes phonons with the axion field changing their velocity and attenuation. At the random phase approximation (RPA) level, this hybridization gives rise to weaker modification of the speed of sound in longitudinal waves propagating parallel to the axionic charge density wave (ACDW) wave vector than in transverse waves. On the other hand, the attenuation is modified by anharmonic phonon interactions beyond the RPA, but the axionic contribution to this attenuation is negligible. While the corrections on sound attenuation might be too weak to observe, the corrections to the speed of sound should be accessible in ultrasound propagation experiments. In the presence of a magnetic field, these corrections are sensitive to the magnetic field through the value of the ACDW gap and the axion velocity, but not through the axial anomaly, implying that these effects can be observed in the absence of an applied electric field. Finally, we also discuss the importance of axial electron-phonon interactions with respect to the more conventional vector interactions in these systems.

We generalize the topological response theory to detect the boundary anomalies of linear subsystem symmetries. This approach allows us to distinguish different subsystem symmetry-protected topological (SSPT) phases and uncover new ones. We focus on the cases where the mixed anomaly exists within the adjacent subsystems. Using numerical simulations, we demonstrate the power of this method by identifying strong and weak $Z_2^{\tau }\times Z_2^{\sigma }$ SSPT phases in a tunable tensor network state. Our analysis reveals an intrinsic $Z_2$ SSPT phase characterized by its degenerate entanglement spectrum. Furthermore, we extend the anomaly indicator to mixed-state density matrices and show that quantum anomalies of subsystem symmetry can persist under both uniform and alternating disorders. This finding establishes a connection between boundary quantum anomalies in pure and mixed states. Our work provides a numerical method to detect quantum anomalies of subsystem symmetries, offering new insights into the study of topological quantum phases.

We study the diagonal and off-diagonal matrix elements of observables in the eigenstates of the extended $\mathrm{spin}\text{−}\frac{1}{2}$ Heisenberg chain, which exhibits the non-Abelian SU(2) symmetry. We explore integrable and nonintegrable regimes and consider observables that preserve the SU(2) symmetry of the Hamiltonian as well as observables that break it. We study in detail the low-frequency behavior of the off-diagonal matrix elements at and away from integrability. In the nonintegrable regime, we test the non-Abelian eigenstate thermalization hypothesis, paying special attention to the effect of the spin, which is the distinctive conserved quantity introduced by the SU(2) symmetry.

Various topological phases, including topological insulators, topological semimetals, and topological superconductors, along with the controllable topological phase transitions, have attracted considerable attention due to their promising applications in spintronics and quantum computing. In this work, we propose two distinct methods for manipulating topological phase transitions in magnetic materials. First, by varying the strength of electron correlation effects, we induce a series of topological state transitions within the $\mathrm{Eu}{M}_2{X}_2$ ($M$ = Zn, Cd; $X$ = P, As, Sb) family of Zintl materials, including magnetic topological crystalline insulators (TCIs) and magnetic Dirac semimetals. Our findings indicate that strong electron correlation effects tend to influence the emergence of topological phases. Second, by reducing the electronegativity of the pnictogen $X$ (from P to As and Sb), we observe a similar transition from trivial insulator to magnetic Dirac semimetal or magnetic TCI. This suggests that weaker electronegativity favors the emergence of topological phases. Furthermore, we establish a Heisenberg model to describe the magnetic interactions of the $\mathrm{Eu}{M}_2{X}_2$ system, based on which we perform Monte Carlo simulations of specific heat and magnetic susceptibility, yielding Néel temperatures that perfectly match the experimental data. This suggests that the local magnetic moment framework provides an accurate description of the magnetization behavior in this family of materials. This work provides the potential for the experimental manipulation of topological phase transitions and their possible applications, while also enhancing the understanding of the magnetic interactions within the $\mathrm{Eu}{M}_2{X}_2$ system and offering a theoretical foundation for future applications in magnetism.

For many materials, Raman spectra are intricately structured and provide valuable information about compositional stoichiometry and crystal quality. Here we use density-functional theory calculations, mass approximation, and the Raman intensity weighted $\mathrm{\Gamma }$-point density of state approach to analyze Raman scattering and vibrational modes in zincblende, wurtzite, and hexagonal BX (X = N, P, and As) structures. The influence of crystal structure and boron isotope disorder on Raman line shapes is examined. Our results demonstrate that long-range Coulomb interactions significantly influence the evolution of Raman spectra in cubic and wurtzite BN compounds. With the evolution of the compositional rate from ${}^{11}\mathrm{B}$ to ${}^{10}\mathrm{B}$, a shift toward higher frequencies, as well as the maximum broadening and asymmetry of the Raman peaks, is expected around the 1:1 ratio. The calculated results are in excellent agreement with the available experimental data. This study serves as a guide for understanding how crystal symmetry and isotope disorder affect phonons in BX compounds, which are relevant to quantum single-photon emitters, heat management, and crystal quality assessments.