We propose an approach for investigating the many-body effects on the phonon spectrum in an electron-phonon coupled system by taking into account the electron self-energy and vertex corrections which respect the Ward identity representing the conservation of electronic charge. Our approach provides a systematic diagrammatic expansion of the phonon self-energy ${\mathrm{\Pi }}_{\mathbf{q}}\left(\omega \right)$ in powers of the electron-phonon scattering strength squared $\left(g^2\right)$. In this approach the many-body corrections to the phonon spectrum vanish identically for the $\mathbf{q}=0$ mode due to an exact cancellation between the contributions arising from electron self-energy and vertex corrections. This cancellation holds irrespective of the microscopic details of the system such as dimensionality, adiabaticity, strength of electron-phonon scattering, etc. Our results demonstrate that the contributions of electron self-energy and vertex corrections are not only comparable but they also tend to cancel each other so that the phonon spectrum remains nearly unaffected due to many-body effects in the regime of long-wavelength excitations ($\mathbf{q}\to 0$). Our results provide another constraint for the applicability of the Migdal theorem.

Altermangetism is newly identified as the third fundamental class of collinear magnetism with zero net magnetization while hosting spin-split bands which break the time-reversal symmetry and Kramers degeneracy. Here, we propose a $\mathbf{k}·\mathbf{p}$ model for a two-dimensional altermagnetic lattice, in which instead of neglecting them, the spin-orbit couplings play the role of driving the system into a topological insulating region. We term this topological phase as an altermagnetic topological insulator, as opposed to an antiferromagnetic topological insulator such as ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. A spin Chern number is attributed as the topological invariant. We also derive the selection rules for optical conductivity measurements based on our minimal model, with which the elliptically polarized lights will serve as powerful probes to detect altermagnetism and excite individual spin degrees of freedom of altermagnetic compounds through light-induced anomalous Hall effects and longitudinal spin currents.

Atomistic simulations hold significant value in clarifying crucial phenomena such as phase transitions and energy transport in materials science. Their success stems from the presence of potential energy functions capable of accurately depicting the relationship between system energy and lattice changes. In magnetic materials, two atomic scale degrees of freedom come into play: the lattice and the spin. However, accurately tracing the simultaneous evolution of both lattice and spin in magnetic materials at an atomic scale is a substantial challenge. This is largely due to the complexity involved in depicting the interaction energy precisely, and its influence on lattice and spin-driving forces, such as atomic forces and magnetic torques, which continues to be a daunting task in computational science. Addressing this deficit, we present DeepSPIN, a versatile approach that generates high-precision predictive models of energy, atomic forces, and magnetic torques in magnetic systems. This is achieved by integrating first-principles calculations of magnetic excited states with deep learning techniques via active learning. We thoroughly explore the methodology, accuracy, and scalability of our proposed model in this paper. Our technique adeptly connects first-principles computations and atomic-scale simulations of magnetic materials. This synergy presents opportunities to utilize these calculations in devising and tackling theoretical and practical obstacles concerning magnetic materials.

Interaction between spins forms diverse classes of magnetic materials. The interaction can be carried out not only by electrons and photons but also by phonons. We consider a general symmetry-allowed spin-phonon Hamiltonian in $C_{3v}$ systems which consists of spins interacting with symmetric and antisymmetric lattice deformations. The derived model is used to calculate the phonon-mediated spin-spin interaction—the interaction is a quadrupole-quadrupole interaction. We first consider phonons in a homogeneous elastic medium, which leads to a spin-spin interaction with unphysical oscillations as a function of distance between the spins. We overcome this by extending the theory for lattice systems and confirm that the interaction strength decays as $1/r^3$. The effect of surface acoustic waves is also considered. The general theory is demonstrated for nitrogen vacancy centers in diamond as a prominent example. Furthermore, we provide an estimation of the magnitude of the spin-spin interaction and discuss the effect of the phonon-mediated spin-spin interaction on the energy level scheme of two interacting spins.

The superconductivity driven by the strong coupling of $\sigma$-bonding electrons with interlayer covalent bond-stretching modes presents a promising pathway for achieving high-${\mathit{T}}_c$ superconductivity under atmospheric conditions. Herein, we conduct high-throughput first-principles calculations to comprehensively investigate potential superconductivity in two-dimensional (2D) metal borocarbides ($M{\mathrm{B}}_2{\mathrm{C}}_2$, $M$ = metal). Our analysis of 41 $M{\mathrm{B}}_2{\mathrm{C}}_2$ films reveals that 23 demonstrate dynamical stability and 17 of them are potential superconductors. Moreover, we identify six promising candidates within this subset with critical temperatures $T_c\ge$ 75 K, i.e., ${\mathrm{LiB}}_2{\mathrm{C}}_2$ (75 K), ${\mathrm{NaB}}_2{\mathrm{C}}_2$ (81 K), ${\mathrm{KB}}_2{\mathrm{C}}_2$ (102 K), ${\mathrm{CaB}}_2{\mathrm{C}}_2$ (88 K), ${\mathrm{SrB}}_2{\mathrm{C}}_2$ (91 K), and ${\mathrm{LaB}}_2{\mathrm{C}}_2$ (94 K). Based on comprehensive analysis of the electronic and vibrational properties, we propose two key descriptors for filtering and diagnosing high-$T_{c}M{\mathrm{B}}_2{\mathrm{C}}_2$ films: one involving $\sigma$ electrons of covalent B-C bonds driven metallic and the other focusing on large deformation potentials for $\sigma$ bands near the Fermi level originating from frozen-in in-plane B-C bond-stretching modes at the zone center. Utilizing two descriptors, we expediently identify the ${\mathrm{KLaB}}_4{\mathrm{C}}_4$ film as a potential high-${\mathit{T}}_c$ candidate (70 K) among 15 bimetal borocarbides. These findings provide valuable insights into the electronic and vibrational properties that contribute to enhanced superconducting behavior, aiding in the design and discovery of new 2D materials with the potential to break the $T_c$ record for conventional superconductivity.

We discuss methods for calculating Chern numbers of two-dimensional lattice systems using spiral boundary conditions, which sweep all lattice sites in one-dimensional order. Specifically, we establish the one-dimensional representation of Fukui-Hatsugai-Suzuki's method, based on lattice gauge theory, and the Coh-Vanderbilt's method, which relates to electronic polarization. The essential point of this discussion is that the insertion of flux into the extended one-dimensional chain generates an effective current in the perpendicular direction. These methods are valuable not only for a unified understanding of topological physics in different dimensions but also for numerical calculations.

Topological materials with nontrivial spin structure have received considerable attention because they exhibit varieties of novel quantum phenomena. Here, we report a combined experimental and theoretical study of magnetic and magnetotransport properties of EuAuSb, an itinerant antiferromagnet with low Néel temperature, $T_N\sim$ 3.5 K. The concomitant change in the field and temperature dependence of the electrical resistivity and that of the magnetization suggest that the charge conduction mechanism in EuAuSb is strongly influenced by the spin configuration of the Eu. Below $T_N$, both longitudinal magnetoresistance (LMR) and transverse magnetoresistance (TMR) are large and positive at low fields, but negative at high fields. TMR becomes positive above 20 K, while LMR remains negative up to the highest measured temperature of 100 K. The negative LMR well above the $T_N$ is attributed to the chiral anomaly associated with the Weyl fermion state, while the low-field positive LMR and TMR are due to the weak antilocalization (WAL) effect. The WAL effect in TMR can be described well by the Hikami-Larkin-Nagaoka model, while the WAL effect in LMR is explained using the generalized Altshuler-Aronov model. The Hall resistivity indicates that holes are the majority charge carriers in EuAuSb with concentration $\sim {10}^{20}{\mathrm{cm}}^{-3}$ and mobility $\sim {10}^3{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ (at 2 K). The Shubnikov–de Haas oscillation in TMR has been analyzed to determine several important physical parameters related to the Fermi surface of EuAuSb. The detailed analysis unveils the large topological Hall effect, which is attributed to the presence of Weyl fermions and complex magnetic ordering, as confirmed by the $ab$ initio simulation. Our theoretical calculations reveal topologically nontrivial surface Fermi arcs and suggest competition among various low-energy magnetic phases, including an altermagnetic phase, mediated by specific crystalline symmetry present in EuAuSb.

Quantum spin liquids represent exotic states of spin systems characterized by long-range entanglement and emergent fractionalized quasiparticles. It is generally believed that disorder is hostile to quantum spin liquids. In our study, we investigated the magnetic properties of a kagome system, ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_6[{\left({\mathrm{Cl}}_x{\mathrm{Br}}_{1-x}\right)}_{3-y}{\left(\mathrm{OH}\right)}_y]$. Within this system, some of the hexagons exhibit alternate bonds along the Cu-O-Cu exchange paths, while others remain uniform. We found that a long-range antiferromagnetic order emerges when uniform hexagons dominate. Conversely, a possible quantum-spin-liquid state arises when the number of alternate-bond hexagons exceeds about 2/3. Therefore, the alternate-bond hexagons, typically considered as disorders, actually serve as the building blocks of the quantum spin liquid in this system. Notably, the low-temperature properties of the quantum spin liquid are directly associated with the height of the out-of-plane yttrium ions, which may be linked to changes in superexchange energies. Our results suggest that understanding the magnetic ground states in this system lies beyond the theoretical framework of the Heisenberg model constructed on the kagome lattice.

Electronic fluids can display exciting dynamical properties. In particular, due to Landau damping, the collective-mode spectrum of an electronic system with multipolar interactions is non-Hermitian, and can present non-Hermitian degeneracies called exceptional points. In this work, we want to explore the dynamical properties of these degeneracies using laser control. We show that by using a light pulse, we can control the collective-mode spectrum and tune a non-Hermitian $\mathcal{PT}$ phase transition in which two exceptional points annihilate each other. At this transition, the gap closes with a cubic root signature, which defines a third-order exceptional point.

Parafermions are anyons with the potential for realizing nonlocal qubits that are resilient to local perturbations. Compared with Majorana zero modes, braiding of parafermions implements an extended set of topologically protected quantum gates. This, however, comes at the price that parafermionic zero modes cannot be realized in the absence of strong interactions, posing a challenge for their theoretical depiction. In this paper, we construct a simple lattice model for interacting spinful electrons with parafermionic zero-energy modes. The explicit microscopic nature of the considered model highlights realization avenues for these exotic excitations in recently fabricated quantum dot arrays. By density matrix renormalization group calculations, we identify a broad range of parameters, with well-localized zero modes, whose parafermionic nature is substantiated by their unique $8\pi$ periodic Josephson spectrum.

Photocurrent acts as one of measurable responses of material to light, which has proved itself to be crucial for sensing and energy harvesting. Topological semimetals with gapless energy dispersion and abundant topological surface and bulk states exhibit exotic photocurrent responses, such as quantized circular photogalvanic effect observed in Weyl semimetals. Here we find that for a topological nodal-line semimetal with special ring bulk states and drumhead surface states (DSS), a significant photocurrent can be produced by an electromagnetic (EM) wave by means of the quantum Hall effect. The Hall current is enabled by electron transfer between Landau levels (LLs) and triggered by both the electric field and magnetic field components of an EM wave. This Hall current is physically connected to an unusually large quantum-Hall conductivity of the zeroth LLs resulting from quantized DSS. These LLs are found to be highly degenerate because of the unique band-folding effect associated with magnetic-field-induced expansion of a unit cell. We found that the Hall current generated solely by an in-plane linearly polarized EM wave is a quantized entity, regardless of its frequency and energy, which distinguishes it from the photocurrent observed thus far. This discovery opens up possibilities for Hall rectifiers and sensors, with potential industrial and space applications.

We report the observation of a three-photon resonant transition of charge-carrier spins in an organic light-emitting diode using electrically detected magnetic resonance (EDMR) spectroscopy at room temperature. Under strong magnetic-resonant drive (drive field $B_1\sim$ static magnetic field $B_0$), a $B_0$-field swept EDMR line emerges when $B_0$ is approximately three times the one-photon resonance center. Ratios of drive-induced shifts of this line to the shifts of two- and one-photon lines agree with analytical expressions derived from the Floquet Hamiltonian and confirm the nature of these three-photon transitions, enabling access of spin physics to a hitherto inaccessible domain of quantum mechanics.

Device applications of topological semimetals await the development of epitaxial films in the ultrathin limit. Weak antilocalization (WAL) has been extensively utilized in the understanding of surface states in topological insulators and shows promise for use in elucidating the properties of thin film topological semimetals. Here, we report insights from WAL in the surface state and interface transport properties of our recently synthesized single-crystal-like thin films of the Weyl semimetal TaAs(001) grown on GaAs(001). We observe robust, anisotropic WAL in the magnetoconductance from 2 to 20 K in films from 10 to 200 nm thick. We link the anisotropic WAL magnetoconductance to anisotropic mobility stemming from film topography. We conclude that WAL in the films likely originates from the antilocalization of topological surface states. The WAL magnetoconductance is impacted by the film thickness and topography, solidifying the useful role of WAL in the study of topological semimetal/semiconductor heterointerfaces.

Research on topological models unveils fascinating physics, especially in the realm of dynamical quantum phase transitions (DQPTs). However, the understanding of entanglement structures and properties near DQPT in models with longer-range hoppings is far from complete. In this work, we study DQPTs in the quenched extended Su-Schrieffer-Heeger model. Anomalous DQPTs, where the number of critical momenta exceeds the winding number differences between the prequench and postquench phases, are observed. We find that the entanglement exhibits local maximum (minimum) around the anomalous DQPTs, in line with the level crossings (separations) around the middle of the correlation matrix spectrum. We further categorize the phases in the equilibrium model into two classes and distinctive features in the time evolution of the entanglement involving quenches within and across the two classes are identified. The findings pave the way to a better understanding of topological models with longer-range hoppings in the out-of-equilibrium regime.

Magnons are electrically neutral bosonic quasiparticles emerging as collective spin excitations of magnetically ordered materials, and they play a central role in next-generation spintronics due to its obviating Joule heating. A difficult obstacle for quantum magnonics is that the magnons do not couple to the external electric field directly so that a direct electric manipulation via bias or gate voltage as in conventional charge-based devices seems not to be applicable. In this work, we propose a mechanism in which magnons can be excited and controlled by an electric field of light directly. Since the electric field of light can be tuned in a wide and easy way, the proposal should be of great interest in realistic applications. We call it the magnon spin photogalvanic effect (SPGE), which comes from five contributions: Drude, Berry curvature dipole (BCD), injection, shift, and rectification, with distinct geometric origins. We further show that the responses to linearly polarized or circularly polarized light are determined by a band-resolved quantum metric or Berry curvature, both of which, when combined, comprise a quantum geometric tensor. The proposed magnon SPGE can be measured by a characterized topological phase transition. We also discuss a breathing kagome-lattice model of ferromagnets, and we suggest possible candidate materials to implement it.

The topological kagome superconductor ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ exhibits rich quantum phenomenology of correlated electronic phases including unconventional charge order and superconductivity. Understanding how the singularities inherent to the kagome lattice are linked to the observed many-body phases is a topic of great interest. Here, by using Shubnikov–de Haas oscillation measurements, we report the detailed evolution of electronic band structures in ${\mathrm{CsV}}_{3-x}{\mathrm{Mo}}_x{\mathrm{Sb}}_5$ single crystals, where Mo substitution causes a suppression of superconductivity and an enhanced charge density wave. The obvious decrease of oscillation frequency $\left(F_{\beta }\right)$ corresponding to the nontrivial band from 72 to 59 T and smaller cyclotron effective mass $(\sim 0.069m_e)$ reveal that the van Hove singularities from the vanadium orbitals near $M$ are abnormally lifted and promote the nesting condition for the charge density wave. Meanwhile, the electric conduction changes from a hole-dominated multiband feature to a single electron band feature and the anomalous Hall effect becomes stronger. In conjunction with the simple schematics of band structures, the promoted Fermi-surface nesting is dominant in the unusual enhanced charge density wave, offering insight to comprehend the delicate interaction between the intertwined orders in this kagome system.

Monolayer electrocaloric (EC) materials have emerged as promising candidates to achieve economic and green solid-state refrigeration, especially in micro- or nanoscale chip cooling in the post-Moore law period. In this paper, we trained a machine-learning-based deep potential (DP) model of monolayer group-IV monochalcogenides $\mathit{MX}\mathrm{s}$ ($M$ = Ge, Sn; $X$ = S, Se) with a database from first-principles calculations, which incorporates the accuracy of ab initio molecular dynamics and efficiency of classical method. The DP model was further applied to study the EC effect (ECE) in monolayer $\mathit{MX}\mathrm{s}$ by simulating the temperature-driven phase transitions and electric polarization dynamics under different external electric fields. The results indicate $\mathit{MX}\mathrm{s}$ featuring giant reversible isothermal entropy change (Δ$S$) and adiabatic temperature change (Δ$T$) near their order-disorder phase transition. Particularly, for $E$ = 100 MV/m, |Δ$S$| = 68 J/(kg K) and |Δ$T$| = 75 K are obtained for GeS, which individually rival the state-of-the-art ECE figures of merit, surpassing most other ferroelectric materials, particularly the two-dimensional (2D) CuInPS and strained $\mathrm{SrTi}{\mathrm{O}}_3$ films. Furthermore, electric field shifts of the order of 10 MV/m yield huge reversible EC strengths of Δ$S$/Δ$E$ = 5.4 $\mathrm{J}\mathrm{m}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}\mathrm{M}{\mathrm{V}}^{-1}$ and Δ$T$/Δ$E$ = 6 $\mathrm{K}\mathrm{m}\mathrm{M}{\mathrm{V}}^{-1}$. The origin of the giant ECE in $\mathit{MX}\mathrm{s}$ was explained through macroscopic thermodynamic ratios, phenomenological Landau theory, and microscopic phonon vibration analysis. Interestingly, the entropy change can be approximated to be proportional to the square of the polarization change ($\mathrm{\Delta }{P}^2$), and the application of electric field shifts the low-frequency phonons to the higher-frequency range, with the $M$ atom contributing more to the entropy change than the $X$ atom. In this paper, we provide important insights for exploration and design of 2D EC materials in future practical applications.