The algebraic or ring structure of anyons, called the fusion rule, is one of the most fundamental research interests in contemporary studies on topological orders (TOs) and the corresponding conformal field theories (CFTs). Recently, the algebraic structure realized as generalized symmetry, including noninvertible and categorical symmetry, captured attention in the fields. Such non-Abelian anyonic objects appear in a bulk CFT or chiral CFT (CCFT), but it has been known that the construction of a CCFT contains theoretical difficulties in general. In this work, we propose the fusion rules in $Z_N$ extended CCFT and bulk CFT and the corresponding TOs. We explicitly construct a nontrivial expression of subalgebra structure in the fusion rule of a bulk CFT. We name this subalgebra bulk semion. This corresponds to the fusion rule of the CCFT and categorical symmetry of the TO or $Z_N$ graded symmetry topological field theory. This gives a bulk-edge correspondence based on the symmetry analysis and corresponds to an anyon algebraic expression of topological holography in the recent literature. The recent topological holography is expected to apply to systems in general space-time dimensions. Moreover, we present a concise way of unifying duality (or fractional supersymmetry), generalized or categorical symmetry, and Lagrangian subalgebra. Our method is potentially useful to formulate and study general TOs, fundamentally only from the data of bulk CFTs or vice versa, and gives a clue in understanding CCFT (or ancillary CFT more generally).

We introduce a second-quantized field theory for Chern insulators in which the Hamiltonian features a static vector potential that has the periodicity of the crystal's lattice and spontaneously breaks time-reversal symmetry in the system's ground state. Such a vector potential generates a magnetic field at the microscopic level that may be thought of as arising from local moments associated with one or more magnetic ions in each unit cell. Considering spinor electrons, we study the Chern invariants characterizing the topology of the occupied valence bands of Chern insulators in both two and three dimensions – the Chern number and the Chern vector, respectively – and we derive expressions for these topological invariants that are globally defined across the Brillouin zone and involve the full band structure of the system. We also study the long-wavelength response of a Chern insulator to electromagnetic fields at finite frequency, generalizing the quantum anomalous Hall effect in the static limit to the optical regime.

The Hall effect in the superconducting mixed state serves as a crucial probe of vortex dynamics. Here, we report a systematic magnetotransport study on the vortex Hall effect in exfoliated FeSe flakes with varying thickness. In flakes of intermediate thickness (e.g., 159 nm), the Hall resistivity ${\rho }_{xy}$ in the superconducting mixed state exhibits a double sign reversal as a function of temperature, characterized by a pronounced peak-dip structure. This behavior evolves with magnetic field and current, and is qualitatively consistent with the predictions of vortex dynamics theory (Wang, Dong, and Ting theory). However, the complex evolution of the sign reversal across different thicknesses cannot be explained by existing models. We propose a unified physical picture that incorporates Magnus force, equivalent Lorentz force, and carrier-type effects to explain the sign reversals and their thickness-dependent evolution. Finally, we discuss the connection between the unconventional Hall response and the microscopic origin of vortex pinning in FeSe. Our results advance the understanding of vortex transport and the anomalous Hall effect in iron-based superconductors.

Exceptional points (${\mathrm{EP}}_{\mathrm{S}}$) can enhance sensitivity for weak signal detection, but noise typically degrades their performance. Here, contrary to this conventional wisdom, we theoretically introduce and experimentally demonstrate a noise-assisted sensing paradigm leveraging stochastic resonances near a driven-dissipative nonlinear fourth-order exceptional point (${\mathrm{EP}}_4$). Using a minimal two-site model with asymmetric dissipation and single-site driving, we realize an ${\mathrm{EP}}_4$ exhibiting fourfold degeneracy in steady-state eigenamplitudes under fixed-frequency driving. Crucially, this ${\mathrm{EP}}_4$ coexists with third-order ${\mathrm{EP}}_{\mathrm{S}}$ and second-order exceptional lines, partitioning a two-parameter space into mono-, bi-, and tristable regions. We demonstrate that noise induces bi- and multistable stochastic resonances, synergizing with the quartic-root dispersion around ${\mathrm{EP}}_4$ to dramatically amplify weak signals and enhance signal-to-noise ratios. Experimental validation with nonlinear electrical circuits confirms these predictions. Our work establishes driven-dissipative nonlinear higher-order ${\mathrm{EP}}_{\mathrm{S}}$ with eigenamplitude degeneracy as a potent platform for noise-enhanced sensing, harnessing nonlinear multistability and EP physics to transcend conventional noise limitations.

We demonstrate a graphene nanoribbon (GNR) metagrating on a rectangular dielectric ridge that exhibits plasmonically induced transparency (PIT) through the excitation of both odd- and even-order dark modes. The metagrating integrates a top bright mode GNR coupled directly to light and a sidewall dark mode GNR isolated from direct excitation. Increasing the dark mode width generates sequentially ordered dark mode based PIT effects. Taking the PIT effects formed by the fundamental bright mode coupled to the first six-order dark modes as examples, we employ Fabry-Pérot theory, Lorentzian oscillator modeling, and finite-difference time-domain (FDTD) simulations to reveal the underlying physics: The resonant phase remains fixed near $\pi /2$ at the bright mode distal edge but transitions continuously from $-\pi /2$ to $+\pi /2$ at its bright mode facing edge. Consequently, the corresponding phase shift is nearly invariant at the distal edge but varies substantially at the facing edge. This transitional resonant phase—together with the resulting asymmetric phase shift—permits noninteger mode orders which correspond to the conversion from the high-frequency mode of the $j\mathrm{th}$-order PIT to the low-frequency mode of ($j+1$)th-order PIT under variation of the sidewall GNR width while high absorption is maintained. Finally, using refractive index sensing as an example, we demonstrate that the high-order modes of this PIT device outperform conventional gratings and other lower-order PIT devices in key metrics, including the quality factor and figure of merit.

Quantum tunneling allows electrons to be transferred between two regions separated by an energetically forbidden barrier. Performing a position measurement that finds a particle in the barrier forces the tunneling electrons to transition from having a classically forbidden energy to an energy above the barrier height. We exploit this effect to define quantum tunneling engines that can use the unconditioned detection of virtually occupied states as a resource for power generation and cooling. Leveraging energy exchange with the detector, we show that the device can operate in a hybrid regime, enabling simultaneous cooling and power generation. Furthermore, we demonstrate measurement-assisted autonomous refrigeration and checkpoint cooling driven purely by a thermal bias, without the need for an applied potential. We also find a purification by noise effect when the measurement drives the system into a stationary dark state. These results underscore the intriguing dual role of measurement as a thermodynamic resource and a dark state generator.

Competing exchange interactions in frustrated three-dimensional spin lattices offer a promising route to realize rich physical phenomena, including spin liquids with exotic low-energy excitations. In this work, we focus on the three-dimensional frustrated magnet ${\mathrm{MgCrGaO}}_4$, where ${\mathrm{Cr}}^{3+}$ ions occupy a pyrochlore-like network. Due to intrinsic disorder and partial occupation of the pyrochlore sites by magnetic ions, the actual structure highlights the famous closed loops of the pyrochlore lattice. Our thermodynamic, electron spin resonance (ESR), muon spin relaxation ($\mu \mathrm{SR}$), and inelastic neutron scattering (INS) techniques detect no signature of magnetic order or spin freezing down to 57 mK, despite a sizable exchange interaction ($J=58\text{K}$) between ${\mathrm{Cr}}^{3+}$ moments. Below the characteristic exchange energy scale, all probes reveal the emergence of antiferromagnetic short-range spin correlations, corroborated by magnetic diffuse scattering in the wave vector dependence of low-energy magnetic excitations centered on $Q=1.5{\text{Å}}^{-1}$ in inelastic neutron scattering experiments. The low-temperature specific heat follows a near-quadratic dependence suggesting the presence of nontrivial low-energy excitations. These results establish ${\mathrm{MgCrGaO}}_4$ as a rare three-dimensional spin liquid with exotic excitations, offering a strong impetus for the experimental realization of spin liquids in higher-dimensional frustrated quantum magnets.

Spin Hall magnetoresistance (SMR), the variation in resistance of a heavy metal (HM) with the magnetization orientation of an adjacent ferromagnet (FM), has been extensively studied as a powerful probe of surface magnetic moments in a variety of magnetic materials. While conventional SMR relies on the angular rotation of an assumed rigid magnetization of fixed magnitude, we report a SMR arising from magnetic-field modulation of spin fluctuations in the FM, with its magnetization direction kept fixed parallel to the spin Hall accumulation in the HM. In contrast to conventional SMR, which scales with the magnetization and vanishes near the Curie temperature ($T_c$), such “longitudinal” SMR, though suppressed at low temperatures, becomes critically enhanced at $T_c$, reaching a magnitude comparable to conventional SMR amplitudes. Our work highlights the overlooked importance of the magnetization-magnitude degree of freedom in spin transport and opens a promising avenue for electrically detecting enhanced spin fluctuations in magnetic systems.

The recent experimental observation of fractional quantum anomalous Hall (FQAH) states in rhombohedral multilayer graphene has attracted significant attention. One of the most intriguing observations is that the FQAH states at various fractional fillings give way to IQAH states as the temperature is lowered. In this work, we propose a mechanism for the appearance of FQAH states within a finite temperature range in a toy model. The model consists of a flat Chern band and impurities, and we analyze the effects of impurities on the system's behavior at finite temperatures. Because a doped FQAH state has a large entropy due to the abundant quasiparticle excitations, we believe that the crossover may arise from the competition between the energy penalty for thermal excitations and the increase in entropy. We support our theoretical argument with numerical calculations using exact diagonalization. Our results suggest that impurities may play a crucial role in the crossover from the FQAH to IQAH states in rhombohedral pentalayer graphene.

Out-of-time ordered correlators are a probe of how the information of an initial perturbation is effectively scrambled under unitary time evolution, widely used to study quantum chaos. They have also been used to demonstrate that information is trapped in the zero-dimensional edge modes of topological insulators and superconductors, and does not become scrambled. Here we study scrambling in two-dimensional topological models. In the bulk the butterfly velocity, the speed at which the out-of-time ordered correlator spreads, gains a directional dependence from the underlying lattice. Furthermore when there are chiral or helical edge modes present these cause a form of dynamical scarring. The information about an initial perturbation on the boundary of the system travels around the edge, carried by the edge modes, but is not scrambled over very long time scales. The direction and speed of the scars are given by the velocities of the linearly dispersing edge modes. We further show that these scars do not interact, passing through each other. We back up these results with analytical and numerical calculations on exemplary models.

We present a combined x-ray and polarized neutron scattering study on chiral, polar and magnetoeletric ${\mathrm{NiCo}}_2{\mathrm{TeO}}_6$ single crystals with different net crystal chiralities as characterized by optical methods. The rastering images taken with a micrometer-sized polarized x-ray beam unambiguously reveal the coupling of crystal and magnetic chiralities in a heterochiral sample. Spherical neutron polarimetry experiments on a different, structurally enantiopure sample—as evidenced by polarized x-ray scattering—reveal a homochiral magnetic spiral, which proves the stabilization of a single helical handedness despite the intertwined structural helices in the ferri-chiral crystal structure.

Antiskyrmions (ASks) exhibit an electrically tunable antiskyrmion Hall effect, enabling zero-Hall-angle propagation compared to skyrmions. However, the fundamental mechanism governing ASks formation in two-dimensional systems is rarely explored. Here, we demonstrate that the ${MX}_2$ (${\mathrm{NbO}}_2, {\mathrm{NbS}}_2, {\mathrm{NbSe}}_2, {\mathrm{MoS}}_2$, and ${\mathrm{MoSe}}_2$) monolayers with $D_{2d}$ symmetry host an intrinsic sizable anisotropic Dzyaloshinskii-Moriya interaction (DMI) enabling ASks stabilization. Crucially, in 2D ${\mathrm{MoS}}_2$, biaxial strain dramatically tunes the anisotropic DMI strength ($|d_{\parallel }|/J_1=0.07–0.16$) and the magnetic frustration ratio ($|J_2|/J_1=0.18–0.5$), cooperatively driving sequential magnetic phase transitions from an antiskyrmion lattice to an ASks-wormlike-domain mixture and ultimately to distorted spin spiral states. A comprehensive investigation of magnetic parameters further reveals that frustration reduces the critical DMI threshold for ASks formation by 70% compared to frustration-free systems while minimizing the antiskyrmion diameter to sub-2 nm, greatly expanding their stability window. This study elucidates the fundamental mechanisms and provides valuable information for achieving multichiral topological spin configurations in low-dimensional magnets.

Inspired by the successful synthesis of two-dimensional (2D) ${\mathrm{MoSi}}_2{\mathrm{N}}_4$ and ${\mathrm{WSi}}_2{\mathrm{N}}_4$ [Y. L. Hong et al., Science 369, 670 (2020)], which demonstrates that Si-N layers can act as effective modification layers on 2D materials, we investigate superconductivity and charge density waves (CDWs) of hexagonal boron nitride $\left(h\text{−}\mathrm{BN}\right)$ passivated with a Si-N layer based on first-principles calculations. Our results demonstrate that $h$-BN undergoes a transition from an insulator to a phonon-mediated superconductor with the transition temperature $\left(T_c\right)$ of 14.3 K when it is functionalized with a Si-N layer on one side. The electron-phonon coupling (EPC) of ${\mathrm{BN}}_2\mathrm{Si}$ is primarily attributed to the coupling between electrons in N-$p_z$ orbitals and the low-frequency in-plane vibrational modes of Si and N atoms, as well as higher-frequency out-of-plane vibration modes of N and B atoms. By applying $5\%$ biaxial tensile strain, the EPC constant $\lambda$ increases from 0.66 to 1.82, resulting in a significantly enhanced $T_c$ of 34.9 K. However, when the biaxial tensile strain reaches $6\%$, an obvious soft mode emerges in the lowest acoustic branch of phonon curves, indicating the presence of a CDW. The origin of the instabilities is analyzed based on Lindhard electron susceptibility and the phonon linewidths, revealing that the CDW is driven by both Fermi-surface nesting and EPC. Thus, the predicted ${\mathrm{BN}}_2\mathrm{Si}$ presents a promising platform for exploring 2D superconductivity and CDWs.

The dynamics of a cycloidal spin structure driven by an ac magnetic field is theoretically studied in the weak-field limit. A specific model Hamiltonian describing the cycloidal spin structure in a ferromagnetic thin film is constructed, and its dynamics is analyzed using the collective-coordinate approach within the Lagrangian formalism. We demonstrate that the cycloidal spin structure exhibits a unidirectional gliding motion under an ac magnetic field applied along a specific direction, and an expression for the average velocity is derived as a function of the magnitude, the direction, and the frequency of the ac magnetic field. We compare our theoretical predictions with the results of micromagnetic simulations and identify two resonance frequencies determined by the eigenenergies of the excitation modes. Furthermore, evaluating spin motive forces induced by the dynamics reveals a substantial dc voltage, which may be exploited in energy-harvesting devices utilizing ambient electromagnetic radiation.

We propose a model of metallic critical point which we study at $T=0$ in the large-$N$ limit. We start with two species of fermions $u_i,d_i$, each with $N$ flavors and a gas of matrix bosons $b_{ij}$ with $N^2$ components. The fermions interact with each other via the intermediate boson as $\int b_{ij}^{†}{u}_i^{†}{d}_j$. The bosons have a bare dispersion ${\varepsilon }_{\mathbf{q}}^b={\lambda }_z{\left|\mathbf{q}\right|}^z$ and we study the problem in $d$ spatial dimensions. We show that for $d=z+1,$ the electronic self-energy shows marginal Fermi liquid behavior. We first evaluate the fermionic self-energy $\mathrm{\Sigma }\left(i\omega \right)$ using the standard approximate boson self-energy $\mathrm{\Pi }(\mathbf{q},i\nu )\propto \left|\nu \right|/\left|\mathbf{q}\right|$ and find that $\mathrm{\Sigma }\left(i\omega \right)\sim \omega ln(N/|\omega \left|\right)$ which shows a much weaker dependence on $N$ when compared with similar results from non-SYK large-$N$ Ising-nematic models. Then we evaluate $\mathrm{\Sigma }\left(i\omega \right)$ again using a more precise form of $\mathrm{\Pi }(\mathbf{q},i\nu )$ which allows us to study the interplay between $N\to \infty$ limit for which $\mathrm{\Sigma }\left(i\omega \right)\sim \omega ln(1/|\omega \left|\right)$, and the $\omega \to 0$ limit where we recover $\mathrm{\Sigma }\left(i\omega \right)\sim \omega ln(N/|\omega \left|\right)$. We also use the full bosonic self-energy to obtain the correction to the bosonic-specific heat as $\frac{T}{N}ln(1/T)$. Since there are $N^2$ bosons and $N$ fermions, the bulk heat capacity for both fermions and bosons shows nearly identical functional form $NVTln(N/T)$ and $NVTln(1/T)$, respectively, for $T\to 0$. This suggests that coupling the hybridization operator $u^{†}d$ to nonrelativistic bosons for $d=3$ and relativistic bosons for $d=2$ provides a simple route to marginal Fermi liquid scaling.

We investigate the orbital-selective electronic structure of orthorhombic ${\mathrm{CsPbI}}_3$ bulk perovskite using density functional theory combined with dynamical mean-field theory. By considering realistic values of the on-site Coulomb repulsion and spin–orbit coupling, we reveal characteristic features in the spectral functions of the active Pb-$6p$ orbitals, including the formation of spin–orbit–induced low-energy bound states. Our results further demonstrate that electron doping drives a substantial reconstruction of the electronic structure, leading to Pb-orbital selectivity. These findings provide microscopic insights into the interplay between electronic plus spin–orbit interactions and doping in orthorhombic ${\mathrm{CsPbI}}_3$ crystal, offering a framework to understand its correlated electronic state.

Half-Heusler (hH) compounds are currently considered promising thermoelectric (TE) materials owing to their favorable thermopower and electrical conductivity. Accurate estimates of their TE performance are therefore highly desirable and require a detailed microscopic understanding of the mechanisms that limit carrier transport. To enable such estimations, we carry out comprehensive first-principles computations of the electron-phonon $(e-ph)$ interactions in two hH semiconductors (LiZnAs and ScAgC). Our study first investigates their electron and phonon dispersions and then examines the temperature-induced renormalization of the electronic states within the nonadiabatic Allen-Heine-Cardona formalism. We then solve the Boltzmann transport equation (BTE) both iteratively and within multiple relaxation-time approximations (RTAs) to evaluate the carrier transport properties. Phonon-limited electron and hole mobilities computed using the linearized self-energy and momentum RTAs (SERTA and MRTA) are compared with the iterative BTE (IBTE) results. The electrical transport coefficients for TE performance are subsequently evaluated under these two RTA schemes and compared with constant RTA (CRTA) results. The lattice thermal conductivity, determined from phonon-phonon interaction, is further reduced through nanostructuring. In bulk form, LiZnAs (ScAgC) attains a maximum figure of merit $zT$ of $\sim 1.05$ (0.78) at 900 K for an electron concentration of ${10}^{18}$ $\left({10}^{19}\right)$ ${\mathrm{cm}}^{-3}$ under the MRTA. For a 20-nm nanostructured sample, the corresponding $zT$ increase to $\sim 1.53$ (1.0). The remarkably high $zT$ achieved through inherently present phonon-induced electron scattering effects, combined with grain-boundary engineering, opens a promising path for discovering highly efficient and accurate next-generation hH TEs.

Layered van der Waals material, $1T-\mathrm{TaS}{\mathrm{e}}_2$ in its star-of-David charge density wave (CDW) phase has attracted significant research interest with several unresolved issues. The current study addresses these issues for monolayer and bilayer $1T-\mathrm{TaS}{\mathrm{e}}_2$ from a perspective of combined intra- and interlayer (quasi)bonding interactions: namely, the $p$-orbital mediated intra- and interlayer d-d orbital interactions, and the interlayer interaction is quasibonding (QB) in nature, mediated by the p-p orbital interaction across adjacent layers. For the CDW phase, within a monolayer, the d-d interaction between supercells is small and leads to the formation of a narrow half-filled single band, in which a small spin-splitting gap of 0.11 eV is exhibited. From monolayer to bilayer, the interlayer interaction gives an energy splitting of 0.5 eV, which is larger than the spin-splitting gap, and hence a transition from spin-polarized insulator to non-spin-polarized insulator occurs. Moreover, we find that the interlayer interaction is multilevel in nature, namely, the bandedge of bilayer is derived from not only the energy level close to Fermi level but also correlated to a deep level with the same orbital character. The interlayer QB interaction also affects the relative stability of different interlayer-stacking configurations. This study provides an intra- and interlayer (quasi)bonding perspective for understanding the electronic structure and stability of the CDW phase monolayer and bilayers, and hence help broaden the understanding of CDW materials.

Significant progress in manipulating heat diffusion has been achieved with the advent of non-Hermitian physics and topology. However, previous studies on diffusive systems have primarily concentrated on isolated cases, where fields decay exponentially over time. In practical scenarios, systems inevitably interact with external environments, making it essential to study their responses to external heat signals. This, in turn, relies on analyzing the scattering behavior of these signals. In our work, we experimentally realize thermal scattering in a diffusive anti-parity-time (APT) system. We define key parameters of the temperature field—amplitude, phase, and chirality—and reveal that the scattering symmetry of the APT diffusive system only arises when temperature signals with different chiralities interact. Such mechanism is induced by the channel's intrinsic time-reversal antisymmetry (anti-T symmetry), which gives rise to unique dispersion properties in diffusive systems, where positive and negative frequencies are inequivalent, corresponding to different chiralities. Our findings therefore highlight the pivotal role of scattering channels in dictating the symmetry and phase transitions of non-Hermitian systems, and our work provides an experimental platform to observe and control these strongly dissipative phenomena.