We propose a formula for the transformation law of anyons in topologically ordered phases or topological quantum field theories (TQFTs) through a gapped or symmetry-preserving domain wall. Our formalism is based on the ring homomorphism between the $\mathbb{C}$-linear commutative fusion rings, also known as symmetry topological field theories (SymTFTs). The fundamental assumption in our formalism is the validity of the Verlinde formula, applicable to commutative fusion rings. By combining it with more specific data of the settings, our formula provides classifications of anyons compatible with developing categorical formulations. It also provides the massless renormalization group (RG) flows between conformal field theories (CFTs), or a series of measurement-induced quantum phase transitions, in the language of SymTFT, through the established correspondence between CFTs and TQFTs. Moreover, by studying the correspondence between the ideal structure in the massless RG and the module in the related massive RG, one can make the Nambu-Goldstone-type arguments for generalized symmetry. By combining our formula with orbifolding, extension, and similarity transformation, one can get a series of classifications for the corresponding extended models, or symmetry-enriched topological orders and quantum criticalities.

We study the electronic properties of a linear trans-polyacetylene (tPA) molecule capacitively coupled to an external gate voltage $V_g$ of width $d$. We describe this system using the Takayama-Lin-Liu-Maki model, a continuum version of the Su-Schrieffer-Heeger model, and analyze it within the Abelian bosonization formalism, which allows us to treat both electronic and lattice degrees of freedom and to incorporate the effects of repulsive Coulomb interactions among electrons. The global ground state describing simultaneously the electronic charge-density field as well as the lattice dimerization field of a tPA molecule is shown to consist of multikink solutions of a modified sine-Gordon equation for the charge-density field, which is controlled by $V_g$, the width $d$, and the Luttinger parameter $K$ encoding the strength of electron-electron interactions. We show that these solutions belong to distinct topological sectors labeled by an integer invariant $q$ that simultaneously quantifies both the bound charge and the number of domain walls in the dimerization pattern induced at the gated region. Increasing $V_g$ drives a sequence of topological phase transitions characterized by abrupt changes in $q$. We further examine the effect of repulsive Coulomb interactions on the resulting topological phase diagram, and, finally, we discuss the relevance of our findings for potential nanoelectronic devices based on gated tPA molecules.

The light metal Al was predicted to have strong orbital Hall and Rashba effects from its bulk and interface, respectively. In this Letter, we report experimental evidence that neither the bulk nor the interface of the Al contributed a detectable torque on adjacent Co and FePt layers with significant spin Hall effect, spin-orbit coupling, and resistivity mismatch with Al. These results suggest minimal orbital-spin conversion in Al and negligible orbital transport and spin-vorticity torque in Co/Al, Al/Co, and Al/FePt bilayers. Our findings suggest poor generality and/or effectiveness of torque contributions by the orbital Hall effect, the interfacial orbital Rashba effect, and the spin-vorticity coupling.

The quantum boomerang effect (QBE) is a unique dynamical signature of Anderson localization, characterized by a launched wave packet that initially drifts but ultimately returns to its initial position due to fundamental quantum interference. In this work, we theoretically establish and quantitatively characterize the QBE in a time-crystalline structure using a periodically driven quantum particle in a one-dimensional potential well. By constructing maximally localized Floquet-Wannier states and introducing temporal disorder, we rigorously map the continuous Floquet dynamics onto a discrete disordered tight-binding lattice. By positioning a detector at a fixed spatial coordinate, we monitor the temporal evolution of the wave packet to extract the mean temporal center of mass of the probability density in a time-crystalline structure. This mean temporal center of mass exhibits an initial ballistic expansion, followed by a pronounced U-turn, and ultimately returns to its initial temporal position after long-time evolution. These results confirm the existence of the complete QBE in the time domain. They also demonstrate that nontrivial dynamics can be explored within time-crystalline systems, even though these structures already possess an inherent temporal periodicity.

Antiferromagnetic spintronics, a promising technology for ultrafast electronic devices, faces several challenges, including the lack of materials simultaneously hosting robust antiferromagnetism and adequate Rashba-like interaction. We design a heterostructure of ${\mathrm{BaMnO}}_3|{\mathrm{KTaO}}_3$ with the idea of proximity-inducing moderate Rashba spin-orbit interaction from the ${\mathrm{KTaO}}_3$ part to the ${\mathrm{BaMnO}}_3$ part, where the latter is already a robust antiferromagnet. Within our DFT calculations, the heterostructure reveals ${\mathrm{BaMnO}}_3$ bands near the Fermi level with a significant magnetic moment per Mn atom and a decent ordering temperature. Further, the ${\mathrm{BaMnO}}_3$ bands in the heterostructure exhibit linear Rashba interaction with a sizable Rashba coefficient, owing to its proximity to ${\mathrm{KTaO}}_3$. Our work can motivate future research by demonstrating the road map to proximity-induced Rashba interaction for antiferromagnetic spintronics.

The present study revisits the lattice stability of pure Cr in BCC, FCC, and HCP structures using ab initio calculations with PBE and ${\mathrm{r}}^2\mathrm{SCAN}$ functionals. A key advance is that ${\mathrm{r}}^2\mathrm{SCAN}$ directly captures stable antiferromagnetic (AFM) states at equilibrium volume without auxiliary techniques such as warm-start calculations (WSCs), while PBE often fails to maintain magnetic order. In addition, phonon calculations show that AFM configurations eliminate imaginary modes in FCC and HCP Cr, enabling reliable quasi-harmonic free-energy evaluations. The resulting temperature-dependent lattice stabilities agree markedly better with SGTE/CALPHAD values. Finally, the analysis of Cr-X $(X=\mathrm{Fe}, \mathrm{Ni}, \mathrm{Co})$ FCC solid solutions reveals characteristic local distortions and AFM spin arrangements on Cr sites in Cr-rich phases. Using relaxed AFM FCC-Cr as the end-member reference significantly improves agreement between ab initio mixing and formation enthalpies and CALPHAD assessments, indicating that AFM-based lattice stabilities of Cr should be adopted as the physically consistent reference for thermodynamic modeling.

We report reproducible magnetization anomalies appearing below room temperature in copper-doped apatite materials belonging to the LK-99 family synthesized via hydrothermal methods. These anomalies are observed consistently across samples prepared under comparable conditions. Although the extracted Mydosh parameter lies within the range often associated with vortex-glass behavior in superconductors, a detailed analysis of DC magnetization, AC susceptibility, field dependence, and magnetic memory effects demonstrates that the observed phenomena are not related to superconductivity. Instead, the data are consistent with glassy magnetic freezing of interacting clusters. Compositional and structural analysis identifies covellite (CuS), one of the constituent phases in these multiphase materials, as the primary origin of the observed behavior. Our results clarify the magnetic origin of LK-99-related anomalies and highlight the importance of phase complexity in interpreting apparent superconducting signatures in this family of materials.

We explore the limitations of using imbalance dynamics as a diagnostic tool for many-body localization (MBL) and show that spatial averaging can mask important microscopic features. Focusing on the strongly disordered regime of the random-field XXZ chain, we use state-of-the-art numerical techniques (Krylov time evolution and full diagonalization) to demonstrate that site-resolved spin autocorrelators reveal a rich and complex dynamical behavior that is obscured by the imbalance observable. By analyzing the time evolution and infinite-time limits of these local probes, we reveal resonant structures and rare local instabilities within the MBL phase. These numerical findings are supported by an analytical, few-site toy model that captures the emergence of a multiple-peak structure in local magnetization histograms, which is a hallmark of local resonances. These few-body local effects provide a more detailed understanding of ergodicity-breaking dynamics, and also allow us to explain the finite-size effects on the long-time imbalance, and its sensitivity to initial conditions in quench protocols. Overall, our experimentally testable predictions highlight the necessity of a refined, site-resolved approach to fully understand the complexities of MBL and its connection to rare-region effects.

${\mathrm{CeTe}}_3$ is a van der Waals antiferromagnet composed of magnetic ${\left[\mathrm{CeTe}\right]}^{+}$ layers coupled to highly conducting ${\mathrm{Te}}^{0.5-}$ square nets. Its simple quasi-two-dimensional electronic structure and cleavable nature make it an appealing platform for exploring correlated magnetism in reduced dimensions. To clarify the nature of its low-temperature state, we performed single-crystal neutron diffraction down to 0.3 K, complemented by scanning tunneling microscopy. A magnetic transition near 1.5 K gives rise to incommensurate Bragg peaks at $q_{\pm }\sim (\pm 0.17,0,0.31)$, consistent with a double-$q$ magnetic order whose moments are predominantly aligned along the $c$ axis. The strongly reduced ordered moment is consistent with enhanced quantum fluctuations driven by $c\text{−}f$ hybridization, while the deviation of the propagation vectors from simple nesting suggests a coupling to residual charge-density-wave instabilities of the quasi-one-dimensional Te-derived bands. These results indicate that ${\mathrm{CeTe}}_3$ hosts a correlated magnetic ground state where spin and itinerant charge degrees of freedom are intimately linked in the van der Waals limit.

Quantum interference of electrons in disordered conductors is a sensitive probe of the internal structure of quasiparticles, revealing universal signatures of symmetry through weak localization (WL) and weak antilocalization (WAL). While these phenomena are well understood for conventional Schrödinger and Dirac-Weyl fermions, their fate in the broader class of multifold chiral fermions remains largely unexplored. We develop a unified framework for semiclassical transport and quantum interference in three-dimensional disordered fermions with an arbitrary pseudospin $s$. Starting with a general short-range matrix disorder $\mathcal{M}$, we derive compact expressions for elastic lifetimes and ladder vertex corrections for arbitrary pseudospin with multiband effects. We then show that, in the scalar-disorder limit, while the Drude conductivity is strongly pseudospin and helicity dependent, the leading quantum-interference correction exhibits a striking universality: its magnitude remains identical to that of conventional diffusive metals and Weyl fermions, while its sign is determined solely by the parity of $2s$, placing half-integer pseudospins in the symplectic class (WAL) and integer pseudospins in the orthogonal class (WL). We also analyze the role of interband and intervalley scattering for $s=3/2$. By solving the resulting coupled Bethe-Salpeter equations, we demonstrate that channel mixing suppresses WAL and drives a crossover toward localization. Our results establish a general theory of localization across the full pseudospin hierarchy, revealing the interplay between internal geometry, symmetry class, and transport universality.

Janus engineering provides a promising route for converting two-dimensional (2D) antiferromagnets into altermagnets, yet the implications of the resulting symmetry breaking and built-in electric field remain poorly understood. Using first-principles calculations, we identify Janus $\mathrm{M}{\mathrm{n}}_2{\mathrm{P}}_2{X}_3{Y}_3$ ($X\ne Y=\mathrm{S}$, Se, Te) monolayers as a multifunctional 2D altermagnetic platform. We find that the built-in electric field induces a valley-contrasting Rashba effect, which we elucidate through a $k·p$ model incorporating the second-order spin-orbit coupling term. Crucially, spin-group symmetry enforces spatial decoupling of charge and pure spin shift currents, allowing dynamic switching of their directions via light polarization. Furthermore, strain engineering drives a semiconductor-to-metal transition in telluride members, accompanied by subsequent magnetic easy axis reorientation. Our study establishes $\mathrm{M}{\mathrm{n}}_2{\mathrm{P}}_2{X}_3{Y}_3$ monolayers as theoretical platforms for exploring tunable optospintronic and valleytronic physics, and provides symmetry-based design strategies for future practical device applications.

The tunneling valley Hall effect (TVHE) provides high-efficiency conversion from charge to valley, which is crucial to valleytronic devices. Recently, TVHE in two-dimensional junctions has attracted increasing attention. Here, we comprehensively study the TVHE and other tunneling Hall effects in monolayer $1T^{\prime }\text{−}{\mathrm{MoS}}_2$ (TMS) junctions. Monolayer TMS, a representative two-dimensional transition-metal dichalcogenide, hosts gapped and tilted Dirac fermions with spin splitting tunable by an out-of-plane electric field. The tunneling Hall effects for valley and other degrees of freedom reflect the evolution of the unique electronic structure featured by the reversible spin splitting and the topological transition. For the monolayer TMS at zero electric field, the intrinsic valley Hall effect is absent due to the opposite spin Berry curvature in each valley, which makes the TVHE the dominant valley Hall mechanism for valleytronic applications. We further demonstrate the resonant enhancement of TVHE through the transmission pattern and show the electrically tunable high conversion ratio. For the monolayer TMS at nonzero electric field, the TVHE is closely related to the tunneling spin Hall effect due to the valley-spin locking, whose sign and magnitude changes can be used to distinguish the direction of the spin splitting and to provide an indirect signature for the topological transition, respectively. For the tunneling charge Hall effect, a universal conversion ratio is analytically derived and numerically confirmed. This study provides a comprehensive understanding of tunneling Hall effects in monolayer TMS junctions and provides an opportunity for two-dimensional transition-metal dichalcogenides in valleytronics and spintronics.

First-principles analysis of the spectroscopic signatures of correlated quantum materials poses significant challenges due to the interplay between spin-orbit and vibronic couplings, as well as the need to describe both dynamic and static electron correlation to reach decent accuracy. In this work, we apply the equation-of-motion coupled-cluster (EOM-CC) method to derive the spin-orbit-lattice entangled vibronic states and predict the Re $L_3$ edge resonant inelastic x-ray scattering (RIXS) spectra of ${\mathrm{Ba}}_2{\mathrm{MgReO}}_6$. The EOM-CC yields interaction parameters in close agreement with those extracted from RIXS spectra, with errors of less than 5%. In particular, the EOM-CC method allowed us to determine the weak vibronic coupling to the $T_{2g}$ vibrations, which is difficult to address experimentally. The simulated spectra indicate that vibronic coupling to the $T_{2g}$ modes gives rise to a shoulder on the elastic peak. Going beyond the conventional treatment, which focuses solely on $E_g$ modes, we show that vibronic couplings to both $T_{2g}$ and $E_g$ modes are required to account for the fine structure of the RIXS spectra. This work demonstrates that the EOM-CC method is a powerful tool for accurately predicting the complex local states at metal sites and spectroscopic signatures of correlated insulating materials.

Typical finite-energy-density eigenstates of nonintegrable systems are expected to obey the eigenstate thermalization hypothesis and to reproduce thermal local observables. In integrable systems, typical states are instead finite-entropy Bethe macrostates, or generalized Gibbs ensembles, with smooth quasiparticle occupations. Here we show that the spin-$\frac{1}{2}$ XXX Heisenberg chain contains an exactly solvable exception. By biasing mutually commuting conserved charges, we use the ground state of a selector Hamiltonian to construct rare eigenstates of the undeformed XXX Hamiltonian. These states are atypical, ordered, chiral, current-carrying, critical, zero-entropy Bethe macrostates at tunable XXX energy densities. They lie outside the finite-entropy manifold dominating generalized Gibbs ensembles, yet remain exact XXX eigenstates with sharp Bethe occupations, finite scalar chirality, nonthermal local observables, and gapless Luttinger-liquid correlations. A finite-interval thermodynamic Bethe ansatz reveals an asymmetric chiral Bethe sea whose zero-field limit selects an extensive spin sector through $SU\left(2\right)$ symmetry breaking. A commuting exchange bias moves the same ordered macrostate through the full thermodynamic XXX energy band, including its Hilbert-space trace center. Finite-size DMRG and exact-diagonalization benchmarks indicate that the magnetochiral signatures persist under weak integrability breaking over prethermal time scales. The construction provides a controlled integrable realization of ETH-violating, scar-like large-deviation eigenstates and a route to ordered critical matter deep inside a many-body spectrum.

The crossing points in band structures play an important role in several physical phenomena. In this paper, we focus on the group information of these crossing points, rather than on the specific $k·p$ models. Specifically, each crossing point can be described by a matrix group and the corresponding set of basis functions. We identify the minimal abstract group that captures all the essential information regarding the crossing point, and then decompose the matrix representation into irreducible representations (irreps) using orthogonality relations. The abstract group and irrep coefficients can be regarded as crossing point indicators. Such indicators are independent of the specific representation matrices and lattice coordinates. As an example, we applied our method to charge-1 Weyl points in 1651 magnetic space groups. We found that although as many as 9988 distinct Hamiltonians may exist before classification, they can ultimately be reduced to only nine abstract groups and 18 distinct symmetry indicators. This significantly reduces the complexity of identifying and characterizing crossing points in band structures. Our findings provide an algebraic classification of crossing points in band structures, which significantly simplifies the analysis and prediction of topological semimetals.

Altermagnets are a class of metallic magnets characterized by spin-split electron bands. As antiferromagnets they lack spontaneous bulk magnetization. The initial description of the momentum-dependent spin splitting of electron bands in altermagnets was based on the spin-group approach, which is valid when relativistic interactions are neglected. Then, spin-orbit coupling has been taken into account in accordance with time-reversal-odd, even-parity irreducible representations of centrosymmetric point groups considered by Fernandes et al. [Phys. Rev. B 109, 024404 (2024)]. Here, we show the inadequacy of this formal approach. The problem of electron band splitting should be discussed based on the crystal symmetry of a concrete altermagnet material. The band spin splitting in the hexagonal altermagnet CrSb is established using the magnetic group formalism that allows the discovery of the additional spin splitting missed in the frame of the exchange approximation. Another type of spin splitting takes place in so-called hidden altermagnets. These types of materials do not possess symmetry with respect to space and time inversion but are symmetric with respect to the product of these operations known as toroidal symmetry. Real-space spin splitting in materials with toroidal symmetry is demonstrated.

Recent experiments engineered special spin-degenerate Andreev bound states in atomic cages of adatoms on superconductors, the Machida-Shibata states, a promising building block for quantum matter. Here, we investigate the formation of time-reversal symmetric bands by hybridizing multiple such states and analyzing their electronic topological properties assuming small on-site electron repulsion. The low-energy theory shows that competing emerging singlet and triplet superconducting pairings drive the formation of topologically nontrivial phases in symmetry class DIII. Therefore, we predict that Kramers pairs of Majorana zero modes will appear at the ends of Machida-Shibata chains, while two-dimensional lattices will host helical Majorana edge modes. Additionally, we discover extended regions in the Brillouin zone with vanishing superconducting pairings, which are lifted by the repulsive electron interactions. Our findings offer new perspectives for manipulating topological superconductivity and pairings in nonmagnetic adatom systems.

The current through a small contact between two 2D regions is theoretically studied. The electron gas viscosity that arises due to electron-electron and electron-impurity scattering is considered. It is found the electron flow corresponds to the ideal Fermi-liquid model rather than the ideal gas one at strong viscosity. It is shown that an electron density inhomogeneity results in the finite contact resistance of the almost ideal flow of the electron gas. The temperature dependence of the resistance is found. The agreement between theory and experiment is discussed.

We report the formation of large-scale steady-state whirlpools in a GaAs-based two-dimensional electron liquid and demonstrate them by straightforward transport measurements. A whirlpool forming inside a circular cavity adjoining a wide conducting channel appears as a negative four-terminal resistance over a broad range of temperatures and cavity sizes. The effect scales with the Gurzhi length, in quantitative accord with the hydrodynamic analogy. Obtained results firmly establish this analogy and probe the limits of its applicability.