We investigate ($3+1$)d topological orders (TOs) in fermionic systems with anomalous ${\mathbb{Z}}_{2N}^F$ symmetry, where its ${\mathbb{Z}}_2^F$ subgroup is the fermion parity. Such an anomalous symmetry arises as a discrete subgroup of the chiral U(1) symmetry of $\nu$ copies of Weyl fermions of the same chirality. Inspired by the crystalline correspondence principle, we deform the anomalous ${\mathbb{Z}}_{2N}^F$ symmetry of a (3 + 1)d Weyl fermion to the anomalous $C_N\times {\mathbb{Z}}_2^F$ symmetry. Then we microscopically construct symmetry preserving gapped boundary states of the closely related ($4+1$)d $C_N\times {\mathbb{Z}}_2^F$ symmetry protected topological state (with $C_N$ being the $N$-fold rotation), whenever it is possible. For $\nu =N$, we show that the ($3+1$)d symmetric gapped state admits a topological ${\mathbb{Z}}_4$ gauge theory description at low energy and propose that a similar theory saturates the corresponding ${\mathbb{Z}}_{2N}^F$ anomaly. For $N\nmid \nu$, our construction admits no topological quantum field theory (TQFT) symmetric gapped state; while for $\nu =N/2$, we find a non-TQFT symmetric gapped state via stacking lower-dimensional ($2+1$)d non-discrete-gauge-theory TO inhomogeneously. For other values of $\nu$, no symmetric gapped state is possible within our construction, which is consistent with the no-go theorem by Cordova-Ohmori.

Anisotropic magnetoresistance (AMR) plays a critical role in spintronic memory and magnetic sensing devices. Although AMR is generally weak in bulk magnets, it is markedly enhanced in two-dimensional systems. However, its systematic evolution with dimensionality remains largely unexplored. Here we investigate the dimensional dependence of AMR in the van der Waals antiferromagnet ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ using density functional theory and Wannier-interpolated Boltzmann transport methods. Our results reveal a pronounced increase in the out-of-plane AMR as the sample thickness decreases, rising from 19.57% in the bulk to 42.93%, 52.17%, and 60.97% in the trilayer, bilayer, and monolayer, respectively. We uncover a mechanism governing this evolution: magnetization reorientation modulates the out-of-plane orbital hybridization between Bi and Te atoms, an effect that is strongly enhanced in thinner samples. This orbital hybridization variation directly tunes the spin-orbit coupling strength, leading to considerable band splitting that depends critically on the magnetization direction. Our work provides a unified microscopic understanding of dimension-dependent AMR and establishes ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ as a promising platform for designing tunable spintronic devices.

Bound states in the continuum (BIC) have emerged as an effective platform for realizing vibrational strong coupling (VSC) in the midinfrared spectrum because of their highly localized electric field and extremely low optical loss. However, the traditional VSC system based on quasi-BIC (QBIC) is constrained by the static structure design, lacking real-time control capabilities, which severely limits its practical application potential. Here, we proposed a chiral metasurface constructed by the phase-change material ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ (GST) and successfully realized a chiral QBIC mode with circular dichroism (CD) value reaching 0.99 by synergistically breaking in-plane and out-of-plane symmetries. We achieved strong coupling between chiral QBIC modes and molecular vibrations for the first time by integrating a PMMA molecular layer onto the metasurface, observing the Rabi splitting of 13 meV. Using the coupled oscillator model, we revealed the coupling strength of the hybrid system and the evolution of the chiral QBIC mode and molecules in the vibrational polariton. We also demonstrated dynamic tuning of coupling strength through phase transitions between crystalline and amorphous states of GST materials, which originates from the positive correlation between electric field intensity of chiral QBIC modes and the volume fraction $f$ of GST. Notably, the chiral strong coupling system exhibits coherent energy exchange processes exceeding 2000 fs (approximately six Rabi cycles), which is significantly longer than that observed in conventional plasmonic systems. Our studies not only deepen the understanding of chiral light-matter interactions but also provide a universal platform for developing chiral quantum optoelectronic devices in the midinfrared frequency range.

Van der Waals heterostructures of transition metal dichalcogenides offer a versatile platform for valleytronic applications, owing to their spin-valley locking and layer-dependent optical selection rules. Here, we demonstrate the twist-angle-controlled helicity switching of interlayer exciton (IX) emission by showing that the polarizations of the IX photoluminescence can be engineered by altering the stacking geometry of ${\mathrm{WS}}_2/{\mathrm{WSe}}_2$ heterobilayers. It is also found that a sufficiently large ($\sim 5\text{T}$) out-of-plane magnetic field can enhance the polarization degree of the IX emission up to $\sim 60\%$, which enables controlled valley population imbalance of the IXs. The findings establish twist angle as a control knob for IX helicity and highlight magnetic fields as an efficient means of reinforcing valley polarization, paving the way toward valley and twist-angle based optoelectronic devices.

The Moiré superlattices in twisted two-dimensional materials give rise to extraordinary electronic and thermal properties. While twist-angle tuning has been extensively explored for electronic applications, its synergistic effects with substrate coupling on thermal transport remain less understood. This study decouples the distinct roles of in-plane and out-of-plane phonons in the thermal conductivity of twisted bilayer graphene supported by a substrate. We demonstrate that increasing the twist angle enhances the inhomogeneity of the local stacking structure at small angles, leading to a rapid decrease in the contribution of out-of-plane phonons. In contrast, the in-plane phonon contribution exhibits remarkable structural stability, showing only minor variation. Furthermore, substrate coupling induces a pronounced layer-dependent modulation: The out-of-plane phonon contribution in the substrate-adjacent layer (Layer 2) is significantly suppressed due to constrained vibrations, while its in-plane contribution is enhanced by a more uniform stress distribution. Through atomic-scale analysis of interaction energies and stress, we spatially identify the primary scattering centers: AA stacking and saddle point (SP) stacking domains for out-of-plane phonons, and SP domains for in-plane phonons. These findings elucidate the synergistic mechanism by which twist angle and substrate coupling regulate thermal transport, providing crucial theoretical guidance for the design of thermal management systems and functional devices based on twisted two-dimensional materials.

Flat bands (FBs) and Dirac cones represent two distinctive features of topological electronic systems; however, a unified mechanism enabling transitions between them has remained elusive to date. Here, we demonstrate a symmetry-governed and tunable transition from flat bands to Dirac cones in AB-stacked bilayer kagome lattices. This transition is mediated by the interplay among destructive quantum interference (DQI), $C_3$ rotational symmetry, and spatial inversion symmetry. Strong interlayer coupling enhances DQI and stabilizes compact localized states that produce FBs, while weaker coupling allows $C_3$ and inversion symmetries to dominate, giving rise to robust Dirac nodal points. Using a minimal tight-binding model, we map the continuous evolution of topological states, including type-II and type-III Dirac cones, spin-1 Dirac cones, and partial flat bands, as a function of interlayer coupling. We further demonstrate this transition mechanism by examining an AB-stacked bilayer derived from the experimentally synthesized ${\mathrm{Nb}}_3{\mathrm{TeCl}}_7$ structure. In particular, first-principles calculations on bilayer ${\mathrm{Nb}}_3{\mathrm{TeCl}}_7$ reveal that vertical strain (or pressure) modulates the interlayer interactions, enabling the full FB-Dirac cone transition sequence.These findings establish a realistic pathway for gaining deeper insight into flat-band physics and for engineering tunable topological phases in two-dimensional materials.

The non-Hermitian skin effect (NHSE) fundamentally invalidates the conventional bulk-boundary correspondence (BBC), leading topological diagnostics into a crisis. While the non-Bloch polarization $P_{\beta }$, defined on the generalized Brillouin zone, successfully captures momentum-space topology, a purely real-space characterization of non-Bloch topology has remained unclear. In this work, we establish a correspondence between $P_{\beta }$ and the entanglement polarization $\chi$ of the biorthogonal ground state, understood as a geometric and entanglement-based indicator rather than a physical electric polarization. By introducing a quasireciprocal Hamiltonian $\tilde{H}$, which removes the NHSE while preserving bulk spectrum and topology, we rigorously prove the fundamental identity $P_{\beta }\equiv \chi \left(\tilde{H}\right)(mod1)$ in the thermodynamic limit under the quasilocality assumption. Crucially, we demonstrate that this equivalence transcends the locality constraints that limit traditional topological invariants. While the conventional Resta polarization fails when $\tilde{H}$ becomes nonlocal due to the divergence of position variance, we reveal that $\chi \left(\tilde{H}\right)$ remains robustly quantized, protected by the Fredholm index of Toeplitz operators. Our work thus identifies entanglement as the unique real-space diagnostic capable of capturing non-Bloch topology beyond the breakdown of locality, successfully restoring the BBC across diverse non-Hermitian systems such as line-gap, point-gap, and gapless phases, thereby unifying the geometric and entanglement paradigms in non-Hermitian physics.

Whether short-range electron pairing can be stabilized in graphene remains a central question because pristine graphene is a semimetal with vanishing density of states at the Dirac point. We show that geometry alone can enhance short-range pairing correlations in confined graphene. Using real-space quantum Monte Carlo with correlated trial wavefunctions, we control a simple geometric knob, the commensurability of the simulation cell with the Dirac points, which creates or removes a small, single-particle gap in finite graphene samples. Diffusion quantum Monte Carlo reveals a clear dichotomy, when this geometry-induced gap is present, a resonance-valence-bond(RVB)-like state is energetically favored. Whereas when the spectrum is gapless and cell includes the Dirac points, no RVB energy gain is found. The effect persists in large cells at fixed geometry, establishing that confinement and commensurability can tip the energetic balance toward singlet pairing, while pristine bulk graphene shows no intrinsic RVB instability. These results identify a practical, geometry-controlled route to amplify pairing tendencies in nanoscale graphene devices and provide many-body benchmarks for interpreting finite-cell ab initio calculations. Our results also suggest design principles, via shape, aspect ratio, or mild superlattice modulations, to engineer stronger electronic correlations in carbon-based nanoelectronics.

The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of boundary states with nonzero topological invariants in the bulk. Widespread attention has been paid to extending topological phases to nonlinear and non-Hermitian systems. However, the BBC and topological invariants of non-Hermitian nonlinear systems remain largely unexplored. Here, we establish a complete BBC and topological characterization of the topological phases in a class of non-Hermitian nonlinear-eigenvalue systems by introducing an auxiliary system. We restore the BBC broken by non-Hermiticity via employing the generalized Brillouin zone on the auxiliary system. Remarkably, we discover that the interplay between non-Hermiticity and nonlinearity creates an exotic complex-band topological phase that coexists with the real-band topological phase. Our results enrich the family of nonlinear topological phases and lay a foundation for exploring novel topological physics in metamaterial systems.

Amorphous graphene (a-G), the disordered counterpart of crystalline graphene (c-G), holds promise for flexible electronics, catalysis, and energy storage, yet its atomic-scale structure and property origins remain elusive. Here, we introduce a helium potential-wall method within ab initio molecular dynamics accelerated by machine-learning force fields to enable stable melt-quench simulations of two-dimensional (2D) a-G. We generate 100 statistically representative models that ensure convergence of calculated properties. Structural analysis unveils a buckled, ${\mathit{sp}}^2$-hybridized continuous random network dominated by five- to eight-membered rings, with a mean bond length of 1.43 Å and broadened bond-angle distributions mainly spanning ${108}^{\circ }–{135}^{\circ }$. Electronically, disorder induces $p_x/p_y$ mixing near the Fermi level, resulting in localized $\pi$ states and a pronounced reduction of in-plane conductivity compared to crystalline graphene, as revealed by the Kubo-Greenwood formalism, with a consistent qualitative trend across representative configurations. Mechanically, ensemble-averaged stiffness yields a Young's modulus $\overline{E}\approx 315$ N/m ($\sim 7\%$ lower than c-G) and shear modulus $\overline{G}\approx 133$ N/m ($\sim 10\%$ lower), indicating a disorder-induced flexibilization of the network and macroscopic in-plane isotropy. This framework elucidates disorder's role in governing a-G properties and provides a transferable protocol for exploring other 2D amorphous materials.

Magnetoelastic coupling plays a crucial role in magnetic-field-induced transitions in anisotropic ferromagnets. Ultrasonic methods are suitable for experimental investigations of these phenomena. We investigate elastic constants in ${\mathrm{EuAl}}_{12}{\mathrm{O}}_{19}$, a quasi-two-dimensional anisotropic ferromagnet, by measuring sound velocity in magnetic fields perpendicular to spontaneous magnetization. The shear modulus $C_{44}$ exhibits dramatic softening at the field-induced transition from the ferromagnetic to a paramagnetic phase with magnetic moments forced to polarize along the applied transverse field. The softening is attributed to strong magnetic fluctuations near a second-order phase transition. Theoretical calculations based on magnetization data qualitatively reproduced the observed behavior within a strain-exchange mechanism. These results demonstrate that magnetoelastic coupling in ${\mathrm{EuAl}}_{12}{\mathrm{O}}_{19}$ arises primarily from exchange striction and provide a framework for modeling similar transitions in other anisotropic ferromagnets.

Color centers in diamond provide a possible hardware for quantum computation, where the most basic quantum information processing unit are nitrogen-vacancy (NV) centers, each in contact with adjacent carbon nuclear spins. With specifically tailored dynamical decoupling sequences, it is possible to execute selective, high-fidelity two-body gates between the electron spin of the NV center and a targeted nuclear spin. In this work, we present a method to determine the optimal execution time that balances the trade-off between fidelity and execution speed for gates generated by adaptive XY sequences. With these optimized gates, we use the nuclear spin environment as a code space for quantum error correction within a color center register.

Efficient numerical routines are developed for numerical studies of the dependence of the equilibrium magnetic states, excitations, and microwave power absorption on temperature and composition in transition-metal/rare-earth ferrimagnets, including the reversal of the Néel vector occurring on both temperature and the concentration of the rare-earth atoms. It results in a drastic change in the behavior at the magnetization and angular-momentum compensation points. Dominant uniform oscillation modes are obtained numerically by computing the magnetization correlation function. They are compared with the analytical solution, which is analyzed in detail. The fluctuation-dissipation theorem is used to compute the frequency dependence of the absorbed microwave power. A good agreement with analytical results is demonstrated. Disorder caused by random positions of rare-earth atoms in a diluted rare-earth system leads to multiple localized modes that converge into broad absorption maxima as the size of the system increases. The power absorption integrated over frequency exhibits a minimum at the compensation point.

We performed muon spin rotation and relaxation ($\mu \mathrm{SR}$) experiments to investigate the microscopic mechanism behind the high ionic conductivity ($\sigma$) exhibited by hydride (${\mathrm{H}}^{-}$) ions in lanthanum hydroxide ${\mathrm{LaH}}_{3-2x}{\mathrm{O}}_x$. The $\mu \mathrm{SR}$ spectra observed at 5–300 K in a sample with $x\approx 0.25$ consist primarily of two components, which are attributed to muons occupying tetrahedral (Tet) and octahedral (Oct) sites common to ${\mathrm{H}}^{-}$. The spectra also indicate that muons at the Oct sites (${\mathrm{Mu}}_{\mathrm{O}}$) appear nearly stationary in the timescale of $\mu \mathrm{SR}$ ($\approx {10}^{-5}\mathrm{s}$), whereas those at the Tet sites (${\mathrm{Mu}}_{\mathrm{T}}$) are subject to the fluctuating local fields. The cusp-like peak in the fluctuation rate around 160 K and the decrease in linewidth at higher temperatures probed by ${\mathrm{Mu}}_{\mathrm{T}}$ suggest that the jump motion of both ${\mathrm{Mu}}_{\mathrm{T}}$ (via the vacant Oct sites) and surrounding Oct-site ${\mathrm{H}}^{-}$ contributes to spin relaxation and to a widely distributed fluctuation frequency. These results indicate that the implanted Mu behave as ${\mathrm{Mu}}^{-}$ and that the jump motion of ${\mathrm{Mu}}^{-}/{\mathrm{H}}^{-}$ is restricted by the availability of nearby vacant sites. On the other hand, the activation energy for the jump is estimated to be 0.11(3) eV, which is significantly different from $\approx 1.3\mathrm{eV}$ evaluated from the temperature dependence of $\sigma$ at high temperatures ($\gtrsim 400\mathrm{K}$). In our attempt to resolve this discrepancy, we discuss problems inherent in interpreting $\sigma$ using the Arrhenius equation, and demonstrate that the behavior of ${\mathrm{H}}^{-}$ ions can be better explained as a viscous fluid exhibiting a glass transition.

The search for new quantum spin liquid materials relies on systems with strong frustration such as spins on an ideal kagome lattice. However, lattice imperfections can have substantial effects which are as yet not well understood. In recent work, the two-dimensional kagome system ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_6\left[{\left({\mathrm{Cl}}_x{\mathrm{Br}}_{(1-x)}\right)}_{3-y}{\left(\mathrm{OH}\right)}_y\right]$ has emerged as a leading candidate hosting a Dirac spin liquid which appears to survive at least for $x<0.4$, associated with alternating-bond-hexagon (ABH) disorder. Here in magnetic samples with $x=0.58,y=0.1$ we report unusual in-plane ferromagnetic canting (FM) of the in-plane antiferromagnet (AFM), with an unusually wide regime of short-ranged order, and propose theoretical models to explain this behavior. First, we show that Kitaev-type exchanges naturally arise on the kagome lattice to second order in the known Dzyaloshinskii-Moriya exchanges, and that these interactions can produce the unusual in-plane FM canting from antichiral AFM. Second, we propose a phenomenological model of weakly FM-canted spin clusters to describe the short-ranged regime and analyze quantum fluctuations in an ABH toy model to show how ABH disorder can stabilize this regime. The combination of experimental observation and theory suggests that kagome-Kitaev interactions and ABH disorder are necessary for describing the magnetic fluctuations in this family of materials, with potential implications for the proposed proximate spin liquid phase.

We investigate the role of four-spin interactions in stabilizing multiple-$Q$ topological spin textures and demonstrate their ability to realize a skyrmion crystal. While such higher-order interactions are known to be important, their intricate nature makes systematic model construction challenging. To address this issue, we develop a theoretical framework that connects microscopic real-space four-spin couplings to their effective interactions in momentum space, providing a clear route to engineer target magnetic phases. Applying this framework to a frustrated Heisenberg model with designed four-spin interactions, we identify the stabilization of the zero-field skyrmion crystal with a skyrmion number of two per magnetic unit cell via simulated annealing. Furthermore, our momentum-space analysis reveals the intrinsic mechanism by which the well-known ring-exchange interaction also favors the skyrmion crystal. Our findings not only present a concrete model for a higher-order skyrmion crystal but also offer a general methodology for understanding and designing a wide range of complex multiple-$Q$ magnetic orders driven by multispin interactions.

Bright localized structures in incoherently pumped exciton-polariton condensates are generally challenging to realize under uniform pumping. We propose an experimentally accessible method to generate self-localized solitonlike peak using finite-sized uniform pumping. By using a homogeneous condensate generated through large-area pumping as the initial state, localized waves emerge from the boundaries and converge toward the center, forming a stable, high-intensity localized structure on the condensate background. This self-localization is enabled by the delicate balance between gain and loss inherent to exciton-polariton condensates, allowing for higher condensate densities even at relatively low pumping strengths due to boundary-induced effects. Our results extend the range of soliton solutions to regimes where homogeneous condensates are weakly stable or weakly unstable. Furthermore, the intensity, width, and stability of the solitonlike peak can be tuned through the strength and the shape of the pump beam, as well as other key system parameters, providing a practical pathway for controlled manipulation. Our findings hold for both one-dimensional and two-dimensional configurations, offering insights into nonlinear dynamics and interaction mechanisms in nonequilibrium systems.

The spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on the pyrochlore lattice (PAFH) is arguably the most well-known strongly frustrated quantum magnet in three spatial dimension. However, because of the rapid scaling of Hilbert space with the linear size of such a three-dimensional system, most previous studies of this model are conducted on rather small clusters and the nature of its ground state in the thermodynamic limit remains elusive after about 30 years of intense debate. Here, we apply a recently developed powerful algorithm to perform large-scale unrestricted variational optimization of the ground state of the spin-$\frac{1}{2}$ PAFH from the perspective of the resonating valence bond (RVB) theory. The largest cluster that we have attempted contains as many as 2048 sites and the corresponding variational wave function contains as many as 16 777 216 variational parameters. Through such a large-scale variational optimization, we find a highly competitive candidate ground state for the spin-$\frac{1}{2}$ PAFH. This state features a maximally resonating valence bond crystal (VBC) pattern with $2{\vec{a}}_1\times 2{\vec{a}}_2\times 2{\vec{a}}_3$ periodicity. There are at least four levels of hierarchical structure in such a VBC state, with the first and the second level of hierarchy related to the breaking of the inversion and the translational symmetry. As a result, there is strong disparity in the extent of ice rule violation between up and down tetrahedrons in this state. Intriguingly, we find that within the RVB framework such a maximally resonating VBC state is almost degenerate with a recently proposed VBC state obtained from dressing hard hexagon covering of the pyrochlore lattice, although the extent of ice rule violation is totally uniform in the latter case. We find that further symmetry breaking will occur in the dressed hard hexagon VBC state under unrestricted optimization. In particular, strong disparity in the extent of ice rule violation for up and down tetrahedrons will also emerge in this state. We show that the maximally resonating VBC state found here will be favored by a tiny next-neighboring exchange coupling over the dressed hard hexagon VBC state.

We investigate the periodic Anderson model composed of an itinerant $c$ band and a strongly localized $f$ band, featuring on-site electron-electron interactions in the $f$ orbitals. The two bands interact via a hybridization term with spin-orbit coupling, which enables spin-flip processes. In the noninteracting limit, these profoundly alter the electronic structure, leading to the emergence of flat bands, van Hove singularities, and, most notably, Dirac cones within a single Kondo-Dirac semimetal order. The strongly interacting regime is explored via the determinant quantum Monte Carlo method, in the absence of the sign problem, where we unveil a complete ground-state phase diagram revealing two distinct phases, the Kondo-Dirac semimetal phase and a novel antiferromagnetic semimetal phase. Their characterization by the spectral functions establishes an orbital-selective Mott transition in the antiferromagnetic semimetal phase, marked by the opening of a gap exclusively in the $f$ orbital while Dirac cones persist in the $c$ orbital. Conversely, in the Kondo-Dirac semimetal phase, both $c$ and $f$ orbitals sustain robust Dirac cones. We establish that spin-orbit coupling in the hybridization term gives rise to Dirac cones, which, combined with additional symmetry-breaking conditions, can generate novel topological states.

Numerical simulations of strongly correlated fermions at finite temperature are essential for studying high-temperature superconductivity and other quantum many-body phenomena. The recently developed tangent-space tensor renormalization group (tanTRG) provides an efficient and accurate framework by representing thermal density operators as matrix product operators. However, the particle number generally varies during the cooling process. The conventional strategy of fine tuning chemical potentials to reach a target filling is computationally demanding. Here we propose a fixed-$N$ tanTRG algorithm that stabilizes the average particle number by adaptively tuning the chemical potential within the imaginary-time evolution. We benchmark its accuracy on exactly solvable free fermions, and further apply it to the square-lattice Hubbard model. For hole-doped cases, we study the temperature evolution of charge and spin correlations, identifying several characteristic temperature scales for stripe formation. Our results establish fixed-$N$ tanTRG as an efficient and reliable tool for finite-temperature studies of correlated fermion systems.