Recent studies have proposed Majorana polarization as a diagnostic tool for identifying topological Majorana bound states (MBS) in engineered $p$-wave heterostructures. In this work, we analyze the behavior of Majorana polarization in two systems: a one-dimensional semiconducting nanowire and a quasi-one-dimensional semiconducting system, both subject to Rashba spin-orbit coupling, proximity-induced superconductivity, and disorder. Our analysis shows that Majorana polarization provides valuable information on the spatial structure of low-energy states, but by itself does not fully differentiate true topological MBS from partially separated Andreev bound states (psABS) or quasi-Majorana modes in realistic disordered systems. While earlier literature proposes that true topological MBS must satisfy the condition ${\mathcal{P}}_{\mathrm{left}}^{*}·{\mathcal{P}}_{\mathrm{right}}\approx -1$, where ${\mathcal{P}}_{\mathrm{left}}$ and ${\mathcal{P}}_{\mathrm{right}}$ denote the Majorana polarizations in the left and right halves of the wire, it is well-established that two additional criteria must also be met for the identification of topological MBS and their applicability in topological quantum computation: the presence of a topological band gap and the localization of wave functions at the edges. We identify scenarios where the condition ${\mathcal{P}}_{\mathrm{left}}^{*}·{\mathcal{P}}_{\mathrm{right}}\approx -1$ is satisfied without fulfilling the two additional conditions mentioned above. Our conclusions remain robust irrespective of the chosen definition of Majorana polarization, whether based on the chiral or the particle-hole framework. Taken together, our results place Majorana polarization within a broader set of complementary diagnostics and provide clear guidelines for reliably distinguishing true MBS from trivial modes in disordered systems, with direct relevance for topological quantum computation.

Graphene/hexagonal boron nitride (hBN) heterostructures represent a promising class of metal–insulator–semiconductor systems widely explored for multifunctional digital device applications. In this work, we demonstrate that graphene, when influenced by carrier-dependent trapping in the hBN spacer, triggered by a localized potential from Kelvin probe force microscopy (KPFM), can exhibit the behavior of a valley transistor under specific conditions. We employ a tight-binding model that self-consistently incorporates a Gaussian-shaped potential to represent the effect of the tip gate. Crucially, we show that the heterostructure can function as a field-effect transistor (FET), with its operation governed by the bias gate (which shifts the Fermi level) and the tip-induced potential (which breaks electron–hole symmetry by selectively trapping electron or hole quasiparticles). Our results reveal that, under specific conditions involving lattice geometry, pulse frequency, and gate voltages, the device exhibits valley transistor functionality. The valley current $(I_{K_1=-K} \text{or} I_{K_2=+K})$ can be selectively controlled by synchronizing the frequencies and polarities of the tip and bias gate voltages. Notably, when both gates are driven with the same polarity, the graphene channel outputs a periodically modulated, pure valley-polarized current. This enables the device to switch between distinct ON/OFF valley current states even at finite bias. Interestingly, when the $I_{K_1=-K}$ current is in the ON (forward current) state, the $I_{K_2=+K}$ current is OFF. Reversing the gate polarity inverts this behavior: $I_{K_1=-K}$ becomes OFF, while $I_{K_2=+K}$) turns ON (reversed-current). These findings pave the way toward realizing low-voltage valley transistors within metal–insulator–semiconductor architectures, offering avenues for multifunctional applications in valleytronics and advanced gating technologies.

Coherent phonon control using ultrashort pulse trains is the key to realizing structural phase transitions in solids by nonthermal pathways. By combining double-pulse excitation and time-resolved second harmonic generation techniques under high-density electronic excitation in a two-dimensional layered material, ${\mathrm{WTe}}_2$, we demonstrate that the lattice symmetry switching from the Weyl semimetallic $T_d$ to the semimetallic $1T^{\prime }$ phases is independent of the amplitude of the coherent interlayer shear phonons after the arrival of the second pump pulse. This finding provides different insights into the mechanisms for symmetry switching in which electronic excitation-driven shear sliding plays a dominant role.

van Hove singularities (VHS) located close to the Fermi level in kagome superconductors $A{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$ ($A=\mathrm{K}$, Rb, Cs) have a profound influence on their electronic and transport characteristics. Specifically, magnetotransport and susceptibility measurements on $\mathrm{Cs}{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$ reveal an anomalous temperature dependence of the upper critical field $H_{c2}\left(T\right)$, characterized by a pronounced upward curvature for both in-plane and $c$ axis magnetic fields, with zero-temperature $H_{c2}$ values of $\sim 6.0$ T and $\sim 1.2$ T, respectively. Our theoretical analysis, using a newly developed single-band model incorporating VHS and gap anisotropy, suggests that the observed upper critical field behavior is predominantly driven by the anisotropy of the Fermi velocity originating from VHS, instead of multiband effects or gap anisotropy. Increased electron scattering introduced by proton-irradiation defects smears out the VHS, reduces anisotropy, and recovers the conventional $H_{c2}\left(T\right)$ behavior, corroborating our proposed model.

Spatial localization of quantum states is one of the focal points in condensed matter physics and quantum simulations, as it signatures profound physics such as nontrivial band topology and nonreciprocal non-Hermiticity. Yet, in higher dimensions, characterizing state localization becomes elusive due to the sophisticated interplay between different localization mechanisms and spacial geometries. In this Letter, we unveil an exotic type of localization phenomenon in higher-dimensional non-Hermitian systems, termed anisotropic scaling localization (ASL), where localization lengths follow distinct size-dependent scaling rules in an anisotropic manner. Assisted with both analytical solution and numerical simulation, we find that ASL can emerge from two different mechanisms of effective bulk couplings or one-dimensional junction between different 1D edges, depending on how nonreciprocity is introduced to the system. The competition between ASL states and edge non-Hermitian skin states are further identified by their complex and real eigenenergies, respectively. Our results resolve the subtle coexistence of looplike spectrum and skinlike localization of boundary states in contemporary literature and provide a framework to classify the intricate higher-order non- Hermitian localization regarding their localization profiles.

Exciton-phonon interactions play a fundamental role in phonon-assisted radiative recombination and exciton dynamics in solids. In this work, we present a first-principles framework for computing phonon-assisted radiative lifetimes and exciton dynamics at finite temperatures. Starting from the solution of the Bethe-Salpeter equation, we construct an effective excitonic Hamiltonian that incorporates both exciton-photon and exciton-phonon interactions. Phonon-assisted radiative lifetimes in anisotropic media are evaluated using time-dependent second-order perturbation theory. We further analyze the temperature and phonon-mode dependence of phonon-assisted radiative lifetime and compare our results with available experimental data. We explain the nonmonotonic temperature dependence of the phonon-assisted radiative lifetime by different mechanisms at low- and high-temperature regimes. Finally, we perform real-time exciton relaxation at the diagonal approximation of Lindbladian dynamics for time-resolved exciton occupation, providing insights into ultrafast thermalization and scattering pathways. Our ab initio theory offers a detailed microscopic understanding of phonon-mediated exciton relaxation and recombination processes and provides in-depth perspectives on phonon-assisted many-body interactions and their influence on optical properties for light-emitting and optoelectronic applications.

We demonstrate that a conventional hollow conductor waveguide filled with a material exhibiting the coexistence of chiral magnetic and anomalous quantum Hall effects supports the propagation of transverse electromagnetic modes. This simple setup provides a direct and optically feasible method to probe the simultaneous presence of these phenomena, potentially enabling the detection of an emergent axion-like field within condensed matter systems.

We investigate the spontaneous emission of a single quantum emitter coupled to quasibound states in the continuum (QBICs) supported by dielectric gratings. Using quasinormal mode theory, we calculate the radiative enhancement induced by both regular and dimer grating structures. This approach allows us to determine the optimal dimer grating and to study the impact of structural disorder on these structures. We show that structural disorder can convert symmetry-protected bound states in the continuum in regular gratings into QBICs, opening radiative channels at normal incidence. Through statistical simulations, we identify the respective roles of dimensional and positional disorder. Finally, we show that dimer gratings retain high radiative efficiency for moderate disorder strengths below $10\%$. Beyond this threshold, both structures exhibit comparable efficiencies.

Möbius topological insulators have dispersive edge bands with Möbius twists in momentum space, which are protected by the combination of chiral and ${\mathbb{Z}}_2$-projective translational symmetries. In this work, we reveal a unique type of Möbius topological insulator, whose edge bands can twist around the quasienergy $\pi$ of a periodically driven system and are thus of Floquet origin. By applying time-periodic quenches to an experimentally realized Möbius insulator model, we obtain interconnected Möbius edge bands around zero and $\pi$ quasienergies, which can coexist with a gapped or gapless bulk. These Möbius bands are topologically characterized by a pair of generalized winding numbers, which are integer-quantized as a result of an emergent chiral symmetry at a high-symmetry point in momentum space. Numerical investigations of the quasienergy and entanglement spectra provide consistent evidence for the presence of such Möbius topological phases. A protocol based on the adiabatic switching of edge-band populations is further introduced to dynamically characterize the topology of Floquet Möbius edge bands. Our findings thus extend the scope of Möbius topological phases to nonequilibrium settings and unveil a unique class of Möbius-twisted topological edge states without static counterparts.

Aharony and Fisher showed that nonlocal dipolar effects in magnetism destabilize the Heisenberg fixed point in real ferromagnets, leading to a new fixed point called the dipolar fixed point. The nonperturbative nature of the new fixed point, however, has not been uncovered for many decades. Inspired by the recent understanding that the dipolar fixed point is scale invariant but not conformal invariant, we perform the Monte Carlo simulation of the local Heisenberg-dipolar model on the lattice of ${40}^3$ by introducing the local cost function parameterized by a parameter $\lambda$ and study its critical exponents, which should become identical to the dipolar fixed point of Aharony and Fisher in the infinite coupling limit $\lambda =\infty$. We find that the critical exponents become noticeably different from those of the Heisenberg fixed point for a finite coupling constant $\lambda =8$ [e.g., $\nu =0.601\left(2\right){(}_{-2}^{+0}){{(}_{-4}^{+5})}_{{\beta }_c}$ in the local Heisenberg-dipolar model while $\nu =0.712\left(1\right){(}_{-0}^{+3}){{(}_{-1}^{+1})}_{{\beta }_c}$ in the Heisenberg model], and the spin correlation function has a feature that it becomes divergence free, implying the lack of conformal invariance.

Multidomain states of square artificial spin ice show a range of different morphologies ranging from simple stripelike domains to more organically shaped coral domains. To model the relevant dynamics leading to the emergence of such diverse domain structures, simplified descriptions of the switching behavior of individual nanomagnets are necessary. In this work, we employ kinetic Monte Carlo simulations of the demagnetization of square artificial spin ice toward its ground state and compare how the choice of transition barriers affect the emergence of mesoscale domains. We find that the commonly used mean-field barrier model (informed by equilibrium energetics only) results in propagation of ground-state string avalanches. In contrast, taking into account chiral barrier splitting enabled by state-dependent local torques supports the emergence of complex-shaped coral domains and their successful relaxation towards the ground state in later relaxation stages. Our results highlight that intrinsic contributions to switching barriers, in addition to the effect of extrinsic defects often attributed to nanofabrication irregularities, can subtly shift favored transition pathways and result in different emergent mesoscale features. Future kinetic Monte Carlo models that describe the evolution of artificial spin systems should thus account for these effects.

Altermagnetism (AM) is a recently proposed compensated magnetic state that exhibits the characteristics previously thought to be absent in conventional collinear antiferromagnets (AFMs), including the nonrelativistic spin splitting and a possible anomalous Hall effect (AHE). In two-dimensional (2D) A-type AFM bilayers with intralayer ferromagnetic and interlayer AFM coupling, interlayer operations serve as effective strategies to expand the family of 2D AM candidates. In this work, we systematically investigate the symmetry conditions enabling the AHE in collinear A-type AFM bilayers. We demonstrate that the in-plane Néel vector can induce finite anomalous Hall conductivity (AHC) in both twisted and mirror-stacked A-type AFM bilayers. However, spin splitting only exists in twisted bilayers and is absent in mirror-stacked ones. We further calculate the AHC in ${\mathrm{VS}}_2$ bilayers as a prototype and analyze the correlation between the direction of in-plane Néel vector and the AHC.

We show that a two-dimensional $s$-wave superconductor may become topological in the presence of a magnetic field that leads to the formation of an Abrikosov vortex lattice. Below the upper critical field, a superconducting state with a nontrivial even topological number emerges, which we call the Abrikosov-Chern superconducting state. Deeper in the superconducting domain, the topological number changes in steps, always remaining even and thus not supporting Majorana states, and eventually reaches zero. Our theory uncovers the nature of evolution from an integer quantum Hall state having a cyclotron gap above the upper critical field to the topologically trivial $s$-wave superconductor carrying finite-energy Caroli–de Gennes–Matricon levels at low field. Topological transitions manifest as changes in the number of edge modes, detectable through tunneling spectroscopy and thermal or spin transport measurements.

We investigate the localization of electronic states in the integer quantum Hall effect using a magnetic localization landscape (MLL) approach. By studying a continuum Schrödinger model with disordered electrostatic potential, we demonstrate that the MLL, defined via a modified landscape function incorporating magnetic effects, captures key features of quantum state localization. The MLL effective potential reveals the spatial confinement regions and provides predictions of eigenstate energies, particularly in regimes where traditional semiclassical approximations break down. Numerical simulations show that below a critical energy, states localize around minima of the effective potential, while above it they cluster around maxima—with edge effects becoming significant near boundaries. Bridging the gap between semiclassical intuition and full quantum models, the MLL offers a robust framework to understand transport and localization in disordered quantum Hall systems and extends the applicability of landscape theory to magnetic systems.

${\mathrm{GdRu}}_2{\mathrm{Si}}_2$ has recently drawn significant attention as a centrosymmetric magnet capable of hosting a short-period skyrmion square lattice (SkL) in the absence of Dzyaloshinskii-Moriya interaction (DMI). In this system, Gd atoms are arranged on a square lattice, forming 2D layers separated by the Ru-Si network in the out-of-plane direction. RKKY-type exchange between the Gd moments results in an exchange frustration, which is the main source of non-collinearity in the spiral phases of the system. So far, the literature has emphasized the importance of in-plane $\vec{Q}$ vectors in understanding the magnetic phases of the system as they appear and have been observed in the 2D Gd layers. In this work, we calculate the Gd-Gd magnetic exchange interactions ($J_{ij}$) and perform atomic spin dynamics (ASD) simulations, providing new insights about ${\mathrm{GdRu}}_2{\mathrm{Si}}_2$. Our calculated $J_{ij}$ shows that the strongest magnetic interaction occurs between Gd atoms along the [111] body-diagonal direction of the unit cell. This, along with the body-centered tetragonal structure of the Gd sublattice, points to the presence of a hitherto ignored modulation vector, ${\vec{Q}}_{\left[111\right]}$, along the [111] direction in the spiral phases of the system. We confirm this with ASD simulations and establish that the magnetic phases in ${\mathrm{GdRu}}_2{\mathrm{Si}}_2$ are far more complex than they appear to be in the 2D Gd layers. This interlayer modulation vector ${\vec{Q}}_{\left[111\right]}$, along with the intralayer ${\vec{Q}}_{\left[100\right]}$ and ${\vec{Q}}_{\left[010\right]}$, determines the total magnetic ordering of the system. Despite its layered appearance, both structurally and magnetically, it is in reality a strong 3D magnet, requiring additional considerations for its proper theoretical modeling. Taking these into account, our ASD simulations provide an excellent description of the experimentally observed magnetic phase transitions. Furthermore, our work reveals the critical influence of dipolar interactions on the ground-state magnetic properties of ${\mathrm{GdRu}}_2{\mathrm{Si}}_2$, a direct consequence of the large magnetic moment of Gd. We observed a competition between dipolar interactions and uniaxial anisotropy, with each favoring a different magnetic ordering. However, the dominance of the dipolar interaction is evident in the observed ground state. This suggests a weak uniaxial anisotropy in the system, which aligns with the spherical symmetry of the Gd $4f$ states. Our findings offer a deeper understanding of ${\mathrm{GdRu}}_2{\mathrm{Si}}_2$'s complex magnetism and highlight the potential for similar important interlayer effects in other layered magnetic systems.

We investigate the Josephson diode effect in an asymmetric SQUID consisting of a sinusoidal Josephson junction formed by a ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ flake and a superconducting Nb nanobridge with a linear and multivalued current-phase relation (CPR). Current-voltage characteristics were measured both in the absence (dc regime) and presence (ac regime) of external microwave irradiation. Our dc measurements reveal only weak critical current asymmetry (i.e. weak Josephson diode effect), while confirming the multivalued behavior of the SQUID. At the same time, the key finding of this work is the observation of strong Shapiro step asymmetry (concerning the dc current direction) in the ac regime at finite magnetic flux. This peculiarity oscillates as a function of magnetic field with the SQUID's periodicity and varies nonmonotonically with the increase in microwave power. Our theoretical model shows that the pronounced Shapiro step asymmetry, despite the small diode effect in critical current, arises from the interplay between the sinusoidal and multivalued CPRs of the junctions.

The braiding of Majorana zero modes (MZMs) paves the way for realizing fault-tolerant topological quantum computation (TQC). We propose a reinterpretation of MZM migration and braiding phenomena in 1D topological superconductors (TSCs), based on a MZM deconfinement-reconfinement transition in open quantum systems, which can be equivalently explained via symmetry perspectives from a Hermitian picture, or via non-Hermitian skin effect (NHSE) perspectives from a non-Hermitian picture. In the deconfinement-reconfinement transition, the MZM in the system first evolves into a deconfined mode in the environment, before reconfines into a localized mode at the edge of the environment. From the symmetry perspective, this is because coupling with the environment breaks the symmetry of the system that protects the MZM as a topological edge state within the system, so the MZM diffuses into the environment. From the NHSE perspective, this is because NHSE has pulled the MZM from the system into the environment. This symmetry/NHSE controlled deconfinement-reconfinement process can be exploited to physically migrate the MZM, which eventually results in their braidings. We also prove that adiabaticity is preserved in the braiding process, realizing a promising avenue for achieving TQC.

Out-of-equilibrium fermionic quantum impurity models (QIM), describing a small interacting system coupled to a continuous fermionic bath, play an important role in condensed matter physics. Solving such models is a computationally demanding task, and a variety of computational approaches are based on finding approximate representations of the bath by a finite number of modes. In this paper, we formulate the problem of finding efficient bath representations as that of approximating a kernel of the bath's Feynman-Vernon influence functional by a sum of complex exponentials, with each term defining a fermionic pseudomode. Under mild assumptions on the analytic properties of the bath spectral density, we provide an analytic construction of pseudomodes, and prove that their number scales polylogarithmically with the maximum evolution time $T$ and the approximation error $\varepsilon$. We then demonstrate that the number of pseudomodes can be significantly reduced by an interpolative matrix decomposition (ID). Furthermore, we present a complementary approach, based on constructing rational approximations of the bath's spectral density using the “AAA” algorithm, followed by compression with ID. The combination of two approaches yields a pseudomode count scaling as $N_{\text{ID}}\sim ln\left(T\right)ln(1/\varepsilon )$, and the agreement between the two approaches suggests that the result is close to optimal. Finally, to relate our findings to QIM, we derive an explicit Liouvillian that describes the time evolution of the combined impurity-pseudomodes system. These results establish bounds on the computational resources required for solving out-of-equilibrium QIMs, providing an efficient starting point for tensor-network methods for QIMs.

The Grassmann time-evolving matrix product operator method has shown great potential as a general-purpose quantum impurity solver, as its numerical errors can be well controlled and it is flexible to be applied on both the imaginary- and real-time axes. However, a major limitation of it is that its computational cost grows exponentially with the number of impurity flavors. In this work, we propose a multiflavor extension of it to overcome this limitation. The key insight is that to calculate multitime correlation functions on one or a few impurity flavors, one could integrate out the degrees of freedom of the rest flavors beforehand, which could greatly simplify the calculation. The idea is particularly effective for quantum impurity problems with diagonal hybridization function, i.e., each impurity flavor is coupled to an independent bath, a setting which is commonly used in the field. We demonstrate the accuracy and scalability of our method for the imaginary-time evolution of impurity problems with up to three impurity orbitals, i.e., six flavors, and benchmark our results against continuous-time quantum Monte Carlo calculations. Our method paves the way of scaling up tensor network algorithms to solve large-scale quantum impurity problems.