We study the effect of subsystem decoherence on an extended cluster state, which is a symmetry-protected topological (SPT) phase. The model includes many subsystem $Z_2$ symmetries. We report that subsystem decoherence induces local charge fluctuations, leading to a mixed SPT state in the unaffected subsystems. If we start from the extended cluster state, hierarchical mixed-state SPT phases emerge in response to step-by-step subsystem decoherences. These mixed-state SPT phases keep strong symmetries, the symmetry of which protects symmetries for the initial cluster SPT. Moreover, these SPT states can be characterized by Rényi-2 string orders. Then, as the subsystems are progressively decohered, the hierarchy of mixed-state SPT phases terminates in a $Z_2$ strong-to-weak spontaneous symmetry breaking (SWSSB) state on the final remaining subsystem, where a long-range entangled state appears, namely, a glassy Greenberger-Horne-Zeilinger (GHZ) state. Our work demonstrates that decoherence is not merely a destructive process, but can induce and organize a series of nontrivial mixed states. This reveals a systematic route from mixed-state SPT order to SWSSB order with the glassy GHZ-type long-range entanglement.

We investigate $s$-wave superconductivity in negatively curved geometries, focusing on Cayley trees and the hyperbolic plane. Using a self-consistent Bogoliubov–de Gennes approach for trees and a BCS treatment of the hyperbolic continuum, we establish a unified mean-field framework that captures the role of boundaries in hyperbolic spaces. For finite Cayley trees with open boundaries, the superconducting order parameter localizes at the edge while the interior can remain normal, leading to two distinct critical temperatures, $T_{\text{c}}^{\text{edge}}>T_{\text{c}}^{\text{bulk}}$. A corresponding boundary-dominated phase also emerges in hyperbolic annuli and horodisk regions, where radial variations of the local density of states enhance edge pairing. We also demonstrate that the enhancement of the density of states at the boundary is significantly more pronounced for the discrete tree geometry. Our results show that, owing to the macroscopic extent of the boundary, negative curvature can stabilize boundary superconductivity as a phase that persists in the thermodynamic limit on par with the bulk superconductivity. These results highlight fundamental differences between bulk and boundary ordering in hyperbolic matter and provide a theoretical framework for future studies of correlated phases in negatively curved systems.

We develop a time-local nonequilibrium Green's function formulation for real-time dynamics in quantum systems coupled to superconducting leads. The superconducting lead self-energy is a strongly frequency-dependent matrix in Nambu space, giving rise to nonlocal memory kernels in the time domain. This makes direct propagation of the Kadanoff-Baym (KB) equations computationally demanding. To overcome this difficulty, we extend the auxiliary-mode expansion, originally developed for normal-metal leads, to Nambu-space self-energies. This allows us to decompose the superconducting lead self-energy into a finite number of exponential modes and to transform the KB equations with memory integrals into a closed set of ordinary differential equations. The resulting time-local equations enable efficient real-time simulations under general time-dependent bias voltages, superconducting phases, and one-body Hamiltonians of the central system, while retaining the memory effects induced by superconducting leads. As an application, we analyze voltage-quench dynamics in a superconductor–quantum-dot–superconductor junction and show that, after a dc bias is suddenly applied, the system evolves through a transient regime and relaxes to an ac Josephson periodic steady state. The resulting periodic steady-state current agrees with the Floquet Green's function solution, validating the present real-time formulation.

We report the first experimental evidence for a quantum-disordered spin-singlet ground state and gapped triplon excitations in quasi-one-dimensional van der Waals materials. The insulating van der Waals trihalides ${\mathrm{MoI}}_3$ and ${\mathrm{MoBr}}_3$ are analyzed in a combined thermodynamic, spectroscopic, and theoretical investigation. These materials contain structurally dimerized atomic chains of face-sharing octahedra with alternating short and long Mo-Mo separations along the chain direction. Temperature-dependent bulk magnetic susceptibility measurements reveal a broad thermally activated response consistent with a large spin gap. Inelastic neutron scattering (INS) spectra provide direct evidence of a collective spin gap at an exceptionally large energy transfer of $\mathrm{\Delta }\approx 30\text{meV}$ ($\approx 348\text{K}$) for ${\mathrm{MoBr}}_3$. The absence of low-energy magnetic spectral weight and the activated susceptibility are inconsistent with a conventional classical antiferromagnetic ground state. Instead, they point to a spin-singlet ground state with a large singlet-triplet excitation gap. To identify the microscopic origin of this gap, we perform density matrix renormalization group (DMRG) calculations on one-dimensional spin chains using exchange constants derived from density functional theory (DFT). The dominance of the single dimer exchange term allows the interdimer coupling along the chain and between chains to be treated using perturbation theory. Intrachain exchange lowers the isolated-dimer triplet energy by producing a dispersive triplon band. INS data show the triplon bandwidth to be $\sim 20\mathrm{meV}$. Interchain coupling produces negligible additional bandwidth on the order of 1 meV. The INS measurements directly establish quantum spin-singlet and triplon physics in ${\mathrm{MoBr}}_3$ with a large singlet-triplet gap on the scale of room temperature, while the susceptibility and theoretical results indicate closely analogous behavior in ${\mathrm{MoI}}_3$.

Strain defects are crucial to the physical properties of solid materials. Among them, strain glass induced by defect engineering provides an important paradigm for nanoscale domain manipulation. Here, we propose purely mechanical moiré strain skyrmions, topologically protected elastic textures whose motion can be controlled by interlayer sliding and the chirality of the moiré bilayer. Using an empirical continuum elastic model combined with symmetry analysis, we demonstrate the skyrmion lattice structure as the elastic ground state. Under interlayer sliding, these moiré strain skyrmions exhibit the skyrmion Hall effect of transverse motion, with a Hall angle determined by bilayer chirality and inversely proportional to the moiré twist angle. Our work establishes interlayer sliding as an efficient, low-energy control knob for topological textures, offering a new paradigm for designing chiral-material-based information transport devices.

Generating fully spin-polarized currents is a key issue in spintronics. Theoretical studies have shown that $d$-wave altermagnets with perfect orthogonal Fermi surfaces in the first Brillouin zone (BZ) can generate 100% spin-polarized currents. However, such ideal orthogonal Fermi surfaces are rarely realized in materials. Two situations are commonly observed: (1) The orthogonal Fermi surfaces are accompanied by additional Fermi pockets at the BZ boundaries, and (2) the Fermi surfaces are no longer perfectly orthogonal. Both scenarios reduce the spin polarization. Using tight-binding models and first-principles calculations, we demonstrate that strain engineering effectively tunes the Fermi surfaces of $d$-wave altermagnets. In the tight-binding models, we show that biaxial strain transforms nonideal Fermi surfaces into perfectly orthogonal ones, and uniaxial strain tunes the transport states of spin-polarized currents. First-principles calculations provide concrete material examples. In two-dimensional (2D) ${\mathrm{Pd}}_2{\mathrm{I}}_2$, biaxial strain eliminates the extra Fermi pockets originating from the $d_{xz}$ and $d_{yz}$ orbitals, yielding orthogonal Fermi surfaces and increasing the spin polarization from 54.5% to 99.5%. In the three-dimensional (3D) altermagnet ${\mathrm{KV}}_2{\mathrm{Se}}_2\mathrm{O}$, in-plane biaxial tensile strain modulates the $d_{xy}$ states and eliminates the extra Fermi pockets near the X and Y points, thereby realizing orthogonal Fermi surfaces in a 3D system. In 2D ${\mathrm{Pd}}_2\mathrm{BrI}$ under hole doping, reversing the uniaxial strain direction enables deterministic on/off control of the fully spin-polarized current, accompanied by a piezomagnetic moment for transport-state readout. These results demonstrate that biaxial strain provides a route to realizing perfect orthogonal Fermi surfaces and fully spin-polarized currents in altermagnets across both 2D and 3D systems, while uniaxial strain provides a feasible approach for designing mechanically tunable spintronic devices.

We report a systematic study of the anisotropic magnetic, magnetocaloric, and magnetotransport properties of ${\mathrm{DyAgSb}}_2$ single crystals, which order antiferromagnetically and exhibit strong easy-plane anisotropy that constrains the Dy moments within the basal plane. Isothermal magnetization measurements reveal successive metamagnetic transitions for in-plane magnetic fields, in contrast to the weak and nearly linear hard-axis response for ${\mu }_{0}H//\left[001\right]$ up to 7 T. The associated field-induced phase evolution produces a strongly anisotropic magnetic entropy change: For $\mathrm{\Delta }{\mu }_{0}H=7\mathrm{T}$, the peak values of $-\mathrm{\Delta }{S}_{\mathrm{M}}$ are 14.78 and $12.74\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ for [110] and [100], respectively. Along [001], an inverse magnetocaloric response yields a minimum of $-\mathrm{\Delta }{S}_{\mathrm{M}}=-5.17\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$. The corresponding rotating entropy changes are $15.2\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ and $13.96\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ for the [001]/[110] and [001]/[100] rotation pairs, respectively. Field-dependent magnetoresistance (MR) exhibits anomalies in the field ranges associated with the in-plane metamagnetic transitions, whereas the hard-axis transverse geometry exhibits a smooth positive MR reaching about $3\times {10}^2\%$ at 2 K and 7 T. A joint analysis of the paramagnetic susceptibility and magnetization isotherms using a crystalline electric field (CEF) plus molecular-field model supports the contribution of single-ion CEF effects to the easy-plane anisotropy. These results reveal a correspondence between the anisotropic magnetic-state evolution, magnetic entropy changes, and magnetotransport anomalies.

Nitrogen (N) doping is an effective strategy for enhancing superconductivity in transition-metal carbides. Orthorhombic ${\mathrm{W}}_2\mathrm{C}$ has been experimentally synthesized and identified as an intrinsic superconductor. However, the influence of N doping on its superconducting and topological properties remains unclear. Herein, we systematically explore N doping in ${\mathrm{W}}_2\mathrm{C}$ via first-principles calculations and reveal that all considered ${\mathrm{W}}_2{\mathrm{C}}_{1-x}{\mathrm{N}}_x$ ($x=0$, 0.25, 0.5, 0.75, 1) compounds exhibit both stability and metallic character. The results show that N doping can reconstruct the electronic structure and drive the Lifshitz transition. Notably, the superconducting transition temperature $T_c$ exhibits a dome-shaped dependence on N concentration. Up to $x=0.75$, the increase in the density of states at the Fermi level $N\left(E_F\right)$, together with the softening of the low-frequency W-dominated phonon modes, enhances the electron-phonon coupling (EPC) strength $\lambda$ and raises $T_c$, whereas at $x=1$, the reductions in $N\left(E_F\right)$ and $\lambda$ lower $T_c$. Microscopically, the dominant EPC arises from the coupling between W-$5d$ electrons and low-frequency vibrations of W. Wannier-based $Z_2$ invariant reveals a doping-induced topological transition from nontrivial to trivial states with increasing N content. These findings provide microscopic insight into N-doping-controlled superconductivity and topological properties in ${\mathrm{W}}_2\mathrm{C}$, and offer theoretical guidance for designing tunable superconducting and topological transition-metal carbides.

Dynamical manipulation of Majorana zero modes and their reliable distinction from topologically trivial states remain paramount challenges in topological quantum computation. Here, we propose a phase-biased altermagnetic Josephson junction as a versatile platform for generating and controlling Majorana corner configurations. Our platform utilizes the macroscopic superconducting phase difference and the Néel-vector orientation as independent control knobs to reshape the boundary mass. This allows the spatial configuration of Majorana corner modes (MCMs) to be selected at different corners of a fixed device geometry. This spatial reconfiguration yields a control-correlated conductance response. Across these configurations, the quantized zero-bias peak appears at the contacted corner in the ideal tunneling model when an MCM is present and is suppressed when it is absent. This correlation connects phase and magnetic control of corner configurations with local tunneling readout.

Smooth electrostatic wells in graphene can support normalizable states at the charge-neutrality (Dirac) point even though electrostatic confinement at nonzero energy is generally leaky. We examine how a spatially varying mass gap reorganizes this mechanism for a circular Lorentzian well under the explicit assumption that the localized mass and scalar potential are strictly coprofiled. A constant spinor-component rescaling gives an exact covariance of the radial equations at finite energy and background gap; the Lorentzian specialization then yields a closed critical-retuning law. The zero-mode manifold contains two regular angular families in each valley, and a weak uniform background gap produces opposite-sign slopes within a restricted localized-mass range, with asymmetric magnitudes when the localized mass is nonzero. Tail-corrected two-point shooting confirms the analytic slopes down to small background gaps and follows all six descendants of the $N=4$ multiplet. The Lorentzian inverse-square tail additionally generates idealized geometric towers of near-edge states in supercritical low-angular-momentum channels. In a gapless exterior, the two angular sectors appear as paired local density of states resonances whose positions approach zero and whose widths collapse rapidly near criticality. These results connect exact coprofile covariance, zero-mode retuning, angular-pair splitting, threshold towers, and tunneling signatures within one two-dimensional Dirac model.

Integrating three-dimensional topological materials into advanced electronic architectures offers a path toward added functionality through low-power quantum devices if we resolve fundamental engineering concerns regarding preferential carrier injection into quantum channels. Using the self-consistent nonequilibrium Green's function approach, we investigate the impact of symmetry protection and low density of states on carrier dynamics at the metal-topological interface. We demonstrate that the topological surface state (TSS) acts as an electrostatic screen, fundamentally altering traditional semiconductor physics: in the diffusive regime $({\varphi }_{\mathrm{MS}}<-0.2\mathrm{eV})$, the TSS results in a significantly reduced diffusion length compared to trivial insulators; in the depletion regime $({\varphi }_{\mathrm{MS}}>-0.2\mathrm{eV})$, the TSS limits the depletion width while facilitating the isolation of surface conduction through the quantum channel. Furthermore, we show that the introduction of magnetic scattering at the interface further enhances injection by hybridizing metallic and topological states. These findings establish application-specific design rules for topological interconnects, enabling the isolation or flooding of surface channels through work-function and interface engineering.

We introduce a generalizable framework for identifying effective Hamiltonians directly from experimental data in solid-state quantum systems. Our unsupervised autoencoder-based approach incorporates the governing physics (here, the S-matrix formalism) directly into the decoder, enabling physically meaningful Hamiltonian inference without labeled Hamiltonian parameters. Through numerical experiments on a triple-quantum-dot chain, we demonstrate automated characterization of programmable solid-state simulators from transport measurements. The model accurately infers Hamiltonian parameters and generalizes beyond the training domain, while exhibiting finite capacity as the parameter space becomes increasingly broad or diverse. We further demonstrate robustness to noisy measurements and show that the model can be trained on transport data generated outside the Hamiltonian family assumed by the physics decoder while still identifying meaningful effective parameters.

Anomalous transports, including the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE), are typical manifestations of time-reversal-symmetry-breaking responses in materials. In general, the two Hall states with opposite Hall conductivities can be regarded as time-reversal pairs coupled to magnetic order, and switching between them relies on reversing the magnetization via an external magnetic field or electric current. Here, we introduce an approach for manipulating anomalous transport through crystal symmetry engineering in two-dimensional (2D) altermagnetic systems. Through symmetry analysis and lattice models, we show that for systems with out-of-plane Néel vectors, breaking the symmetry that connects two magnetic sublattices will induce an anomalous Hall response. Crucially, the signs of the anomalous Hall and anomalous Nernst conductivities can be flexibly controlled via symmetry-breaking perturbations, enabling the realizing tunable sign-reversible anomalous transport. Using first-principles calculations, we investigate crystal-symmetry-controlled anomalous transport in the 2D altermagnetic materials ${\mathrm{V}}_2\mathrm{STeO}$ and ${\mathrm{Cr}}_2{\mathrm{O}}_2$. The results indicate that these systems with out-of-plane Néel vectors exhibit pronounced AHE and ANE signals under uniaxial strain. Remarkably, the sign of the anomalous transport coefficients can be reversed by simply rotating the strain direction by $\pi /2$, thus enabling the switching of anomalous transverse currents without an external magnetic field. Our findings provide a new strategy to manipulate anomalous transport, and should have significant potential applications.

A comprehensive description of notable phenomena of low-dimensional periodic systems, such as the photoexcitation and Dirac point, requires the multiconfigurational electronic structure method beyond the $\mathrm{\Gamma }$-point approximation. Here, we introduce an ab initio framework we call PBC-DMRGCI by achieving the support of complex-valued wave functions; this framework integrates the complete active space configuration interaction (CASCI) approach with periodic boundary conditions (PBC) and the density matrix renormalization group (DMRG) solver. Combined with the supercell method, the PBC-DMRGCI framework enables the accurate treatment of strong electron correlation within the active spaces at any single $\mathbf{k}$ point in the first Brillouin zone. Taking the one-dimensional ${\mathrm{H}}_2$ chain, one-dimensional trans-polyacetylene, and the two-dimensional $\mathrm{Mo}{\mathrm{S}}_2$ supercell as prototypical systems, the PBC-DMRGCI method demonstrates its power in revealing complex many-body effects on both the ground state and excited states. Moreover, by operating at any single $\mathbf{k}$ point in the first Brillouin zone, the PBC-DMRGCI framework facilitates the exploration of electron correlation beyond the $\mathrm{\Gamma }$-point approximation, thereby opening avenues for the study of momentum-resolved excitations in strongly correlated solids.

Polymeric nitrogen frameworks are of interest for high-energy-density materials because their conversion to molecular ${\mathrm{N}}_2$ is associated with substantial energy release, while their experimental synthesis remains challenging. Here we combine particle-swarm structure prediction, first-principles calculations, and laser-heated diamond-anvil-cell experiments to investigate the phase stability and bonding of the In-N system under pressure. Two pressure-stabilized ${\mathrm{InN}}_{10}$ polymorphs were obtained experimentally, with in situ synchrotron x-ray diffraction and Raman spectroscopy supporting their assignment to tetragonal $I4$ at 55 GPa and orthorhombic Ama2 at 80 GPa. The $I4$ phase contains isolated pentazolate ${\mathrm{N}}_5$ rings, whereas the Ama2 structure contains an extended chain-ladder nitrogen framework involving ${\mathrm{N}}_{17}$-based motifs. Electronic-structure and bonding analyses indicate substantial charge transfer from indium to the nitrogen sublattice, with the dominant bonding contributions arising from covalent N-N interactions. The calculated energetic metrics show that Ama2 ${\mathrm{InN}}_{10}$ has a higher volumetric energy density than the other predicted In-N phases, associated with its higher packing density and extended nitrogen connectivity. The results establish two pressure-stabilized ${\mathrm{InN}}_{10}$ polymorphs with distinct ring-based and chain-ladder polynitrogen frameworks and clarify the role of indium in stabilizing different nitrogen connectivities under pressure.

Control of the orientation and size of magnetic domain structures is crucial for the proper functioning of various magneto-optical devices. Here we propose and demonstrate garnet-based heterostructures that allow stabilization of in-plane stripe domain orientation and period under certain conditions. This was achieved using a 5-$\mu \mathrm{m}$-thick epitaxial garnet layer covered with one-dimensional ferromagnetic metal gratings. Using optical polarization microscopy, we show that the interaction between the garnet film and Co/Au or (Co/Pt)${}_{10}$ gratings (with thicknesses on the order of tens of nanometers and periods close to the intrinsic domain width) leads to two key effects: (1) deviation of the stripe domains' orientation from the applied magnetic field direction toward the metal grating and (2) fixation of the stripe domain period within a specific range of external magnetic fields. Second harmonic generation microscopy confirms that this pinning effect is homogeneous throughout the entire thickness of the garnet film. These findings open opportunities for precise control over both domain orientation and width, thereby enhancing the stability of functional magneto-optical heterostructures.

We study the superconducting response induced by a Néel domain wall in a thin superconducting film proximity-coupled to a ferromagnetic layer in the presence of interfacial Rashba spin-orbit coupling. The combined action of the magnetic texture and broken inversion symmetry generates a magnetoelectric coupling that induces spontaneous equilibrium currents. To establish the basic response to a continuously rotating magnetic texture, we first consider a periodic harmonic cycloid as an analytically tractable reference problem. Near $T_c$, this reference problem illustrates how the magnetoelectric coupling modifies the superconducting order parameter, while below $T_c$ it provides a simple setting for describing the phase response, Pearl screening, and the interaction with a vortex. We then turn to the main problem of this work, a single Néel domain wall, and derive analytical expressions for its equilibrium phase profile, spontaneous current, magnetic field, and vortex-wall interaction energy. We show that the Néel wall acts as an extended magnetoelectric source and produces a vorticity-selective pinning landscape controlled by the competition between the wall width and the effective screening length. We further demonstrate that sufficiently strong magnetoelectric coupling can render a bound vortex-antivortex pair energetically favorable relative to the vortex-free state, even in the absence of an applied magnetic field. Our results provide an analytical framework for understanding magnetoelectric vortex pinning and vortex-antivortex nucleation by Néel domain walls in spin-orbit coupled superconducting films.