In a recent experiment, flux-dependent oscillations of the quantum capacitance were observed in a one-dimensional spin-orbit-coupled semiconductor-superconductor heterostructure connected end to end via a quantum dot and threaded by a magnetic flux. In the topological superconducting phase hosted by this type of heterostructure, the oscillations corresponding to different fermion parity sectors are shifted by half a period and can serve as a mechanism for fermion parity readout or fusion operations involving a pair of localized, well-separated Majorana modes. In this work, we demonstrate that flux-induced fermion parity-dependent oscillations of the quantum capacitance in a disordered semiconductor–superconductor–quantum dot system can originate not only from topologically protected, spatially well-separated Majorana zero modes localized at the wire ends but also, generically, from partially separated Majorana modes with significant overlap, as well as from quasi-Majorana modes in the topologically trivial phase, which can be viewed as Andreev bound states whose constituent Majorana wave functions are slightly shifted relative to each other and have nonzero amplitude at opposite ends of the wire. Therefore, while the detection of flux-dependent oscillations of quantum capacitance marks an important experimental advance, such observations alone do not constitute conclusive evidence of the presence of topological Majorana zero modes.

We predict an in-plane, or hidden, Berry curvature (BC) for magnons in electrically insulating quasi-two-dimensional magnets and demonstrate that the hidden magnon Berry curvature gives rise to a previously unrecognized form of vertical, out-of-plane, magnon transport. Combining a semiclassical framework with Boltzmann transport theory, we show that the vertical magnon transport (VMT) currents respond both linearly and nonlinearly to the in-plane gradients of magnetic field and temperature. The linear transport coefficients are tied to the total hidden magnon BC, while the nonlinear (second-order) coefficients for the magnetic field and temperature gradients are determined by the hidden magnon BC dipole and the hidden extended magnon BC dipole, respectively. Using linear spin-wave theory, we find that the hidden magnon BC over the Brillouin zone is given by the expectation value of a pseudo-$\mathcal{Z}$ operator, representing vertical displacements, evaluated in the space of paraunitary matrices that diagonalize the magnon Hamiltonian. We estimate VMT in spin models of realistic magnets with ferro- and antiferromagnetic order, including the buckled honeycomb (BHC) lattice and bilayer chromium trihalide $({\mathrm{CrX}}_3; \mathrm{X}=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ systems. In BHC, both linear and nonlinear VMT arise when time-reversal symmetry is broken by Dzyaloshinskii-Moriya interactions. In ${\mathrm{CrX}}_3$ systems, the nonlinear coefficients dominate, while the linear responses vanish due to time-reversal symmetry. Both systems exhibit distinctive features across a broad range of temperatures and parameters. Therefore, our prediction of VMT and its characteristic signatures is directly testable in present-day magnonic experiments, especially in atomically thin, few-layered van der Waals magnets.

The coupling between valley and layer degrees of freedom provides a powerful route to extend higher-order topological boundary states. Here, we comprehensively investigate the higher-order corner states in two-dimensional bilayer triangular-lattice sonic crystals, arising from the combined effects of valley physics and bilayer topology. By independently rotating the scatterers in each layer, four distinct bulk topological phases are realized, characterized by different Wannier-center configurations and opposite fractional polarizations. Their pairwise combinations give rise to a wide variety of experimentally observed corner states, including layer-mixed, layer-polarized, and layer-locked modes. Moreover, valley-selective geometrical designs further modulate the spatial localization and operating frequencies of these corner states. Our results establish a versatile platform for manipulating topological acoustic states and open avenues for applications such as acoustic multiplexing, selective signal routing, and localized energy harvesting.

The defining property of electronic nematicity, the spontaneous breaking of rotational symmetry, implies an unavoidable coupling between the nematic order parameter and elastic strain fields, known as nematoelasticity. While both quantities are rank-2 tensors, the strain tensor is constrained through the Saint Venant compatibility relations. These constraints, which take the form of three coupled second-order partial differential equations, arise from the lattice displacement vector's role as the potential field. The compatibility relations reflect the underlying gauge invariance of geometric deformations, which are violated only in the presence of crystalline defects. In this work, we develop a theory of nematoelasticity that incorporates elastic compatibility explicitly through a corotating helical basis. Within our formalism, we show that elasticity bestows tensor compatibility upon the electronic nematic order parameter by suppressing incompatible electronic nematic fluctuations. As a result, nematoelasticity is markedly different from bare nematicity. In ideal media devoid of defects, we show that the suppression of incompatible nematicity underlies direction-selective criticality, even in the absence of crystalline anisotropy. In realistic systems with defects, meanwhile, we show that elastic pinning fields emanate from distributions of quenched defects, generating random longitudinal and transverse conjugate fields experienced by the local nematic order parameter. The coexistence of direction-selective nematic criticality with pinning effects from random fields is naturally explained within our theory from the transformation to the helical basis, implying that local experimental probes of nematicity will be influenced by a linear, but nonlocal, combination of long- and short-ranged helical nematic modes. Because the compatibility relations are gauge constraints endowed in the isotropic medium, our results constitute universal features of nematoelastic criticality present in all crystalline systems.

Topological waveguides supporting quantum valley Hall edge states confine waves to interfaces and, due to topological protection, are resistant to backscattering even in the presence of defects. These topological insulators are typically studied by means of an infinite spectral problem. However, practical implementations are necessarily finite. In this work, we propose an alternative framework for analyzing topologically nontrivial states in open, finite systems. Our approach is based on a quasinormal modal expansion method, which directly characterizes the existence and excitation of these modes within the open system. The resulting spectrum is complex and discrete and fully describes the topologically nontrivial states, revealing an analogy of topological mode steering as a dispersive Fabry-Pérot cavity, with a dispersion relation closely related to that of the corresponding infinite (Floquet-Bloch) ribbon problem. Our results illustrate how topologically protected waveguiding can be understood in terms of leaky cavity modes and offers a powerful framework for analyzing finite topological devices.

Quasicrystals, structures that are ordered yet aperiodic, defy conventional band theory and have long resisted analytical predictions, confining most studies to finite-size real-space numerics. In particular, it is not obvious a priori that quasicrystalline potentials should support true energy gaps: such gaps are a hallmark of periodic systems, but are generally absent in fully disordered materials. Here, we overcome this limitation with a configuration-space framework that predicts and explains the positions and microscopic origins of energy gaps in an experimentally realizable eightfold optical quasicrystal. We show that a hierarchy of true gaps arises from resonant hybridization between increasingly distant neighboring sites, and that the integrated density of states below these gaps is pinned to specific irrational areas in configuration space. Large-scale simulations of a lowest-band tight-binding model built from localized Wannier functions show excellent agreement with these predictions. By moving beyond finite-size numerics, this work establishes a route to analytical understanding of quasicrystalline potentials in the infinite-size limit and provides a rigorous foundation for future studies of their transport and many-body quantum properties.

Quantum spin liquid (QSL) phases exist in theory, but real candidate QSL materials are often extraordinarily sensitive to structural defects which disrupt the ground state. Here, we investigate candidate triangular QSL material, ${\mathrm{YbCu}}_{1.14}{\mathrm{Se}}_2$, and discover the absence of magnetic order, but also no compelling evidence of a QSL ground state due to significant structural disorder. We instead look at the results through a lens of a two-dimensional (2D) random singlet phase. We are able to match thermodynamic measurements using a phenomenological model of a distribution of singlet formation. ${\mathrm{YbCu}}_{1.14}{\mathrm{Se}}_2$ behaves strikingly similar to other disordered triangular lattice materials, suggesting universal behavior of random singlet formation in 2D frustrated systems.

The traditional multichannel Kondo effect takes place when several gapless metallic electronic channels interact with a localized spin-$S$ impurity, with the number of channels $n$ exceeding the size of the impurity spin, $n>2S$, leading to the emergence of non-Fermi liquid impurity behavior at low temperatures. Here, we show that the effect can be realized even when the electronic degrees of freedom are strongly correlated and gapped. The system under consideration consists of a single spin-$\frac{1}{2}$ impurity coupled isotropically to $n$ spin singlet superconducting channels realized by one-dimensional leads with quasi-long-range superconducting order. The competition between the Kondo and superconducting fluctuations induces multiple distinct ground states and boundary phases depending on the relative strengths of the bulk and boundary interactions. Using the Bethe Ansatz technique, we identify four regimes: an overscreened Kondo phase, a zero-mode phase, a Yu–Shiba–Rusinov (YSR) phase, and a local-moment phase with an unscreened impurity, each with its own experimental characteristic. We describe the renormalization-group flow, the excitation spectrum, and the full impurity thermodynamics in each phase. Remarkably, even in the presence of a bulk mass gap, the boundary critical behavior in the Kondo phase is governed by the same exponents as in the gapless theory with the low-energy impurity sector flowing to the $SU{\left(2\right)}_n$ Wess–Zumino–Witten (WZW) fixed point, and the impurity entropy monotonically decreases as a function of temperature. In both the overscreened Kondo and zero-mode phases, the residual impurity entropy is $S_{\mathrm{imp}}(T\to 0)=ln[2cos(\pi /(n+2))]$. In the YSR and unscreened phases, on the other hand, the impurity entropy exhibits nonmonotonic temperature dependence and is effectively free at low temperatures with $S_{\mathrm{imp}}(T\to 0)=ln2$.

We study the hard-core Fermi-Hubbard model in the crossover between square and triangular lattices near half filling. As was recognized by Nagaoka in the 1960s, on the square lattice the presence of a single hole leads to ferromagnetic spin ordering. On the triangular lattice, geometric frustration instead leads to a spin-singlet ground state, which can be associated with a ${120}^{\circ }$ spiral order. On lattices which interpolate between square and triangular, there is a phase transition at which the ferromagnetic order becomes unstable to a spin spiral. We model this transition, finding the exact location of the spin-spiral instability.

Repeated local measurements typically have adversarial effects on entangling unitary dynamics, as local measurements usually degrade entanglement. However, recent works on measurement-only dynamics have shown that strongly entangled states can be generated solely through noncommuting random multisite and multispin projective measurements. In this work, we explore a generalized measurement setup in a system without intrinsic unitary dynamics and show that volume-law entangled states can be generated through local, nonrandom, yet noncommuting measurements. Specifically, we construct a one-dimensional model comprising a main fermionic chain and an auxiliary (ancilla) chain, where generalized measurements are performed by locally coupling the system to detector qubits. Our results demonstrate that long-time states with volume-law entanglement or mutual information are generated between different parts of the main chain purely through nonunitary measurement dynamics. Remarkably, we find that such large-entanglement generation can be achieved using only the measurements of one-body operators. Moreover, we show that measurements of nonlocal higher-body operators can be used to control and reduce entanglement generation by introducing kinetic constraints to the dynamics. We discuss the statistics of entanglement measures along the quantum trajectories, the approach to stationary distributions of entanglement or long-time steady states, and the associated notions of limited ergodicity in the measurement-only dynamics. Our findings highlight the potential of nonrandom measurement protocols for controlled entanglement generation and the study of nonunitary many-body dynamics.

Expanding the moiré material library continues to reveal novel quantum phases and emergent electronic behaviors. Here we introduce ${\mathrm{PbI}}_2$ into the moiré family and investigate the magnetotransport properties of a hexagonal boron nitride/graphene/${\mathrm{PbI}}_2$ heterostructure. In the high-field quantum Hall regime, we observe robust dissipationless transport at the charge neutrality point, indicative of incompressible states at filling factor ${\nu }_h=0$. A fractional conductance plateau at $2/3,e^2/h$ emerges, which we attribute to a Chern junction formed between domains with distinct Chern numbers arising from moiré-modulated and conventional quantum Hall states. Additionally, coherent electronic interference appears along trajectories associated with the ${\nu }_m=-2$ Chern state. These observations provide compelling evidence for the formation of moiré domains that nontrivially interrupt incompressible quantum Hall states, reflecting the strong moiré potential in the BN/graphene/${\mathrm{PbI}}_2$ superlattice. We suggest that the moiré Hofstadter spectrum coupled with the proximity-induced spin-orbit interaction from ${\mathrm{PbI}}_2$ gives rise to a high magnetic field topological insulator phase explaining ballistic transport at the charge neutrality point in the graphene monolayer.

Electronic correlations arising from frustration-induced flat band systems exhibit rich physical phenomena, offering a new pathway to realize Kondo physics without $f$-electrons. Here we study a kagome lattice compound ${\mathrm{CsCr}}_6{\mathrm{Sb}}_6$, using scanning tunneling spectroscopy and thermodynamic probes. Atomic-scale spectroscopy measurements reveal the signature of a Fano resonance near the Fermi level, indicating the development of the Kondo effect at low temperature. More interestingly, a change of rotational symmetry within the kagome plane is observed by applying an in-plane magnetic field, which likely arises from competition between the Kondo effect and frustrated magnetism. Such highly tunable correlated states are rarely observed in other systems, and therefore the ${\mathrm{CsCr}}_6{\mathrm{Sb}}_6$ provides a ideal platform to study the interplay of Kondo effect, magnetism and geometric frustration.

Josephson junctions are essential devices in superconducting electronics and quantum computing hardware. Here we predict electrical control of the supercurrent in composite superconductor-insulator-ferroelectric-insulator-superconductor (S-I-FE-I-S) Josephson junctions. Inversion symmetry broken by unequal dielectric barrier thicknesses and/or potentials converts ferroelectric polarization reversal into a substantial change of the critical current. Using a WKB approximation, we model the nonvolatile switching of the critical current with on-off efficiency that is tunable by thicknesses and potential barriers of the insulating layers, as well as the thickness and dielectric constant of the ferroelectric layer. We also derive a compact linear expression for the critical current valid for small polarizations. Our results identify ferroelectric Josephson junctions as electrically programmable superconducting current switches for cryogenic memory and logic applications.

Isometric tensor network states (isoTNS) generalize the isometric form of the one-dimensional matrix product states to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTNS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTNS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTNS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome lattice.

We investigated the magnetoelastic properties of a ${\mathrm{GdRu}}_2{\mathrm{Si}}_2$ single crystal under a magnetic field applied along the crystallographic [001] and [110] directions. We report a series of strong anomalies in the sound velocity that is consistent with the complex phase diagram reported previously for this compound. In particular, in our study we focus on the recently identified magnetic phase in the high-temperature region. We show that while this phase is easily destroyed for magnetic fields applied along [001], it is rather stable for fields along [110]. Furthermore, we introduce a Landau theory and a microscopic toy model describing the elastic response at zero field. We reproduce qualitatively the observed anomalies for different acoustic modes, which suggest that the high-temperature phase weakly breaks the symmetry between the [100] and [010] directions. We discuss candidate magnetic structures consistent with this high-temperature phase, based on the comparison of elastic anomalies for a few different magnetic states.

The parity anomaly for Dirac fermions in two spatial dimensions has shaped perspectives in quantum field theory and condensed matter physics. In condensed matter it has evolved as a mechanism for the half-quantized Hall responses in systems described by massive Dirac fermions. Here we reexamine the issue on a lattice and show that the half-quantized Hall conductivity is absent for massive Dirac fermions when lattice regularization is properly implemented and the translational invariant symmetry is taken into account. We realize that a single massive Dirac cone on a lattice always leads to an integer quantized Hall conductivity and to the half-quantized Hall conductivity only in the unphysical limit of infinite momentum cutoff. The half-quantized Hall conductivity appears with nonzero longitudinal conductance as a signature of a single massless Dirac cone on a lattice. Consequently, the parity anomaly is a property of massless Dirac fermions in a semimetal/metal, not of massive Dirac fermions in an insulator on a lattice.

We study a thin-film yttrium iron garnet sample that exhibits magnetic stripe domains due to a small perpendicular magnetic anisotropy. Using wide-field magneto-optic Kerr effect measurements we reveal the domain pattern evolution as a function of applied field and discuss the role of cubic anisotropy in the domain formation. Rich magnon spectra are observed in the stripe domain states, with a range of excitation conditions providing distinct spectra. The measurements are interpreted using micromagnetic simulations to provide the spatial profiles of each resonance mode. We further simulate domain patterns and resonance spectra accounting for the cubic anisotropy, with good correlation to experiment. This study highlights how noncollinear magnetic domain structures can host complex resonant behavior in a low-damping magnetic material, with potential use in future magnonic applications.

Kagome materials have garnered substantial attention owing to their diverse physical phenomena, yet canonical systems such as the $Z_2$-type ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ family are often obscured by bulk metallic states, spurring an urgent quest for kagome platforms hosting ideal topological states. Recently, Zhou et al. [L. Zhou, F. Yang, S. Zhang, and T. Zhang, Adv. Mater. 36, 2309803 (2024)] proposed the kagome-type IAMX family (IA = alkali metal, M = rare earth metal, and X = carbon group element), which exhibits distinctive ideal topological states; however, their analysis is primarily restricted to the spinless approximation. In this work, we model relativistic effects in the IAMX family, demonstrating that tuning the spin-orbit coupling (SOC) strength drives topological phase transitions and induces novel topological states, resulting in a rich phase diagram. The configuration of topological surface states evolves continuously as the SOC strength is modulated, consistent with the evolution of the topological phase transition. This suggests a viable route toward designing multifunctional topological devices. First-principles calculations performed on three specific IAMX compounds confirm that SOC governs their topological phases, in complete accord with our model analysis.

The melting behavior and transport properties of ${\mathrm{MgSiO}}_3$ at multi-megabar pressures remain poorly constrained despite their importance for high-pressure silicate physics. Here we report the first direct measurements of temperature and optical reflectivity in shock-compressed bridgmanite (${\mathrm{MgSiO}}_3$) using laser-driven decaying shock compression combined with velocimetry and optical pyrometry. Temperature and reflectivity data spanning approximately 4000–60 000 K were used to constrain the ${\mathrm{MgSiO}}_3$ melting curve and to infer its electrical conductivity. We find that the ${\mathrm{MgSiO}}_3$ melting curve becomes shallower than that of iron above 400 GPa, yielding lower melting temperatures in planetary mantles than predicted by several previous theoretical estimates. Across the solid-liquid transition, the inferred electrical conductivity increases significantly, reaching $\sim 2000 \mathrm{\Omega } {\mathrm{cm}}^{-1}$. These results provide experimental benchmarks for theoretical models of silicate melting and transport under extreme pressure-temperature conditions.

${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ is a primary $3d$ Kitaev magnet characterized by strong electronic correlations; however, its properties are not fully understood. In this study, we present a revised nuclear structure based on single-crystal neutron diffraction at ambient conditions, along with spin dynamics under magnetic fields investigated via muon spin relaxation and rotation and inelastic neutron scattering. Structural analysis resolves inconsistencies in the Na-ion ordering by revealing a triangular Na layer between the Co-based honeycomb planes. Transverse-field muon experiments confirm a quantum phase transition induced by a magnetic field at 5.7 T to a quantum-disordered state. Inelastic neutron scattering at 8.55 T applied along the $a$ axis reveals dichotomous magnetic excitations between low-energy magnons coexisting with high-energy spinons. These findings indicate the emergence of a spin liquid–like state within a partially polarized background, highlighting the potential of this system for exploring field-induced quantum phenomena associated with Kitaev magnetism.