The transmission eigenchannels of a disordered medium range from unity transmission and high internal energy density to vanishing transmission and low internal energy density. Although the transmission matrix underlies central ideas in mesoscopic electronic transport, it cannot be measured directly in electronic systems. For classical waves, however, the measurable matrix gives access to eigenchannels that control transmission and energy density within the medium. Coherence underlies transmission-eigenvalue scaling, the bimodal distribution in diffusive samples, and Anderson localization. What has remained unresolved is how interference among modal contributions is organized within individual eigenchannels throughout the sample. Here, microwave transmission-matrix measurements resolve the complex contribution of each incident mode to every transmitted mode of each eigenchannel. In simulations, we construct a flux matrix that generalizes the transmission matrix to every depth and further separate each internal modal contribution into forward- and backward-propagating components. For each eigenchannel, the directional flux in every mode throughout the sample factorizes into the squared modal amplitudes of the incident eigenchannel, coupling between waveguide modes, and modal alignment. In high-transmission eigenchannels, the contributions align increasingly constructively with depth, approaching nearly perfect alignment in the highest channel near the localization crossover. In low-transmission eigenchannels, contributions interfere destructively, producing vanishing transmission at a transmission zero. Because the contributions remain appreciable as their coherent sum approaches zero, transmission far below the noise floor of conventional transmission measurements can be determined. In our measurements, the lowest transmission eigenvalue near a transmission zero is more than nine orders of magnitude below the highest. These results provide a depth-resolved decomposition of the modal contributions and interference among them, which produces the broad range of eigenchannel transmissions.

In chiral magnets, magnetic skyrmions are typically stabilized by the competition between exchange and Dzyaloshinskii-Moriya interactions under an external magnetic field, while the role of lattice degrees of freedom has received comparatively less attention. Here we study how spin-phonon (SP) coupling modifies magnetic interactions and the resulting spin textures in a two-dimensional skyrmion model in the square lattice. Using Monte Carlo simulations, we compare two simplified models describing the SP coupling: the Einstein site-phonon (ESP) and bond-phonon models. Integrating the lattice degrees of freedom, we obtain effective Hamiltonians for each SP model, which involve three-spin interactions and quadratic terms. In both cases, skyrmion crystals are stabilized in field regimes that are topologically trivial in the uncoupled model. Moreover, in certain regimes, the conventional triple-$\mathbf{q}$ hexagonal skyrmion lattice is distorted into a double-$\mathbf{q}$ square skyrmion lattice. Additionally, we find that, in the ESP model, strong phonon coupling affecting the exchange interactions drives the system from typical low-field helical phases to meron-antimeron crystals with no net chirality. Overall, our results show that lattice effects provide a simple mechanism to tune a wide variety of topological magnetic phases, ranging from typical skyrmion crystals to distorted arrangements of skyrmions, elongated bimerons, and meron-antimeron phases.

Spin-motive force, i.e., the electric current induced by magnetization dynamics, is theoretically studied beyond the Thouless-pump paradigm. In contrast to the linear-response regime, where the induced current is purely ac, we show that spin-motive force acquires both a dc component and a second-harmonic component at nonlinear order in magnetization dynamics. We further clarify that both contributions originate from the geometric properties of electronic bands—quantum geometry defined in the mixed parameter space $(\mathit{k},\mathit{m})$ spanned by electron momentum $\mathit{k}$ and magnetization $\mathit{m}$. By applying the theory to a Luttinger model, we demonstrate that our mechanism yields a finite nonlinear current even in the insulating regime, and the resulting electrical signal is measurable in a conventional current-measurement setup. Our findings offer an operating principle of ac-to-dc conversion with magnetic materials, highlighting the pivotal role of the $(\mathit{k},\mathit{m})$-mixed-space quantum geometry in magnetization-dynamics-induced electric currents.

We perform a theoretical investigation of the nature of vortices in chiral $d+id$ superconductors on the kagome lattice. The study is motivated by recent experimental developments reporting evidence of time-reversal symmetry breaking in the superconducting state of kagome metals. Using self-consistent microscopic calculations that incorporate the characteristics of the band structure of the kagome lattice, we find that fractional vortices permeate the ground state condensate in the presence of an external field. Each fractional vortex carries one-third of the superconducting flux quantum and exhibits a characteristic signature related to one of the three sublattice degrees of freedom of the kagome lattice. We discuss the relevance of these results to recent experimental studies of kagome superconductors in the presence of an external magnetic field.

We demonstrate that the dynamical phase transition of the quantum $O\left(N\right)$ model at large $N$ leaves universal fingerprints in the infrared structure of the entanglement spectrum. While the leading contribution to the entanglement entropy at long time follows the conventional volume law associated with ballistic entanglement spreading, its subleading behavior sharply distinguishes the different dynamical regimes. Specifically, quenches at and below the critical point generate gapless low-energy entanglement modes together with logarithmic corrections to the long-time entanglement entropy, whose scaling is governed by the scaling exponent of the transition. Using an infinite-slab bipartition geometry and exact numerical correlation functions in the large-$N$ limit, we characterize these scaling laws across the dynamical phase diagram and relate them to the emergence of long-range correlations during the postquench dynamics. We further show that the entanglement eigenmodes themselves reveal characteristic signatures of the dynamical phase transition through their spatiotemporal structure and degeneracy properties.

We study growth quenches, which are local quenches that may gradually destabilize a false vacuum in certain kinetic constrained quantum lattice models, such as the East-West model. We point out a formal analogy with the dynamics of a local operator in the Heisenberg picture. Exploiting this analogy, we obtain several results on growth quenches by adapting operator-dynamics concepts and methods. First, applying the Krylov approach (recursion method), we conjecture the linear growth of Lanczos coefficients in generic quenches $a_m\sim \nu m$ (diagonal) and $b_m\sim \alpha m$ (off diagonal), extending an operator growth hypothesis. We show that the growth quench dynamics is localized in both Krylov and Fock spaces when $\left|\nu \right|>2\alpha$, and derive a bound for the growth quench analog of Lyapunov exponent ${\lambda }_L\le \sqrt{4{\alpha }^2-{\nu }^2}$ when $\left|\nu \right|<2\alpha$. Second, we realize the Fock localization in large-$N$ solvable growth quenches inspired by Sachdev-Ye-Kitaev (SYK) models. The bound on Lyapunov exponent is saturated in large-$q$ SYK growth quench. By contrast, the growth quench is almost always Fock localized in a nonrandom all-to-all growth quench amenable to semiclassics. Finally, in the one-dimensional East-West model, we interpret Fock-space cage states as the existence of a conserved charge. We show that the latter has ballistic transport due to current conservation. Moreover, adding hopping with a fine-tuned amplitude induces a partial localization due to a flat band. Our work suggests growth quenches as a promising approach to realize nonequilibrium coherent phenomena in many-body systems.

We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we sample a quenched coherent-unitary error realization and subsequently measure stabilizer checks, resulting in a syndrome-dependent post-measurement state. By examining both this syndrome state and the associated syndrome distribution, we identify a phase transition in the behavior of the logical information. In the Clifford/stabilizer setting, the change of logical stabilizer structure in a syndrome branch determines the state-level MAP Pauli-frame return probability for a chosen logical-basis input. We separately use quantum coherent information to diagnose recoverability of arbitrary encoded inputs at the channel level. Below a critical error threshold $p_c$, the syndrome branches remain compatible with the original logical sector, enabling a high state-return probability. Above $p_c$, the data are consistent with effective scrambling of the encoded subspace relative to the stabilizer checks, where the syndrome-resolved logical maps approach a global-Clifford-induced stabilizer instrument. This common post-threshold picture organizes both the toric-code and finite-rate random-stabilizer-code results within the same scrambling mechanism. The syndrome distribution supplies complementary local and global structural diagnostics whose scaling depends on the code family. We refer to this phenomenon as a coherent error induced phase transition. To illustrate this transition, we study two classes of quantum error-correcting codes—the toric code and finite-rate random stabilizer codes—thereby shedding light on the design and performance limits of quantum error correction under coherent errors.

Ferrimagnetic skyrmions offer enhanced tunability due to antiferromagnetically coupled sublattices and reduced net magnetization. In chiral magnetic films at zero magnetic field, skyrmion stability is characterized by a dimensionless parameter $\kappa$, yet its applicability to ferrimagnetic systems remains unclear, as most studies assume a fixed, strong intersublattice exchange coupling $J$. Here we investigate how variations in $J$ govern stable and metastable ferrimagnetic skyrmion configurations and introduce a dimensionless parameter ${\zeta }_{\mathrm{eff}}$ to characterize the crossover between strong and weak intersublattice locking. In the strong-coupling regime, intersublattice locking enables stabilization of skyrmion in a sublattice where intrinsic Dzyaloshinskii-Moriya interaction is absent while the other sublattice has finite DMI, yielding a sublattice with DMI-free ferrimagnetic skyrmions. As $J$ decreases, this locking breaks down, leading to independent sublattice behavior and the failure of an effective $\kappa$-based description. Our results establish a unified framework linking intersublattice exchange and skyrmion phase stability in ferrimagnetic systems.

Adiabatic demagnetization refrigeration (ADR) based on frustrated rare-earth magnets provides a promising route toward helium-free sub-Kelvin cooling, while balancing magnetic entropy and interaction scales is essential for optimizing the ADR functionalities. Here we investigate the low-temperature magnetic and ADR properties of the alkali rare-earth double phosphates ${\mathrm{K}}_{3}Ln{\left({\mathrm{PO}}_4\right)}_2 (Ln$ = Yb, Gd), which crystallize in a monoclinic $P{2}_1/m$ structure containing distorted isosceles triangular lattices of rare-earth ions. Magnetization and specific heat measurements confirm the absence of long-range magnetic ordering down to 0.1 K in both compounds. Direct quasi-ADR measurements demonstrate strongly contrasting refrigeration behaviors: ${\mathrm{K}}_3\mathrm{Yb}{\left({\mathrm{PO}}_4\right)}_2$ reaches a minimum temperature of 29.8 mK from an initial state of 2 K and 6 T, whereas ${\mathrm{K}}_3\mathrm{Gd}{\left({\mathrm{PO}}_4\right)}_2$ exhibits extended hold times below 150 mK associated with its larger magnetic entropy reservoir. Crystal-electric-field calculations confirm a $J_{\mathrm{eff}}=1/2$ ground-state doublet in ${\mathrm{K}}_3\mathrm{Yb}{\left({\mathrm{PO}}_4\right)}_2$, while thermodynamic analysis based on magnetic entropy and interaction scales accounts for the distinct ADR performance of the two compounds. These results identify ${\mathrm{K}}_{3}Ln{\left({\mathrm{PO}}_4\right)}_2$ as a chemically robust platform for rare-earth-tunable solid-state ADR.

We generalize the Landau-Lifshitz-Gilbert equation for classical macrospin precession to include dynamic (frequency-dependent) couplings, which can be either dissipative or nondissipative. Near equilibrium, we find that Onsager reciprocity guarantees quasi-Hermitian dynamics for nondissipatively coupled spins; dissipatively coupled spin systems exhibit the more general pseudo-Hermitian dynamics, provided that the couplings have a bipartite structure. For fixed points away from equilibrium, we find in both cases that fluctuations retain the pseudo-Hermitian property, although the spectral features depend dramatically on the local free energy landscape. When two local precession modes hybridize near a crossing, the spectral behavior takes the form either of an anticrossing or level attraction, with the latter formalized in terms of spontaneous $\mathcal{PT}$-symmetry breaking. Near equilibrium, mixing due to nondissipative interactions results in repulsion, while dissipative mixing results in attraction. In contrast, when the fluctuating degrees of freedom form a free-energy saddle point, we find that nondissipative interactions result in level attraction, while dissipative interactions produce level repulsion. We present illustrative examples of these phenomena and discuss the systematic construction of higher order exceptional points, with sensing of magnetic field gradients as a potential application. Accounting for the effects of local Gilbert damping, we examine the cases in which approximate $\mathcal{PT}$-symmetry breaking is still possible and determine the degree to which the qualitative spectral properties still persist.

We propose a theory of the Overhauser effect in the context of electron spin resonance (ESR), including nuclear spin diffusion and spectral diffusion. It is shown that these processes can be observed at low temperatures and strong magnetic fields. These conditions increase the observed cross-transition times and necessitate accounting for slower diffusion mechanisms. We applied the developed theory to explain the mechanism of nuclear spin polarization of individual ${}^{29}\mathrm{Si}$ atoms in a Si:As crystal under ESR conditions. An approach is proposed for estimating the nuclear spin diffusion coefficient, the spectral diffusion parameters, and the nuclear spin relaxation time. We show that an accurate description of the dynamic nuclear polarization of ${}^{29}\mathrm{Si}$ requires incorporating the frozen core model and estimate the nuclear spin diffusion coefficient inside the frozen core, which was previously assumed to be zero.

We investigate the relation between anisotropic finite-field phase boundaries, low-temperature entropy accumulation, and adiabatic demagnetization in ${\mathrm{Li}}_6\mathrm{Gd}({\mathrm{BO}}_3{)}_3$, a large-spin ${\mathrm{Gd}}^{3+}$ magnet with a structurally quasi-one-dimensional zigzag-chain motif. Magnetization, heat-capacity, and field-down magnetocaloric effect (MCE) measurements for $B\parallel c$ and $B\parallel b$ are complemented by direct demagnetization of a 20.15-g single crystal for $B\parallel b$. In zero field, a $\lambda$-type heat-capacity anomaly marks long-range order at $T_N\approx 0.6\mathrm{K}$, but only about $0.39Rln8$ of the entropy is released by $T_N$, consistent with substantial short-range correlations above the transition. For $B\parallel c$, the phase boundary extrapolates to a zero-temperature field scale near 1.45 T, whereas for $B\parallel b$ two boundaries near 0.4 and 0.8 T enclose an intermediate phase whose spin structure remains unresolved. Classical Monte Carlo simulations of a minimal quasi-one-dimensional $J$ XXZ chain model reproduce the $B\parallel c$ field scale semiquantitatively. Enhanced low-temperature entropy and extrema of the MCE-derived magnetic Grüneisen parameter ${\mathrm{\Gamma }}_B^{\mathrm{MCE}}$ occur near these phase boundaries. Isentropic estimates from 6 T and 1.8 K give terminal temperatures of about 150 mK at 1.45 T for $B\parallel c$ and 108 mK at 0.4 T for $B\parallel b$. Direct demagnetization from 8 T and 1.9 K reaches about 155 mK and resolves cooling minima near both 0.8 and 0.4 T, indicating that the field-dependent distribution of low-temperature magnetic entropy, rather than the zero-field limit alone, governs the optimal demagnetization trajectory.

Spin relaxation of localized charge carriers in semiconductors is primarily governed by hyperfine interaction with the surrounding nuclear spin bath. While this mechanism is well-established in III-V bulk materials and quantum dots, its critical role in metal-halide perovskites (MHPs) has only recently emerged. Their inverted band structure induces an unusual hierarchy of hyperfine couplings, with hole interactions dominating electron interactions, particurlaly in Pb-based perovskites. Here, we adapt a spin relaxation model—originally developed for muon spin spectroscopy—to provide an exact description of longitudinal spin relaxation for localized carriers across arbitrary hyperfine correlation times. This approach is motivated by recent experimental evidence in ${\mathrm{MAPbI}}_3$, which places carrier spins in an intermediate correlation regime, where conventional monoexponential approximations fail. Our analysis reveals distinct hyperfine relaxation channels: electrons couple primarily to halogen nuclei, whereas hole interactions are governed by metal nuclei. This leads to a key prediction—perovskites with lighter halogens and metal cations exhibit significantly extended spin relaxation times. Applied to time-resolved Faraday rotation data obtained from two perovskite samples, our model extracts key microscopic parameters—including the carrier localization volume and hyperfine correlation time—demonstrating the necessity for the exact dynamical solution over a single-exponential approximation. These findings provide microscopic insight into hyperfine-driven spin relaxation in MHPs and establish a robust framework for characterizing carrier localization and spin dynamics.

Understanding how stacking controls the nonlinear optical response of two-dimensional materials is key to designing van der Waals heterostructures with tailored functionalities. Here, we establish a comprehensive symmetry-based framework mapping the structural configuration of ${\mathrm{MoS}}_2$ bilayers across four point groups ($D_{3h}, D_{3d}, C_{3v}, C_3$) to their second-order susceptibility tensor ${\chi }^{\left(2\right)}$. Using group-theory arguments benchmarked against first-principles response-function calculations, we demonstrate how symmetry breaking controls the activation and suppression of individual tensor elements in these systems. We show that the emergence of the in-plane component ${\chi }_{xxx}$ in twisted configurations ($C_3$ group) induces a rigid azimuthal rotation of the second-harmonic generation polar lobes, which remains frequency-independent across the entire optical spectrum, locking to half of the structural twist angle. Our findings establish a direct, wavelength-independent optical route for twist-angle determination and provide a clear roadmap for engineering nonlinear optical responses in two-dimensional materials.

The azimuthal angular dependence of the in-plane magnetoresistance provides a powerful probe for detecting rotational symmetry breaking in superconductors, which has significant implications for understanding the superconducting pairing symmetry and the intertwined orders. However, in two-dimensional or layered superconductors with strong anisotropy between in-plane and out-of-plane critical fields, measuring the in-plane magnetoresistance is particularly challenging as it is extremely sensitive to the field misalignment. Here we perform systematic electrical transport measurements on ultrathin FeSe films grown on $\mathrm{SrTi}{\mathrm{O}}_3$ substrates. By remounting the same FeSe film to change the field misalignment, two qualitatively different angular dependences of the in-plane magnetoresistance are observed in the superconducting transition region, indicating the extreme sensitivity of the measurement to field misalignment. The observed anisotropic in-plane magnetoresistance can be well captured by our geometric model considering the field misalignment effect. Our work provides a practical framework for disentangling the misalignment effect and investigating the in-plane rotational symmetry breaking in two-dimensional or layered superconductors.

We study coherent electric manipulation of magnetic field induced localized states at a double kink of a helical edge in a HgTe/CdHgTe quantum well. An in-plane magnetic field opens a gap in the one-dimensional (1D) edge spectrum, while changes in the edge orientation generate localized in-gap states at the kinks. We show that, for suitable geometry and magnetic field direction, two such states form an effective lithographically defined two-level subsystem. Using an edge-state model that includes both the localized levels and the fully propagating 1D edge states outside the magnetic field induced gap, we calculate the electric-dipole matrix elements and solve the time-dependent problem under resonant driving. The resulting dynamics exhibits Rabi oscillations with linear frequencies of 20–40 GHz for realistic parameters. We find that the propagating 1D edge states provide a leakage channel whose strength is strongly controlled by the driving amplitude: reducing the electric field suppresses leakage below the percent level while preserving GHz-scale coherent oscillations. These results establish a route from magnetic field induced corner-state physics to electrically driven two-level dynamics in a realistic two-dimensional topological-insulator edge geometry.

We performed electrical resistivity and ${}^{13}\mathrm{C}$ nuclear magnetic resonance (NMR) measurements on $\lambda \text{−}{\left(\mathrm{BEDSe}\text{−}\mathrm{TTF}\right)}_2{\mathrm{FeCl}}_4$ under various pressures to obtain insights into the effect of $\pi \text{−}d$ interactions on the antiferromagnetic (AF) phase. The resistivity shows that the insulating state is maintained up to 2.0 GPa. ${}^{13}\mathrm{C}$ NMR measurements reveal that the AF transition occurs at 28, 31, and 23 K under 0.5, 1.0, and 2.0 GPa, respectively, indicating that a single AF phase in $\lambda \text{−}{\left(\mathrm{BEDSe}\text{−}\mathrm{TTF}\right)}_2{\mathrm{FeCl}}_4$ is observed under various pressures, whereas two AF phases were observed in $\lambda \text{−}{\left(\mathrm{BEDSe}\text{−}\mathrm{TTF}\right)}_2{\mathrm{GaCl}}_4$. The difference in phase diagrams between the magnetic anion salt, $\lambda \text{−}{\left(\mathrm{BEDSe}\text{−}\mathrm{TTF}\right)}_2{\mathrm{FeCl}}_4$, and the nonmagnetic anion salt, $\lambda \text{−}{\left(\mathrm{BEDSe}\text{−}\mathrm{TTF}\right)}_2{\mathrm{GaCl}}_4$, is attributed to $\pi \text{−}d$ interactions. These results provide insight into a possible microscopic role of $\pi \text{−}d$ interactions in the Fe salt. The magnetic properties of $\lambda \text{−}{\left(\mathrm{BEDSe}\text{−}\mathrm{TTF}\right)}_2{\mathrm{FeCl}}_4$ are described by the isolated cluster comprising two dimers and two anions with positive and negative $\pi \text{−}d$ interactions, suggesting antiferromagnetic coupling between two dimers in the cluster. We also discuss the possible AF structures of $\lambda \text{−}{\left(\mathrm{BEDSe}\text{−}\mathrm{TTF}\right)}_2{\mathrm{FeCl}}_4$.

We report on the longitudinal magnetoresistance (MR) in thin metal films on an Ising-type antiferromagnetic insulator, ${\mathrm{Na}}_5{\mathrm{Co}}_{15.5}{\mathrm{Te}}_6{\mathrm{O}}_{36}$ ($\mathrm{NCTO}$). Steep changes in the MR spectra with hysteresis were observed at spin-flip transitions driven by magnetic fields applied along the easy axis of the $\mathrm{NCTO}$ crystal. The MR jumps almost follow steplike changes in magnetization at the spin-flip transition. At very low temperatures where $\mathrm{Co}$ moments are partially frozen, the MR anomalies exhibit a tunnel-magnetoresistance-like shape. The observed MR anomalies at the spin-flip transition are attributed to strain effects via magnetostriction upon the magnetic-structure change of the $\mathrm{Co}$ nets in $\mathrm{NCTO}$ because similar MR jumps are observed in $\mathrm{Pt}/\mathrm{NCTO}, {\mathrm{Pt}/\mathrm{SiO}}_x/\mathrm{NCTO}$, and $\mathrm{Cu}/\mathrm{NCTO}$ heterostructures. Interestingly, we find that the high-field slopes of the MR spectra show opposite signs between $\mathrm{Pt}/\mathrm{NCTO}$ and $\mathrm{Cu}/\mathrm{NCTO}$ at low temperatures. Because similar MR spectra are observed for ${\mathrm{Pt}/\mathrm{SiO}}_x/\mathrm{NCTO}$, in which the interface magnetic interaction is negligible, the weak antilocalization due to the strong spin-orbit interaction of the Pt films is likely to contribute to the low-temperature MR.

Stacking polymorphism is a common characteristic of van der Waals layered materials which can substantially modify their physical properties. Here, based on first-principles calculations combined with electron and phonon transport theories, we systematically investigate the thermodynamic stability, electronic structure, lattice dynamics, and thermoelectric performance of ${\mathrm{Sc}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$ with three high-symmetry stacking sequences, namely, AA, AB, and ABC. We find that the AA- and AB-stacked structures are nearly degenerate in energy with the experimentally reported ABC phase and that the maximum sliding barrier among these stacking sequences is only about 10 meV/atom, thereby accounting for the stacking faults observed experimentally. These three stacking sequences exhibit distinct electronic structures, with the conduction band minimum being highly sensitive to the stacking sequence. As a consequence, the conduction band degeneracies are 12, 2, and 8 for the ABC, AA, and AB stackings, respectively, leading to markedly different electronic transport properties near the band edge. The lattice thermal conductivity is governed primarily by three-phonon (3ph) scattering, whereas four-phonon scattering provides an additional reduction, particularly in the ABC stacking. Among the three structures, the AB stacking exhibits the lowest lattice thermal conductivity owing to its stronger 3ph scattering and lower phonon group velocity. As a result, the maximum thermoelectric figure of merit $ZT$ is achieved in the AB structure, followed closely by the ABC structure, whereas the AA structure shows a substantially reduced value. These results demonstrate that the stacking sequence exerts a non-negligible influence on the thermoelectric performance of ${\mathrm{Sc}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6$.