Deep thermalization, where ensembles of pure states on a local subsystem, conditioned on measurement outcomes on its complement, approach universal maximum-entropy ensembles, represents a stronger form of ergodicity than conventional thermalization. We show that this framework fails dramatically for mixed initial states, evolved unitarily, even with infinitesimal initial mixedness. To address this, we introduce an alternate paradigm of deep thermalization for mixed states, fundamentally distinct from that for pure-state ensembles. In our formulation, the deep thermal ensemble arises by tracing out auxiliary degrees of freedom from a maximum-entropy ensemble defined on an augmented system, with the ensemble structure depending explicitly on the entropy of the initial state. We demonstrate that such ensembles emerge dynamically in generic, locally interacting chaotic systems. For the self-dual kicked Ising chain, which we show to be exactly solvable for a class of mixed initial states, we find exact emergence of the so-defined mixed-state deep thermal ensemble at finite times. Our results therefore lead to fundamental insights into how maximum-entropy principles and deep thermalization manifest themselves in unitary dynamics of states with finite entropy.

Photoinduced phase transitions (PIPTs) are typically described within Landau theory for group-subgroup systems. However, transitions between phases with unrelated symmetries—such as the diamond-to-graphite transformation from the cubic Fd-3m space group to the hexagonal $\mathrm{P}{6}_3/\mathrm{mmc}$ space group—lie beyond its scope. Here, we uncover a two-step nucleation mechanism in carbon: the system first passes through a metastable intermediate, which evolves into graphite under weak excitation or into an amorphous state under strong excitation. Real-time mapping of carriers and bond distortions reveals that directional redistribution of photoexcited carriers generates atomic driving forces, breaking C-C bonds along specific directions and steering the lattice toward graphite. In contrast, Si and Ge lack stable π bonds, leading only to amorphization under the same photoexcitation. These findings not only establish a unified framework for understanding PIPT between distinct symmetry groups but also resolve longstanding questions about the distinct phase transition pathways in diamond-based materials.

We present a generalized temporal transfer matrix method (TTMM) for time-varying media that accurately captures wave dynamics in media operating at exceptional points (EPs). The method expands wave fields in the canonical basis of each temporal layer and derives the complete time evolution of all basis vectors. Temporal matching and phase-delay matrices are constructed from the generalized modal matrices and their corresponding eigenvalues. Additionally, an amplitude-boosting matrix is introduced to account for the power-law amplification of field amplitudes associated with EP dynamics. This matrix depends only on the order of the EP and naturally reduces to the identity matrix in its absence. The proposed TTMM is validated through two representative EP media, demonstrating its accuracy and broad applicability.

We report the observation of x-ray linear dichroism (XLD) at the Mn $L_{2,3}$ edges in an epitaxial W/${\mathrm{Mn}}_3\mathrm{Sn}$ thin film with kagome planes oriented out of plane. A finite XLD signal is observed between linear polarizations parallel and perpendicular to the kagome planes, reflecting anisotropic orbital occupation of Mn $3d$ states. The XLD spectra are qualitatively reproduced by atomic multiplet calculations, supporting an orbital-anisotropy origin of the dichroism. The XLD amplitude is comparable to that of the x-ray magnetic circular dichroism (XMCD) arising from the magnetic dipole term, indicating significant spin polarization in the anisotropic orbitals. Furthermore, the calculations of the XMCD and XLD intensities as a function of the octupole orientation provide a basis for future microscopy experiments capable of imaging magnetic and crystallographic domains in noncollinear antiferromagnets.

Magnetic domain wall bimerons (DWBMs) offer a platform for current-driven transport in patterned magnetic stripes. However, soliton-soliton interactions and defect pinning complicate their reliable motion. We demonstrate that periodic defect arrays stabilize multi-DWBM transport and give rise to a distinctive collective state, the magnetic worm. A single DWBM travels at constant speed, with defects reducing this speed while preserving an approximately linear velocity-current relation. For two DWBMs, the center of mass advances nearly uniformly while their separation exhibits bounded oscillations whose frequency increases and amplitude decreases with current. For larger trains, the oscillations lose synchrony, producing segmented, wormlike motion. This pattern emulates wormlike locomotion through retrograde peristaltic waves, effectively modulating surface friction. These findings open pathways toward current-controlled nano-oscillators, phase-coded racetrack logic, and on-chip defect sensing in patterned racetrack devices.

Spin valves are key to spintronics but are typically limited to engineered thin-film heterostructures. Achieving intrinsic spin-valve-like behavior in bulk materials would mark major progress toward scalable spintronics. Here, we report a multiprobe study of the quaternary Heusler alloy CoFeVSb, a rare multifunctional "quantum composite" combining spintronic, thermoelectric, and topological properties. Neutron powder diffraction confirms long-range magnetic order at low temperature and the coexistence of antiferromagnetic (AFM) and ferromagnetic (FM) components due to partial ${\mathrm{DO}}_3$ disorder, forming AFM/FM interfaces and spin pinning at room temperature. Magnetotransport measurements reveal robust asymmetric magnetoresistance at room temperature—a hallmark of spin-valve behavior usually seen in multilayers. Hard x-ray photoemission spectroscopy (HAXPES) resolves the valence-band structure, consistent with density-functional theory (DFT) calculations and confirming a metallic nature. HAXPES further shows that structural disorder stabilizes AFM/FM coexistence, giving rise to the spin-valve-like magnetoresistance. By correlating structure, magnetism, and transport, this work demonstrates intrinsic spin-valve functionality, establishing CoFeVSb as a strong candidate for scalable, multifunctional spintronic platforms.

Strong correlations between magnetic Barkhausen noise (MBN) and the motion of magnetic domain walls (DWs) have been confirmed by experiments. However, the developed MBN probe and the domain pattern observation system have a severe mismatch in time-domain sampling interval and spatial resolutions. This makes it difficult to identify the exact dependency of the DW velocity on the MBN amplitude. In this study, MBN imaging with spatial resolution in submillimeter scale and domain pattern observation with a frame rate of 14 480 fps are realized in an integrated system. Much experimental data are obtained at locations both near and far from the grain boundary in grain-oriented silicon steel. Careful examinations are performed using the fused data, and it is found that linear correlation is only adequate in the stage of magnetization reversal near the coercive field, while strong nonlinear correlation was reported in grain-oriented silicon steel under the near-zero-field reversal stage. The existing theoretical model is derived under a quasistatic magnetic field, and it cannot predict the experimentally observed nonlinear behavior. To solve this problem, an improved model is proposed that takes into account the hinder effect of a microscopic eddy current applied to the domain motion. An empirical formula is derived for predicting the nonlinear dependency of the DW velocity on the MBN amplitude, and its success is validated experimentally.

We report a comprehensive investigation of the anisotropic magnetism and magnetic field-induced transitions in single crystals of the orthorhombic system TbAlGe, a member of the topological $R\mathrm{AlGe}$ (where $R$ denotes rare earth) family with the highest ordering temeprature in the $R\mathrm{Al}X$ ($X=\mathrm{Si},\mathrm{Ge}$) series. With a single rare-earth site with triangular coordination in its $Cmcm$ orthorhombic unit cell, TbAlGe harbors complex magnetic interactions that yield two antiferromagnetic transitions at 40 and 8 K in zero field, and a rich cascade of metamagnetic transitions that only appear for fields directed along the crystallographic $a$-axis. Combining electrical resistivity, magnetization, and heat capacity measurements with magnetotransport experiments performed up to 41.5 T, we construct a magnetic phase diagram mapping the multiple magnetic phases of TbAlGe, and we discuss the complex interplay between localized $4f$ magnetism and itinerant electronic topology, establishing TbAlGe as a compelling platform for exploring tunable magnetic semimetal physics.

We develop a full microscopic theory for the optical conductivity $\sigma \left(\omega \right)$ of a dirty current-carrying superconductor. Within the Keldysh sigma model formalism, we obtain the general analytical expression for $\sigma \left(\omega \right)$, applicable for arbitrary frequency $\omega$, temperature $T$, and dc supercurrent $I$. In addition to altering the usual Mattis-Bardeen conductivity ${\sigma }_1\left(\omega \right)$, a finite supercurrent introduces two new contributions: ${\sigma }_2^{\text{qp}}\left(\omega \right)$ from quasiparticle redistribution and ${\sigma }_2^{\text{SH}}\left(\omega \right)$ from the amplitude (Schmid-Higgs) mode excitation by the ac field. We investigate, both analytically and numerically, the main features of the optical conductivity in the presence of a dc supercurrent. They include a peak in $\mathrm{Re}\sigma \left(\omega \right)$ above the optical gap and a sign change of $\mathrm{Im}\sigma \left(\omega \right)$, with both effects becoming more pronounced at higher $I$ and lower $T$. We also elucidate the role of inelastic relaxation, which governs the low-frequency response, leading to a giant microwave absorption and a suppression of the apparent superfluid density at the critical current. The optical conductivity measurement of a superconductor biased by a finite dc supercurrent enables the direct observation of the Schmid-Higgs mode via transport measurements.

We show that frustrated spin textures can generate anisotropic Josephson couplings between $d$ vectors that can stabilize spatially varying pairing orders in spin-triplet superconductors. These couplings depend on the relative orientation of $d$ vectors, analogous to Dzyaloshinskii-Moriya and $\mathrm{\Gamma }$-type interactions in magnetism, leading to an effective “pliability” of the pairing order that competes with superfluid stiffness. Such couplings cannot originate from spin-orbit coupling; rather, they can arise, for example, when itinerant electrons are coupled to a local exchange field composed of frustrated spin moments. Using a $T$-matrix expansion, we show that coupling to a local exchange field leads to an effective tunneling of itinerant electrons that is dependent on the underlying spin configurations at the barrier between superconducting grains. Furthermore, Josephson tunneling through frustrated spin textures can produce a Josephson diode effect. The diode effect originates either from nonvanishing spin chirality in the barrier, or from antisymmetric Josephson coupling between noncollinear $d$ vectors, both of which break inversion and time-reversal symmetries.

We study the Josephson diode effect in the one-dimensional superconductor/helimagnet/superconductor junctions using the Green's function method. For the spin-singlet $s$-wave pairing in superconductors, it is found that the necessary conditions for the Josephson diode effect are the nonzero chemical potential and the conical magnetic configuration in the helimagnet. The diode efficiency is strongly dependent on the chemical potential, chirality, tilt angle, and exchange coupling in the helimagnet. The high efficiency close to $40\%$ can be obtained for specific parameter values. The sign of the diode efficiency can be tuned by changing the chirality, tilt angle, exchange coupling, and chemical potential. The dependence of the diode efficiency on the number of supercells in the helimagnet is also investigated. The characteristics of the supercurrent nonreciprocity and diode efficiency in the junctions are clarified through the symmetry analysis and the energy band calculations. The diode effect for the spin-triplet $p$-wave pairing in superconductors is also discussed, and the nonzero chemical potential is no longer a necessary condition for the Josephson diode effect due to the equal-spin Cooper pair-mediated transport in the $p$-wave junctions. These results provide a scheme for the Josephson diode effect without spin-orbit coupling, which possesses the potential applications in the design of dissipationless electronic devices.

We present the pressure–temperature phase diagram of the bilayer-type organic conductor (ETTM-STF)${}_2{\mathrm{BF}}_4$, established by ${}^1\mathrm{H}, {}^{19}\mathrm{F}$, and ${}^{77}\mathrm{Se}$- NMR and ac susceptibility measurements under ambient and applied pressures. At ambient pressure, the system exhibits critical slowing down of the conformational dynamics of the ETTM-STF terminal group and undergoes a nonmagnetic transition at 20 K, accompanied by tetramerization associated with molecular shape distortion. Upon applying pressure, the nonmagnetic phase is progressively suppressed and vanishes near 10 kbar. Around this pressure region, clear diamagnetic signals are observed, demonstrating bulk superconductivity. The superconducting transition temperature reaches 8.0 K at 7 kbar, which is notably high among non-BEDT-TTF organic superconductors. Our combined nuclear magnetic resonance (NMR) and ac susceptibility results reveal that the superconducting phase is directly adjacent to the nonmagnetic phase in the pressure-temperature phase diagram. This finding stands in stark contrast to the majority of correlated-electron superconductors, where superconductivity typically emerges in proximity to magnetically ordered phases, suggesting a potentially unconventional pairing mechanism in this system.

We study correlation properties of polaritons at zero temperature in a multiconnected Jaynes-Cummings lattice on a superconducting circuit quantum electrodynamics platform with engineered cross-Kerr nonlinearity that mimics attractive nearest-neighbor interaction. A multiconnected Jaynes-Cummings lattice is a one-dimensional lattice constructed from alternating qubits and resonators with different left and right couplings. The nearest-neighbor interaction or cross-Kerr coupling is implemented dispersively through ladder-type qutrits between each nearest-neighboring pair of resonator modes. Projecting onto the lower-polaritonic manifold, we derive an extended two-mode (bipartite) Bose-Hubbard-like model featuring on-site and attractive nearest-neighbor interactions. Employing a continuum bosonization approach, we express the Hamiltonian in terms of symmetric $(+)$ and antisymmetric $(-)$ collective modes. In the regime where the $(-)$ sector acquires a finite gap, one can reduce the system to an effective single-component Luttinger liquid model for the $+$ sector. The cross-Kerr term reduces the compressibility of the $(+)$ mode, thereby enhancing the corresponding Luttinger parameter $K_{+}$, resulting in the slower algebraic decay of single-particle correlations, $G\left(x\right)\propto {\left|x\right|}^{-1/\left(4K_{+}\right)}$.

The discovery of high-temperature superconductivity (HTSC) in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has aroused significant interest in exploring the pairing mechanism. Previous studies have proposed an effective $d_{x^2-y^2}$-orbital bilayer $t-J_{\parallel }-J_{\perp }$ model, in which the electrons of the $d_{x^2-y^2}$ orbital are charge carriers, which are subject to the intralayer antiferromagnetic (AFM) superexchange $J_{\parallel }$ and the large interlayer AFM superexchange $J_{\perp }$ typically stronger than $J_{\parallel }$, with $J_{\perp }$ transferred from the nearly half filled, and hence localized, $d_{z^2}$ orbital through the strong Hund's rule coupling. Here we study this model by the variational Monte Carlo (VMC) simulation and find a dominant interlayer $s$-wave pairing, in which the SC order parameters have a drastic improvement compared with those of the mean-field (MF)-type theories. In real materials, the Hund's coupling is finite, leading to reduced $J_{\perp }$, dictating that the MF-type theories have difficulty explaining the HTSC. However, our VMC calculations find that even for effective $J_{\perp }$ as weak as $J_{\perp }=J_{\parallel }$, the interlayer pairing is still considerably large and can be compared with the $T_c$ observed in experiments, which is very weak in MF-type theories. This result indicates the important role of the Gutzwiller projection in improving the $T_c$, which is ignored in the MF-type theories. In addition, our results show that suppressed interlayer hopping can promote interlayer pairing, which is consistent with the fact that the interlayer hopping of the $d_{x^2-y^2}$ orbital in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ is very weak. Our research offers a perspective for understanding the pairing mechanism of bilayer nickelates and provides a reference for recent ultracold-atom experiments in mixed-dimensional systems.

The Berry curvature dipole induced by symmetry breaking plays a pivotal role in electronic transport properties and nonlinear responses, such as the nonlinear Hall effect and circular photogalvanic effect. The study of the Berry curvature dipole is often explored in time-reversal symmetric systems, but it should not be limited to such materials. Here, we predicted that the ferroelectricity in monolayer ${\mathrm{CrNBr}}_2$ produces the Berry curvature dipole, leading to the nonlinear Hall effect and circular photogalvanic current. The linear anomalous Hall effect and circularly polarized optical absorption, governed by spin-orbit coupling, are independent of ferroelectric polarization and exhibit extremely small conductance. In contrast, multiferroic monolayer ${\mathrm{CrNBr}}_2$ achieves a large nonlinear Hall conductivity ($\sim 1e^3/\hslash \mathrm{e}{\mathrm{V}}^{-1}$ at 30 K) and circular photogalvanic current, despite its suppression at high temperatures from phonon scattering. The coupling between the ferroelectric polarization and the Berry curvature dipoles (intraband for nonlinear Hall conductance and interband for circular photogalvanic current) allows for nonvolatile switching of these effects, presenting substantial promise for nanoelectronic and optoelectronic devices.

We compute and track the impact of truly nonlocal-correlation effects on the quasiparticle (QP) band structure of hexagonal boron-nitride (h-BN) systems. To that end, we start with the consistent-exchange vdW-DF-cx version [K. Berland et al., Phys. Rev. B 89, 035412 (2014)] of the van der Waals (vdW) density functional (vdW-DF) method for exchange-correlation (XC) functional design and enforce piecewise linearity in the energy changes with partial charging, using the Koopmans-integer (KI) DFT framework [E. B. Linscott et al., J. Chem. Theory Comput. 19, 7097 (2023)]. Our approach and results, denoted KI-CX(CX) to emphasize the importance of consistency in structure and QP predictions, extends present-standard use of KI DFT, denoted KI-PBE (as it is based on the semilocal PBE XC functional but computed at the experimental structure), to capture, for example, the impact of the interlayer coupling on the QP band structure, including a full account of vdW signatures. We find that KI-CX(CX) predictions generally agree with GW studies and also with recent experimental data for bulk h-BN. We contrast QP predictions obtained in KI-CX(CX) and KI-PBE and well as in KI-PBE(PBE) (that is, KI-PBE studies based the PBE structure) and we correlate these with the core (vdW) nature of differences between the PBE and CX functionals. This analysis permits us to provide a precise discussion of what are direct and indirect vdW signatures in these layered systems and to define a new QP-based method, also denoted KI-CX(CX), for testing quality and consistency in XC functionals.

The narrow-gap semiconductor ${\mathrm{FeGa}}_3$ has attracted considerable attention due to its colossal thermoelectric Seebeck effect, intriguing magnetic anomaly, and quantum criticality. Although the quasiparticle excitations in the band gap have been probed and proposed to be directly associated with exotic characters of ${\mathrm{FeGa}}_3$, the physical origin of these in-gap states and their direct connection to either of these puzzling properties are under debate. Here, we report the discovery of the dispersive in-gap states in semiconducting ${\mathrm{FeGa}}_3$ through high-resolution angle-resolved photoemission spectroscopy. Combined with first-principles calculations and comprehensive analysis, the observed coherent in-gap states are tentatively identified as a manifestation of slightly off-stoichiometry induced ordered secondary phase, whose formula and exact lattice structure require further clarification. Notably, these dispersive in-gap states provide a consistent explanation for the exotic electronic and magnetic properties of ${\mathrm{FeGa}}_3$, establishing their origin in the previously overlooked secondary phase rather than in strong correlation effects or the trivial disorders.

Controlling collective electronic states through clean and reversible external stimuli is crucial for realizing functional quantum materials. Here, we report a study on temperature ($T$) and pressure ($P$)-tuned charge-density-wave (CDW) orders in the quasi-one-dimensional system of $\mathrm{NbS}{\mathrm{e}}_3$, through single-crystal x-ray diffraction, and electric and magnetotransport measurements. A refined and extended phase diagram is presented, prompting a reevaluation of earlier claims regarding the coexistence of CDW and superconductivity (SC). Here, SC is found to emerge only once all long-range CDWs are suppressed. Notably, the anomalous Hall and magnetoresistance (MR) effects observed at low pressure ($\mathrm{LP}\sim 0.8\mathrm{GPa}$) may arise from distinct carrier types associated with the two competing CDWs, CDW1 and CDW2. These two coexisting CDWs, characterized by distinct modulation vectors, ${\mathit{q}}_{\mathbf{1}}$ and ${\mathit{q}}_{\mathbf{2}}$, show pressure-induced opposing shifts in their $b^{*}$ axis projections (denoted as $q_1^{b*}$ and $q_2^{b*}$), while preserving a phase-coupling relationship 2(${\mathit{q}}_{\mathbf{1}}+{\mathit{q}}_{\mathbf{2}}$) $\sim \left[111\right]$. Upon gradual suppression of the long range order CDW2 order, $q_1^{b*}$ of CDW1 stabilizes and enters a decoupled regime within $\sim 0.8-1.3$ GPa, followed by a pronounced change in its periodicity between $\sim 1.3$ and 2.9 GPa. Above 2.9 GPa, all long-range CDW orders vanish, giving way to emergent superconductivity (SC).