The finite parts of a large, locally interacting many-body system prepared out of equilibrium eventually equilibrate. Characterizing the underlying mechanisms of this process and its timescales, however, is particularly hard as it requires one to decouple universal features from observable-specific ones. Recently, additional insight was gained by studying how certain symmetries of the dynamics that are broken by the initial state are restored at the level of the reduced state of a given subsystem. This provides a high-level, observable-independent probe. Until now, this idea has been applied to the restoration of internal symmetries, e.g., U(1) symmetries related to charge conservation. Here we show that the same logic can be applied to the restoration of space-time symmetries, and hence can be used to characterize the relaxation of fully generic systems. We illustrate this idea by considering the paradigmatic example of “generic” many-body dynamics, i.e., a local random unitary circuit, where our method leads to exact results. We show that the restoration of translation symmetry in these systems only happens on timescales that are proportional to the subsystem's volume. In fact, for large enough subsystems, the time of symmetry restoration becomes initial-state independent (as long as the latter breaks the symmetry at time zero) and coincides with the thermalization time. For intermediate subsystems, however, one can observe the “quantum Mpemba effect,” where the state of the system restores a symmetry faster if it is initially more asymmetric. We provide an exact characterization of this effect in a nonintegrable system.

We construct a nonlinear fluctuating hydrodynamic effective field theory for Galilean-invariant quantum Hall systems with spontaneously broken translational symmetry. Neglecting the role of energy conservation in a low-temperature regime, the hydrodynamic mode is a magnetophonon with quartic attenuation: $\omega \sim \pm k^2-i{k}^z$ with $z=4$. However, this linear response theory is unstable, and flows to a nontrivial dynamical universality class with $z\approx 3$. We observe this scaling in numerical simulations of many-body classical Hamiltonian dynamics, in a model of an electronic crystal in the lowest Landau level. Observing this magnetophonon decay rate in a quantum Hall crystal represents a promising setting to detect an analog of a “fractonic dynamical universality class” in a solid-state system, e.g., using microwave impedance microscopy.

We study the sine-Gordon quantum field theory at finite temperature by generalizing the method of random surfaces to compute the free energy and one-point functions of exponential operators nonperturbatively. Focusing on the gapped phase of the sine-Gordon model, we demonstrate the method's accuracy by comparing our results to the predictions of other methods and to exact results in the thermodynamic limit. We find excellent agreement between the method of random surfaces and other approaches when the temperature is not too small with respect to the mass gap. Extending the method to more general problems in strongly interacting one-dimensional quantum systems is discussed.

Selenium is an elemental semiconductor with a wide band gap suitable for a range of optoelectronic and solar energy conversion technologies. However, developing such applications requires an in-depth understanding of the fundamental material properties. Here, we study the properties of the majority and minority charge carriers in selenium using a recently developed carrier-resolved photo-Hall technique, which enables simultaneous mapping of the mobilities and concentrations of both carriers under varying light intensities. Additionally, we perform temperature-dependent Hall measurements to extract information about the acceptor level and ionization efficiency. Our findings are compared to results from other advanced characterization techniques, and the inconsistencies are outlined. Finally, we characterize a high-performance selenium thin-film solar cell, and we perform device simulations to systematically address each discrepancy and accurately reproduce experimental current-voltage and external quantum efficiency measurements. These results contribute to a deeper understanding of the optoelectronic properties and carrier dynamics in selenium, which may guide future improvements and facilitate the development of higher-efficiency selenium solar cells.

The application of pressure to induce superconductivity in topological materials has emerged as an effective approach for discovering potential topological superconductors. In this article we report pressure-induced superconductivity, amorphization, and topological quantum phase transitions in the topological semimetal ${\mathrm{MoP}}_4$. Our results demonstrate that ${\mathrm{MoP}}_4$ undergoes an irreversible amorphous phase transition at approximately 60 GPa, with superconductivity emerging around 34 GPa. Notably, accompanied with the amorphous phase transition, pronounced superconducting fluctuations due to the local formation of Cooper pairs are observed below a characteristic temperature, $T_{\mathrm{sf}}$. Both superconducting transition temperature $T_{\mathrm{c}}$ and $T_{\mathrm{sf}}$ increase monotonically with pressure, reaching maximum values of around 9 and 20 K, respectively. Furthermore, first-principles calculations reveal a sequence of pressure-induced topological phase transitions whereby the system evolves from a strong topological semimetal to a weak topological metal, and finally to a trivial state. These findings suggest that ${\mathrm{MoP}}_4$ serves as an ideal platform for probing the interplay between superconductivity, amorphization, and topological properties under pressure.

Spin fluctuations have been proposed as a key mechanism for mediating superconductivity, particularly in high-temperature superconducting cuprates, where conventional electron-phonon interactions alone cannot account for the observed critical temperatures. Traditionally, their role has been analyzed through tight-binding-based model Hamiltonians. In this work we present a method that combines density functional theory with a momentum- and frequency-dependent pairing interaction derived from the fluctuation exchange (FLEX) type random-phase approximation (FLEX-RPA) to compute Eliashberg spectral functions ${\alpha }^{2}F\left(\omega \right)$, which are central to the spin-fluctuation theory of superconductivity. We apply our numerical procedure to study a series of cuprates where our extracted material-specific ${\alpha }^{2}F\left(\omega \right)$ are found to exhibit remarkable similarities characterized by a sharp peak in the vicinity of 40–60 meV and their rapid decay at higher frequencies. Our exact diagonalization of a linearized BCS gap equation extracts superconducting energy-gap functions for realistic Fermi surfaces of the cuprates and predicts their symmetry to be $d_{x^2-y^2}$ in all studied systems. Via a variation of onsite Coulomb repulsion $U$ for the copper $d$ electrons we show that the range of the experimental values of $T_c$ can be reproduced in this approach but is extremely sensitive to the proximity of the spin-density wave instability. These data highlight challenges in building first-principle theories of high-temperature superconductivity but offer new insights beyond previous treatments, such as the confirmation of the usability of approximate BCS-like $T_c$ equations, together with the evaluations of the material-specific coupling constant $\lambda$ without reliance on tight-binding approximations of their electronic structures.

Condensed matter systems can host emergent “vacua” with particles, fields, and dimension different from that of the universe we inhabit. Motivated by the appearance of emergent gauge fields with both electric and magnetic charges, we consider the fate of electromagnetism in two dimensions in the presence of magnetic monopoles. We find that generically electromagnetic fields are damped due to resistive effects. However, we can still identify a magnetohydrodynamic regime. It exhibits magnetosonic waves which, unlike in $d=3$, are isotropic, to which there is a contribution from the odd viscosity coefficient present in the system. Further, we find a dynamo action, which unlike in $d=3$ requires compressibility of the flow.

In multiferroic ${\mathrm{CuFe}}_{0.95}{\mathrm{Al}}_{0.05}{\mathrm{O}}_2$, applying uniaxial pressure $p$ generates a magnetoferroelectric phase distinct from the well-studied spin-driven ferroelectric phase associated with helical magnetic ordering in this system. Using a four-circle neutron diffractometer, the magnetic structure of the $p$-induced magnetoferroelectric phase is determined as the collinear sinusoidal type, which itself does not break the inversion symmetry in this system. Additionally, synchrotron radiation x-ray diffraction experiments are conducted to investigate how the triangular lattice in ${\mathrm{CuFe}}_{0.95}{\mathrm{Al}}_{0.05}{\mathrm{O}}_2$ is distorted by applied $p$. Although lattice distortion during the magnetic phase transition in ${\mathrm{CuFe}}_{0.95}{\mathrm{Al}}_{0.05}{\mathrm{O}}_2$ is mitigated by the substitution of nonmagnetic ${\mathrm{Al}}^{3+}$, the application of $p$ along the conjugate direction revives the latent spin-lattice coupling, causing the triangular lattice to distort during magnetic phase transition. The application of a magnetic filed considerably reduces $p$-induced ferroelectric polarization, but does not affect lattice distortion. These results indicate that $p$-induced ferroelectric polarization is not a consequence of the piezoelectric effect. Instead, the sinusoidal magnetic structure would contribute to the emergence of $p$-induced ferroelectric polarization through spin-lattice coupling.

Recent years have witnessed a great interest in orbital-related electronics (also termed as orbitronics). In the current work, we present a first-principles density functional theory calculation on orbital magnetic moments, intrinsic orbital Hall effect, and ordinary magnetoconductivity effects in rhombohedral graphene multilayers. Our calculations suggest a giant orbital moment that arises from interatomic cycloid motion, reaching over 30 ${\mu }_B$ under an intermediate gate voltage. This leads to a valley polarization under an external magnetic field, as observed in recent experiments [T. Han et al., Nature (London) 623, 41 (2023)]. In addition, the orbital-related transport feature exhibits significant responses that are potentially observed in experiments. We also suggest that under a periodically driven field (such as a high frequency light field), the ungated graphene multilayers could host strong quantum anomalous and orbital Hall effects, engineered by the layer number. As the graphene multilayers are intrinsically nonmagnetic with negligible spin-orbit coupling, the orbital moments will not be entangled by spin-related signals. Thus, they serve as an ideal platform to conduct orbitronic measurements and utilization for next generation information read/write nanodevices.

The unexpected discovery of intrinsic ferromagnetism in layered van der Waals materials has sparked interest in both their fundamental properties and their potential for novel applications. Recent studies suggest near room-temperature ferromagnetism in the pressurized van der Waals crystal ${\mathrm{CrGeTe}}_3$. We perform a comprehensive experimental and theoretical investigation of magnetism and electronic correlations in ${\mathrm{CrGeTe}}_3$, combining broad-frequency reflectivity measurements with density functional theory and dynamical mean-field theory calculations. Our experimental optical conductivity spectra trace the signatures of developing ferromagnetic order and of the insulator-to-metal transition (IMT) as a function of temperature and hydrostatic pressure. With increasing pressure, we observe the emergence of a midinfrared feature in the optical conductivity, indicating the development of strong orbital-selective correlations in the high-pressure ferromagnetic phase. We find a distinct relationship between the plasma frequency and Curie temperature of ${\mathrm{CrGeTe}}_3$, which strongly suggests that a double-exchange mechanism is responsible for the observed near room-temperature ferromagnetism. Our results clearly demonstrate the existence of a charge-transfer gap in the metallic phase, ruling out its previously conjectured collapse under pressure.

Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in spacetime dimension $1+1\mathrm{D}$ correspond to classifications of mechanisms to confine the SymTFT by condensing anyons. In this work, we extend these results to characterize gapless symmetry-protected topological states: symmetry-enriched gapless phases or critical points that exhibit edge modes protected by symmetry and topology. We establish a one-to-one correspondence between $1+1\mathrm{D}$ bosonic gSPTs, and partially confined boundaries of $2+1\mathrm{D}$ SymTFTs. From general physical considerations, we determine the set of data and consistency conditions required to define a $1+1\mathrm{D}$ gSPT, and show that this data precisely matches that of symmetry-preserving partial confinement (or partially gapped boundaries) of $2+1\mathrm{D}$ quantum double models. We illustrate this correspondence through a dimensional reduction (thin-slab) construction, which enables a physically intuitive derivation of how properties of the gSPT such as edge modes, emergent anomalies, and stability to perturbations arise from the SymTFT perspective.

Using inelastic x-ray scattering (IXS), we experimentally investigate the quantum geometry and quantum information in the large-gap insulator, LiF. Using sum rules for the density-density response function measured in IXS, we compute the quantum Fisher information of the equilibrium density matrix of LiF associated with density perturbations. Next, by exploiting universal relations between the quantum Fisher information, the optical conductivity, and the quantum metric tensor, we extrapolate the diagonal $(h,k,l)=(1,0,0)$ component of the quantum metric of LiF, known as the quantum weight. We compare our results to recently proposed bounds on the quantum weight and find that the quantum weight in LiF comes close to saturating a theoretical upper bound, showing that quantum-mechanical delocalization plays an important role even in ionic insulators. Our work serves as a proof of principle that IXS techniques can be used to quantify state-of-the-art quantum geometric quantities of materials, and establishes the quantum Fisher information as an experimentally accessible generalization of quantum geometry to real materials.

The electronic structure and interactions of kagome materials, such as the 1:1 (FeGe) and 1:6:6 $\left({\mathrm{MgFe}}_6{\mathrm{Ge}}_6\right)$ classes, are complicated and involve many orbitals and bands around the Fermi level. Current theoretical models treat the systems in an $s$-orbital kagome representation, unsuited and incorrect both quantitatively and qualitatively to the material realities. In this work, we lay the basis of a faithful framework of the electronic model for this large class of materials. We show that the complicated “spaghetti” of electronic bands near the Fermi level can be decomposed into three groups of Fe $d$ orbitals coupled to specific Ge orbitals via symmetry and chemical analysis. Such a decomposition allows for a clear analytical understanding (leading to different results than the simple $s$-orbital kagome models) of the flat bands in the system based on the $S$-matrix formalism of generalized bipartite lattices. Our three minimal Hamiltonians can reproduce the quasiflat bands, van Hove singularities, topology, and Dirac points close to the Fermi level, which we prove by extensive ab initio studies. We also obtain the interacting Hamiltonian for the $d$ orbitals in FeGe using the constraint random phase approximation (cRPA) method, which faithfully describes the antiferromagnetic phase. We then use FeGe as a fundamental “LEGO-like” building block for a large family of 1:6:6 kagome materials, which can be obtained by doubling and perturbing the FeGe Hamiltonian. We apply the model to its kagome siblings FeSn and CoSn, and also ${\mathrm{MgFe}}_6{\mathrm{Ge}}_6$. We further extend the formalism developed for the 1:1 family to the 1:3:5 family ${AB}_3{Z}_5$ $(A=\mathrm{K}, \mathrm{Rb}, \mathrm{Cs}; B=\mathrm{Cr}, \mathrm{V}, \mathrm{Ti}; Z=\mathrm{Sb}, \mathrm{Bi})$, demonstrating the broad applicability of the LEGO-like building block approach. Moreover, our method has the potential to be applied to a wider range of materials beyond kagome systems, provided that the relevant LEGO-like building blocks in the crystal and electronic structures can be identified. Our work serves as the first complete framework for the study of the interacting phase diagram of kagome compounds.

A time interface (a rapid change of the constitutive parameters of a material in time), applied within an unbounded medium where a wave travels, can enable frequency conversion and is considered the temporal analog of a spatial interface between two materials. Here, we study light-matter interactions in four dimensions, 4D (space, x,y,z, and time, $t$), by exploring the implications of applying time interfaces, not to the entire space where a wave travels, but to certain regions of space in order to create spatial interfaces in time. Different configurations such as induced perpendicular, parallel, and oblique spatial interfaces via a temporal interface are discussed. It is shown how such four-dimensional combination of temporal and spatial interfaces can enable interesting features such as the 4D generalized Snell's law and temporal chirp, temporal lensing, and temporal routing of electromagnetic waves. Such exotic possibilities may provide new ways to manipulate light-matter interactions via a combination of temporal and spatial interfaces.

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline $\mathrm{PbTi}{\text{O}}_3$. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

Magnetic hopfions are three-dimensional localized topological spin textures characterized by the Hopf invariant. Stable hopfions exist in chiral magnetic trilayers consisting of a middle layer with a weaker perpendicular magnetic anisotropy (PMA) and two capping layers with a stronger PMA. The middle layer holds a hopfion, and the capping layers prevent the hopfion from dilating. However, the existence criteria for a stable hopfion are not adequately known. Here, we numerically obtain the phase diagram for stable hopfions in the plane of the middle layer thickness and dimensionless parameter $\kappa$ which measures the relative strength of the Dzyaloshinskii-Moriya interaction (a chiral exchange interaction) compared with the interactions preferring collinear spin alignment (due to the ferromagnetic exchange interaction and the anisotropy). $\kappa$ is also the parameter determining the locality of skyrmions in chiral magnetic films. Our results deepen our understanding of hopfions and provide practical guidance to experimentalists for seeking materials and nanostructures for stable hopfions.

We have conducted a comprehensive investigation into the magnetic properties of the chiral multiferroic material $\mathrm{CoTeMo}{\mathrm{O}}_6$. In contrast with the previous claim of canted antiferromagnetic order with ferromagnetic components [Y. Doi et al., J. Solid State Chem. 182, 3232 (2009)], our investigation reveals an antiferromagnetic ground state with compensated moments, providing an interesting platform for exploring exotic material properties. Through careful measurements of magnetization under a series of applied fields, we demonstrate that there exist two sequential field-induced magnetic transitions in $\mathrm{CoTeMo}{\mathrm{O}}_6$, with one occurring at $H_{c1}=460$ Oe along the $a$ axis, and the other at $H_{c2}=1.16$ T with the field along the $b$ axis. The values of $H_{c1}$ and $H_{c2}$ exhibit strong angular dependence and diverge with different rates as the applied field is rotated 90 ° within the $ab$ plane. This reflects the distinct nature of these transitions, which is further supported by the different critical behavior of $H_{c1}$ and $H_{c2}$, characterized by the values of $\gamma$, in the function of $H_c=H_0{\left(1-T/T_c\right)}^{\gamma }$. Furthermore, we have demonstrated that there exist structural and magnetic twin domains in $\mathrm{CoTeMo}{\mathrm{O}}_6$ that strongly affect the experimental measurement of their macroscopic properties. Intriguingly, these twin domains can be related to the orthorhombicity/chirality of the crystal structure with the space group $P{2}_1{2}_{1}2$. We further explored the magnetic and structural domains with uniaxial pressure and polarized light microscopy. Our results suggest that $\mathrm{CoTeMo}{\mathrm{O}}_6$ could be used as a unique platform for investigating the intriguing physics involving intertwined degrees of freedom. The tunability of the underlying domain distribution and its strong anisotropy could also be useful for developing functional devices and applications.

We show theoretically that specular Andreev reflection occurs stably at altermagnet-superconductor interfaces, which is a phenomenon that has previously been predicted only in a limited range of materials, such as Dirac/Weyl materials with fine-tuned chemical potentials. Furthermore, the characteristic spin-split bands of the altermagnet lead to a distinctive spin polarization in the specular Andreev reflections. By utilizing this feature, we propose a device that integrates the functions of both a Cooper pair splitter and a spin beam splitter, thereby creating energy-entangled electron pairs. The positive nonlocal conductance and the positive noise cross-correlation are unambiguous signatures of specular Andreev reflections in the proposed device.

While the periodic equation-of-motion coupled-cluster (EOM-CC) method promises systematic improvement of electronic band gap calculations in solids, its practical application at the singles and doubles level (EOM-CCSD) is hindered by severe finite-size errors in feasible simulation cells. We present a hybrid approach combining EOM-CCSD with the computationally less demanding $GW$ approximation to estimate thermodynamic limit band gaps for several insulators and semiconductors. Our method substantially reduces required cell sizes while maintaining accuracy. Comparisons with experimental gaps and self-consistent $GW$ calculations reveal that deviations in EOM-CCSD predictions correlate with reduced single excitation character of the excited many-electron states. Our work not only provides a computationally tractable approach to EOM-CC calculations in solids but also reveals fundamental insights into the role of single excitations in electronic-structure theory.

The non-Hermitian skin effect is an intriguing physical phenomenon, in which all eigenmodes of a non-Hermitian lattice become localized at boundary regions. While such an exotic behavior has been demonstrated in various physical platforms, most realizations have been so far restricted to the linear regime. Here, we explore the cooperation between nonlinearity and the non-Hermitian skin effect, revealing extraordinary amplitude-driven skin localization dynamics. By introducing an extension to the Hatano-Nelson model where couplings inherit nonlinear behavior, we demonstrate the existence of unique amplitude-driven non-Hermitian skin modes capable of concentrating the energy of a source at any point of space, depending on the power level. Our theoretical model is supported by numerical simulations and experimental realization via a highly configurable acoustic metamaterial composed of active electroacoustic resonators. In all, our findings open up exciting paths for a new generation of nonreciprocal systems, in which nonlinearities serve as a strategic tuning knob to manipulate the guiding process.