Ionic conductivity in solid electrolytes is commonly expected to exhibit Arrhenius dependence on temperature, determined by a well-defined activation energy. Consequently, a standard approach involves calculating this energy using quasi-static methods and using the Arrhenius form to extrapolate the numerical results from one temperature range to another. Despite the ubiquity of this Arrhenius-based modeling, disagreements frequently arise between theory and experiment, and even between different theoretical studies. By considering a tractable minimal model, we elucidate the reason behind the breakdown of the Arrhenius conductivity form. This breakdown is driven by nontrivial phase-space boundaries between conducting and nonconducting regimes, and depends on the kinetic properties of the system.

Identification of a nontrivial ${\mathbb{Z}}_2$ index in a spinful two-dimensional insulator indicates the presence of an odd, quantized (pseudo)spin-resolved Chern number, ${\mathcal{C}}_s=({\mathcal{C}}_{\uparrow }-{\mathcal{C}}_{\downarrow })/2$. However, the statement is not biconditional. An odd spin-Chern number can survive when the familiar ${\mathbb{Z}}_2$ index vanishes. Identification of solid-state systems hosting an odd, quantized ${\mathcal{C}}_s$ and trivial ${\mathbb{Z}}_2$ index is a pressing issue due to the potential for such insulators to admit band gaps optimal for experiments and quantum devices. Nevertheless, they have proven elusive due to the computational expense associated with their discovery. In this work, a neural network capable of identifying the spin-Chern number is developed and used to identify the first solid-state systems hosting a trivial ${\mathbb{Z}}_2$ index and odd ${\mathcal{C}}_s$. We demonstrate the potential of one such system, ${\mathrm{Ti}}_2{\mathrm{CO}}_2$, to support Majorana corner modes via the superconducting proximity effect.

Pt(111) hosts a surface resonance with peculiar properties concerning energy vs momentum dispersion and spin texture. At variance with the free-electron-like behavior of the $L$-gap Shockley-type surface states on the fcc(111) surfaces of Au, Ag, and Cu, it splits into several branches with distinct spin polarization around the center of the surface Brillouin zone $\overline{\mathrm{\Gamma }}$. Theoretical predictions based on density-functional theory vary depending on the particular functionals used. To clarify this issue, we investigate the atomic structure of Pt(111) by low-energy electron diffraction and the unoccupied electronic structure by spin- and angle-resolved inverse photoemission. The experimental results are backed by theoretical studies using different functionals, which show that the characteristics of the surface band depend critically on the lattice constant. From the analysis of the energy-dependent low-energy electron diffraction intensities, we derive structural parameters of the Pt(111) surface relaxation with high accuracy. In addition, we give an unambiguous definition of the nonequivalent mirror-plane directions $\overline{\mathrm{\Gamma }}\overline{\text{M}}$ and $\overline{\mathrm{\Gamma }}{\overline{\text{M}}}^{\prime }$ at fcc(111) surfaces, which is consistent with band-structure calculations and inverse-photoemission data. Concerning the surface resonance at the bottom of the $L$ gap, we identified a delicate interplay of several contributions. Lattice constant, hybridization with $d$ bands, and the influence of spin-orbit interaction are critical ingredients for understanding the peculiar energy dispersion and spin character of the unoccupied surface resonance.

Picosecond ultrasonics is a fast growing and advanced research field with broad application to the imaging and characterization of nanostructured materials as well as at a fundamental level. The aim of this paper is to provide an advanced 3D model based on atomistic spin-lattice simulations of the laser-induced elastic response in ferromagnetically ordered fcc Ni. The advantage of such an approach is the possibility to take into account the laser radiation interaction with the spins and thus characterize the magnetic contribution to the total stress. We analyze the atomic displacements caused both by the ultrafast thermal expansion of the crystal lattice and by the demagnetization process due to the heating of a certain area of the sample by an ultrashort laser pulse. Subsequently, an attempt is made to propose mathematical expressions for describing the corresponding total stress. The lattice and magnetic contributions have been evaluated, whereupon the former is found to be much greater than the latter.

We report on the observation of the circular ratchet effect excited by terahertz laser radiation in a specially designed two-dimensional metamaterial consisting of a graphene monolayer deposited on a few-layer graphene gate patterned with an array of triangular antidots. We show that a periodically driven Dirac fermion system with spatial asymmetry converts the a.c. power into a d.c. current, whose direction reverses when the radiation helicity is switched. The circular ratchet effect is demonstrated for room temperature and a radiation frequency of 2.54 THz. It is shown that the ratchet current magnitude can be controllably tuned by the patterned and uniform back gate voltages. The results are analyzed in the light of the developed microscopic theory considering electronic and plasmonic mechanisms of the ratchet current formation.

The parent compound ${\mathrm{BaBiO}}_3$ of bismuthate high-temperature superconductors (HTSCs) $\mathrm{BaBi}\left(\mathrm{Pb}\right){\mathrm{O}}_3$ and $\mathrm{Ba}\left(\mathrm{K}\right){\mathrm{BiO}}_3$ with perovskitelike structure exhibits unusual electronic and structural properties, which can be satisfactorily explained if we assume that all charge carriers are in the paired state. However, the prior experiments and the first-principle calculations only indirectly indicate the existence of paired charge carriers in ${\mathrm{BaBiO}}_3$. In this work, we report the direct evidence of initially paired electrons and holes in the upper antibonding Bi $6s-\mathrm{O}2p_{{\sigma }^{*}}$ orbital of the neighboring octahedral complexes in the ground state of ${\mathrm{BaBiO}}_3$ using the time-resolved x-ray absorption spectroscopy (XAS) to monitor the electron dynamics after the femtosecond resonant 633 nm laser excitation. We observe strong changes in the oxygen $K$-edge XAS preedge region, defined by the $\mathrm{Bi}6s-\mathrm{O}2p_{{\sigma }^{*}}$ orbitals. We interpret them as a fast ($\le 0.3$ ps) breaking of charge carrier pairs and slower (0.3–0.8 ps) lattice rearrangement from the distorted monoclinic structure into the new metastable state with a cubic lattice, which persists at least up to 60 ps after the excitation. Analysis of the intermediate state at the fast excitation shows that the bond disproportionation and monoclinic distortion of ${\mathrm{BaBiO}}_3$ structure are energetically favorable due to the charge carrier pairing. Thus the compound ${\mathrm{BaBiO}}_3$ forms a new quantum state that we define as a local pair density wave. Taking into account a large number of similarities between bismuthate and cuprate high-temperature superconductors, we believe that our work will give a new impetus to understanding the nature of superconductivity in perovskite HTSCs.

We establish the quantum mechanics of composite fermions based on the dipole picture initially proposed by Read. It comprises three complimentary components: a wave equation for determining the wave functions of a composite fermion in ideal fractional quantum Hall states and when subjected to external perturbations, a wave-function Ansatz for mapping a many-body wave function of composite fermions to a physical wave function of electrons, and a microscopic approach for determining the effective Hamiltonian of the composite fermion. The wave equation resembles the ordinary Schrödinger equation but has drift velocity corrections that are not present in the Halperin-Lee-Read theory. The wave-function Ansatz constructs a physical wave function of electrons by projecting a state of composite fermions onto a half-filled bosonic Laughlin state of vortices. Remarkably, Jain's wave-function Ansatz can be reinterpreted as the new Ansatz in an alternative wave-function representation of composite fermions. The dipole picture and the effective Hamiltonian can be derived from the microscopic model of interacting electrons confined in a Landau level, with all parameters determined. In this framework, we can construct the physical wave function of a fractional quantum Hall state deductively by solving the wave equation and applying the wave-function Ansatz, based on the effective Hamiltonian derived from first principles, rather than relying on intuition or educated guesses. For ideal fractional quantum Hall states in the lowest Landau level, the approach reproduces the well-established results of the standard theory of composite fermions. We further demonstrate that the reformulated theory of composite fermions can be easily generalized for flat Chern bands.

We propose a new platform to detect signatures of the presence of Majorana bound states (MBSs) in the Fraunhofer pattern of Josephson junctions featuring quantum spin Hall edge states on the normal part and Majorana bound states at the NS interfaces. We use a tight-binding model to demonstrate a drastic change in the periodicity of the Fraunhofer pattern when comparing trivial and nontrivial regimes. We explain these results in terms of the presence of additional parallel-spin electron-hole reflections, which due to the spin-momentum locking, occur as cross Andreev reflections, accumulating a different magnetic flux and yielding a change in the Fraunhofer periodicity. We show that this detection scheme exhibits some advantages compared to previous ones as it is robust against disorder and finite temperature and works in equilibrium. Furthermore, we introduce a scattering model that captures the main results of the microscopic calculations with MBSs and extend our discussion to the main differences found using accidental zero-energy Andreev bound states.

Random matrix theory is a powerful tool for understanding spectral correlations inherent in quantum chaotic systems. Despite diverse applications of non-Hermitian random matrix theory, the role of symmetry remains to be fully established. Here, we comprehensively investigate the impact of symmetry on the level statistics around the spectral origin—hard-edge statistics—and expand the classification of spectral statistics to encompass all the 38 symmetry classes of non-Hermitian random matrices. Within this classification, we discern 28 symmetry classes characterized by distinct hard-edge statistics from the level statistics in the bulk of spectra, which are further categorized into two groups, namely, the Altland-${\mathrm{Zirnbauer}}_0$ classification and beyond. We introduce and elucidate quantitative measures capturing the universal hard-edge statistics for all the symmetry classes. Furthermore, through extensive numerical calculations, we study various open quantum systems in different symmetry classes, including quadratic and many-body Lindbladians, as well as non-Hermitian Hamiltonians. We show that these systems manifest the same hard-edge statistics as random matrices and that their ensemble-average spectral distributions around the origin exhibit emergent symmetry conforming to the random-matrix behavior. Our results establish a comprehensive understanding of non-Hermitian random matrix theory and are useful in detecting quantum chaos or its absence in open quantum systems.

In the kagome superconductors $A{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$ ($A$ = K, Rb, Cs), understanding the charge-density-wave (CDW) state and its entanglement with the superconducting ground state is still a challenging issue. Here, by measuring the electrical transport, magnetic susceptibility, Hall effect, and ${}^{51}\mathrm{V}$ nuclear magnetic resonance (NMR), the evolution of superconductivity (SC) and the CDW is comprehensively studied in $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}\mathrm{M}{\mathrm{o}}_x\right)}_3\mathrm{S}{\mathrm{b}}_5$. In contrast with previously reported results for other doped cases, the CDW transition temperature slightly increases to ∼100 K with increasing Mo doping. Meanwhile, the SC is quickly suppressed and vanishes above $x=0.02$. The anomalous Hall effect (AHE), which is tied to the exotic nature of the CDW state in pristine $\mathrm{Cs}{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$, is also strongly suppressed and completely disappears above $x=0.07$. Further ${}^{51}\mathrm{V}$ NMR investigation on the CDW state in $\mathrm{Cs}{\left({\mathrm{V}}_{0.95}\mathrm{M}{\mathrm{o}}_{0.05}\right)}_3\mathrm{S}{\mathrm{b}}_5$ indicates that a short-range stripelike CDW evolves from the original triple-$Q$ CDW state with increasing Mo doping, which largely reduces the density of states at the Fermi level. This result provides a self-consistent explanation for the disappearance of both SC and the AHE by increasing Mo doping, which offers insights into the competitive behavior between SC and the CDW state in the kagome superconductors $A{\mathrm{V}}_3\mathrm{S}{\mathrm{b}}_5$.

A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) ${\mathbb{Z}}_2$ topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular ${\mathbb{Z}}_2$ topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear-response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system. This contrast between theories of magnetoelectric response in formal bulk models and in real finite-sized materials originates from the distinct approaches required to introduce notions of (electronic) polarization and orbital magnetization in these fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear-response calculations in nonmagnetic ${\mathbb{Z}}_2$ TIs that is more plainly consistent with TRS and use this interpretation to discuss the effect's observation—still absent over a decade after its prediction. Our analysis is reinforced by microscopic bulk and thin-film calculations carried out using a simplified but still realistic effective model for the well established ${\mathrm{V}}_2{\mathrm{VI}}_3 [\text{V}=\text{(Sb,}\text{Bi)}$ and $\text{VI}=\text{(Se,}\text{Te)}]$ family of nonmagnetic ${\mathbb{Z}}_2$ TIs. When a uniform dc magnetic field is included in this model, the anomalous $n=0$ Landau levels (LLs) play the central role, both in thin films and in bulk. In the former case, only the $n=0$ LL eigenfunctions can support a dipole moment, which vanishes if there are no magnetic surface dopants and is quantized in the thick-film limit if magnetic dopants at the top and bottom surfaces have opposite orientation. In the latter case, the Hamiltonian projected into the $n=0$ LL subspace is a one-dimensional Su-Schrieffer-Heeger model with ground-state polarization that is quantized in accordance with the bulk linear-response coefficient calculated for (a lattice regularization of) the starting 3D model. Motivated by analytical results, we conjecture a type of microscopic bulk-boundary correspondence: a bulk insulator with (generalized) TRS supports a magnetoelectric coefficient that is purely itinerant (which is generically related to the geometry of the ground state) if and only if magnetic surface dopants are required for the TME to manifest in finite samples thereof. We conclude that in nonmagnetic ${\mathbb{Z}}_2$ TIs the TME is activated by magnetic surface dopants, that the charge-density response to a uniform dc magnetic field is localized at the surface and specified by the configuration of those dopants, and that the TME is qualitatively less robust against disorder than the integer quantum Hall effect.

Anomalous topological phases, where edge states coexist with topologically trivial Chern bands, can only appear in periodically driven lattices. When the driving is smooth and continuous, the bulk-edge correspondence is guaranteed by the existence of a bulk invariant known as the winding number. However, in lattices subject to periodic discrete step walks the existence of edge states does not only depend on bulk invariants but also on the boundary. This is a consequence of the absence of an intrinsic time dependence or micromotion in discrete step walks. We report the observation of edge states and a simultaneous measurement of the bulk invariants in anomalous topological phases in a two-dimensional synthetic photonic lattice subject to discrete step walks. The lattice is implemented using time multiplexing of light pulses in two coupled fibre rings, in which one of the dimensions displays real-space dynamics and the other one is parametric. The presence of edge states is inherent to the periodic driving and depends on the properties of the boundary in the implemented two-band model with zero Chern number. We provide a suitable expression for the topological invariants whose calculation does not rely on micromotion dynamics.

Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same fermion parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to charge noise acting on the potential of each dot, as well as fluctuations of the (weak) interdot tunneling. At weak interdot tunneling, relaxation is suppressed because of disjoint qubit states. However, for strong interdot tunneling the system is protected against noise affecting each quantum dot separately (energy-level noise, dot-superconductor tunneling fluctuations, and hyperfine interactions). Finally, we describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages.

We show that rotating two-dimensional Fermi gases possess a nonrelativistic scale and conformal invariance at weak but nonzero interactions, where the scale invariance of universal short-range interactions is not yet broken by quantum effects. We demonstrate the symmetry in the excitation spectrum of few-fermion ensembles in a harmonic trap obtained by exact diagonalization. The excitation spectrum is shown to split in a set of primary states and derived excited states that consist of breathing modes as well as two different center-of-mass excitations, which describe cyclotron and guiding-center excitations of the total particle cloud. Furthermore, the conformal symmetry is manifest in the many-body wave function, where it dictates the form of the hyperradial component, which we demonstrate using Monte Carlo sampling of few-body wave functions.

At ambient conditions ${\mathrm{SrAl}}_4$ adopts the ${\mathrm{BaAl}}_4$ structure type with space group $I4/mmm$. It undergoes a charge-density-wave (CDW) transition at $T_{\mathrm{CDW}}=243$ K, followed by a structural transition at $T_S=87$ K. Temperature-dependent single-crystal x-ray diffraction (SXRD) leads to the observation of incommensurate superlattice reflections at $\mathbf{q}=\sigma {\mathbf{c}}^{*}$ with $\sigma =0.1116$ at 200 K. The CDW has orthorhombic symmetry with the noncentrosymmetric superspace group $F222\left(00\sigma \right)00s$, where $F222$ is a subgroup of $Fmmm$ as well as of $I4/mmm$. Atomic displacements mainly represent a transverse wave, with displacements that are 90 deg out of phase between the two diagonal directions of the $I$-centered unit cell, resulting in a helical wave. Small longitudinal displacements are provided by the second harmonic modulation. The orthorhombic phase realized in ${\mathrm{SrAl}}_4$ is similar to that found in ${\mathrm{EuAl}}_4$, except that no second harmonic could be determined for the latter compound. Electronic structure calculations and phonon calculations by density functional theory (DFT) have failed to reveal the mechanism of CDW formation. No clear Fermi surface nesting, electron-phonon coupling, or involvement of Dirac points could be established. However, DFT reveals that Al atoms dominate the density of states near the Fermi level, thus corroborating the SXRD measurements. ${\mathrm{SrAl}}_4$ remains incommensurately modulated at the structural transition, where the symmetry lowers from orthorhombic to $\mathbf{b}$-unique monoclinic. The present work draws a comparison on the modulated structures of nonmagnetic ${\mathrm{SrAl}}_4$ and magnetic ${\mathrm{EuAl}}_4$ elucidating their similarities and differences, and firmly establishing that although substitution of Eu to Sr plays little to no role in the structure, the transition temperatures are affected by the atomic sizes. We have identified a simple criterion that correlates the presence of a phase transition with the interatomic distances. Only those compounds $X{\mathrm{Al}}_{4-x}{\mathrm{Ga}}_x$ $(X=\mathrm{Ba}, \mathrm{Eu}, \mathrm{Sr}, \mathrm{Ca}; 0<x<4)$ undergo phase transitions, for which the ratio $c/a$ falls within the narrow range $2.51<c/a<2.54$.

Artificial monopoles have been engineered in various systems, yet there has been no systematic study of the singular vector potentials associated with the monopole field. We show that the Dirac string, the line singularity of the vector potential, can be engineered, manipulated, and made manifest in a spinor atomic condensate. We elucidate the connection among spin, orbital degrees of freedom, and the artificial gauge, and show that there exists a mapping between the vortex filament and the Dirac string. We also devise a proposal where preparing initial spin states with relevant symmetries can result in different vortex patterns, revealing an underlying correspondence between the internal spin states and the spherical vortex structures. Such a mapping also leads to a new way of constructing spherical Landau levels, and monopole harmonics. Our observation provides insights into the behavior of quantum matter possessing internal symmetries in curved spaces.

We study the orbital Hall effect (OHE) in the AC regime using bilayer graphene (BLG) as a prototypical material platform. While the unbiased BLG has gapless electronic spectra, applying a perpendicular electric field creates an energy band gap that can be continuously tuned from zero to high values. By exploiting this flexibility, we demonstrate the ability to control the behavior of AC orbital Hall conductivity. Particularly, we demonstrate that the orbital Hall conductivity at the neutrality point changes its signal at a critical frequency, the value of which is proportional to the perpendicular electric field. For BLG with narrow band gaps, the active frequency region for the AC OHE may extend to a few terahertz, which is experimentally accessible with current technologies. We also consider the introduction of a perpendicular magnetic field in the weak-coupling regime using first-order perturbation theory to illustrate how the breaking of time-reversal symmetry enables the emergence of the AC charge Hall effect in the charge-doped situation and modifies the AC orbital Hall conductivity. Our calculations suggest that BLG with narrow band gaps is a practical candidate for investigating time-dependent orbital angular momentum transport.