Time-dependent control of superconducting quantum circuits is a prerequisite for building scalable quantum hardware. The quantum description of these circuits is complicated due to the electromotive force (emf) induced by time-varying magnetic fields. Here, we examine how the emf modifies the fractional Josephson effect. We show that a time-varying flux introduces a new term that depends on the geometry of both the circuit and the applied magnetic field. This term can be probed via current and charge measurements in closed-loop and open-circuit geometries. Our results refine the current understanding of how to properly describe time-dependent control of topological quantum circuits.

We study the evolution of the electronic structure of the intermetallic series ${\mathrm{Gd}}_6{\left({\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\right)}_{23}, x=0.0–0.75$, which shows nonmonotonic ferrimagnetic ordering temperatures $T_C$ but with a systematic reduction of the total bulk magnetization upon increasing Fe content, $x$. We have carried out hard x-ray photoemission spectroscopy to elucidate the relation between electronic structure and properties of the series. The Gd $3d$ and Gd $4d$ core-level spectra indicate trivalent ${\mathrm{Gd}}^{3+}$ multiplets in the intermediate-coupling scheme with features due to $L\text{−}S$ and $j\text{−}J$ coupling. The Fe $2p$ core levels show asymmetric single peak metal-like spectra, while the Mn $2p$ core levels show asymmetric doublet peaks. The relative intensities of the Mn $2p$ doublets as a function of $x$ indicate occupancy changes of distinct crystallographic sites associated with Mn up-spin and down-spin states. The valence band spectra identify the Gd $4f$ states at high binding energies ($\sim 7.4$ eV). The Mn $3d$ states occur at the Fermi level and as a broad feature between 2 and 5 eV binding energy in ${\mathrm{Gd}}_6{\mathrm{Mn}}_{23}$. Upon substitution, the Fe $3d$ states show up as small shifts to higher binding energies compared to Mn $3d$ states. The Fe $3s$ and Mn $3s$ spectra show exchange split peaks, allowing an estimate of the Mn and Fe magnetic moments using a Van Vleck analysis, which also provides a quantification of occupancy changes with $x$. The overall results are consistent with the bulk net magnetization, indicating that Mn up-spin sites become Fe down-spin sites on substitution, while the nonmonotonic $T_C$ originates in a change from Mn sublattice to Fe sublattice derived ordering.

We investigate how symmetry and topological order are coupled in the ($2+1$)–dimensional ${\mathbb{Z}}_N$ rank-2 toric code for general $N$, which is an exactly solvable point in the Higgs phase of a symmetric rank-2 $\text{U}\left(1\right)$ gauge theory. The symmetry-enriched topological order present has a nontrivial realization of square-lattice translation (and rotation and reflection) symmetry, where anyons on different lattice sites have different types and belong to different superselection sectors. We call such particles “position-dependent excitations.” As a result, in the rank-2 toric code anyons can hop by one lattice site in some directions while only by $N$ lattice sites in others, reminiscent of fracton topological order in $3+1$ dimensions. We find that while there are $N^2$ flavors of $e$ charges and $2N$ flavors of $m$ fluxes, there are not $N^{N^2+2N}$ anyon types. Instead, there are $N^6$ anyon types, and we can use Chern-Simons theory with six $\text{U}\left(1\right)$ gauge fields to describe all of them. While the lattice translations permute anyon types, we find that such permutations cannot be expressed as transformations on the six $\text{U}\left(1\right)$ gauge fields. Thus, the realization of translation symmetry in the ${\text{U}}^6\left(1\right)$ Chern-Simons theory is not known. Despite this, we find a way to calculate the translation-dependent properties of the theory. In particular, we find that the ground-state degeneracy on an $L_x\times L_y$ torus is $N^{3}gcd(L_x,N)gcd(L_y,N)gcd(L_x,L_y,N)$, where $gcd$ stands for “greatest common divisor.” We argue that this is a manifestation of UV/IR mixing which arises from the interplay between lattice symmetries and topological order.

Studying many-body versions of Landau-Zener-like problems of non-interacting electrons in the Slater formalism for several $\mathbf{k}·\mathbf{p}$ models representing Weyl and Dirac semimetals, we systematically include non-adiabatic corrections to a quantum limit of chiral charge pumping in these models. In this paper, we show that relative homotopy invariant [Sun et al., Phys. Rev. Lett. 121, 106402 (2018)] and Euler class invariant [Bouhon et al., Nat. Phys. 16, 1137 (2020)] non-trivially manifest in the non-adiabatic corrections to the quantum limit of chiral charge pumping. These corrections could affect conductivity channels connected with the presence of chiral anomaly. Moreover, we show that, for non-symmorphic systems, this contribution is sensitive to the direction of the applied magnetic field (in respect to the so-called non-symmorphic nodal loop), suggesting that the conjectured direction-selective chiral anomaly in non-symmorphic systems [Bzdušek et al., Nature (London) 538, 75 (2016)] could lead to a strongly anisotropic longitudinal magnetoresistance. The presented approach can be easily applied to other $\mathbf{k}·\mathbf{p}$ or tight-binding models.

We unveil an interesting connection of Lorentz-violating quantum field theories, studied in the context of the standard model extension, and Hubbard-type models of topological crystalline phases. These models can be interpreted as a regularization of the former and, as hereby discussed, explored with current quantum simulators based on ultracold atoms in optical Raman lattices. In particular, we present a complete analysis of the Creutz-Hubbard ladder under a generic magnetic flux, which regularizes a Gross-Neveu model extension and presents a characteristic circulating chiral current whose nonzero value arises from a specific violation of Lorentz invariance. We present a complete phase diagram with trivial insulators, ferromagnetic and antiferromagnetic phases, and current-carrying topological crystalline phases. These predictions are benchmarked using tools from condensed matter and quantum-information science, showing that self-consistent Hartree-Fock and strong-coupling Dzyaloshinskii-Moriya (D-M) methods capture the essence of the phase diagram in different regimes, which is further explored using extensive numerical simulations based on matrix-product states.

Two-monolayer-thick In film with a $\surd 7\times \surd 3$-rect structure is known to show superconductivity at 3.18 K on the $\mathrm{Si}\left(111\right)7\times 7$ substrate. We synthesized the $\surd 7\times \surd 3$-In-rect film on the $\mathrm{Si}\left(111\right)\surd 3\times \surd 3\text{−}\mathrm{B}$ substrate and found that it also became a superconductor at $T_c$ = 2.38 K. The In film on the $\surd 3\text{−}\mathrm{B}$ substrate showed the two-dimensional free-electron-like circular Fermi surface as on the $7\times 7$ substrate. However, the butterfly-wing-like shape contour at the Fermi surface was found to be shifted and enlarged on the $\surd 3\text{−}\mathrm{B}$ substrate. Density functional calculations revealed that it was caused by the difference of the substrate. $T_c$ on the $\surd 3\text{−}\mathrm{B}$ substrate was considered to be identical to that on the $7\times 7$ substrate in consideration of the recently reported surface defect density dependence of $T_c$. These results indicated that the interaction with the substrate does not play a crucial role in the superconductivity of the two-monolayer-thick In film.

The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized plateaus. In tilt multi-Weyl semimetals (mWSMs) lattice models, we systematically study Landau levels (LLs) and magneto-Hall conductivity both under the parallel and perpendicular magnetic field (referenced to the Weyl node's separation), i.e., $\mathit{B}\parallel z$ and $\mathit{B}\parallel x$, to explore the impact of tilting and nonlinearity in the dispersion. We make use of two (single) node low-energy models to qualitatively explain the emergence of mid-gap chiral (linear crossing of chiral) LLs on the lattice for $\mathit{B}\parallel z$ $(\mathit{B}\parallel x)$. Remarkably, we find that the sheet Hall conductivity becomes quantized for $\mathit{B}\parallel z$ even when two Weyl nodes project onto a single Fermi point in two opposite surfaces, forming a Fermi loop with $k_z$ as the good quantum number. On the other hand, the Fermi loop, connecting two distinct Fermi points on two opposite surfaces, with $k_x$ being the good quantum number, causes the quantization in sheet Hall conductivity for $\mathit{B}\parallel x$. The quantization is almost lost (perfectly remained) in the type-II phase for $\mathit{B}\parallel x$ $(\mathit{B}\parallel z)$. Interestingly, the jump profiles between the adjacent quantized plateaus change with the topological charge for both cases. The momentum-integrated three-dimensional Hall conductivity is not quantized; however, it bears the signature of chiral LLs resulting in the linear dependence on $\mu$ for small $\mu$. The linear zone (its slope) reduces (increases) as the tilt (topological charge) of the underlying WSM increases.

Magnetic frustration, the competition among exchange interactions, often leads to novel magnetic ground states with unique physical properties which can hinge on details of interactions that are otherwise difficult to observe. Such states are particularly interesting when it is possible to tune the balance among the interactions to access multiple types of magnetic order. We present antlerite ${\mathrm{Cu}}_3{\mathrm{SO}}_4{\left(\mathrm{OH}\right)}_4$ as a potential platform for tuning frustration. Contrary to previous reports, the low-temperature magnetic state of its three-leg zigzag ladders is a quasi-one-dimensional analog of the magnetic state recently proposed to exhibit spinon-magnon mixing in botallackite. Density functional theory calculations indicate that antlerite's magnetic ground state is exquisitely sensitive to fine details of the atomic positions, with each chain independently on the cusp of a phase transition, indicating an excellent potential for tunability.

Magnetic skyrmions and their antiparticles, the antiskyrmions, are stable magnetic solitons existing down to the nanometer scale. Their stability and size as well as the possibility to propel them by, e.g., electric currents make them promising candidates for use in memory devices, such as racetrack memories. Skyrmions and antiskyrmions share those same advantages individually, but may annihilate each other when they coexist in the same device. Yet, combining them to represent logical bits of 0 (skyrmion) and 1 (antiskyrmion) in one device opens new possibilities to create new types of densely packed racetrack memory devices. For this, a controlled creation and annihilation procedure, i.e., a writing or deletion operation, is necessary. Here, we propose a method to create arbitrary sequences of coexisting skyrmions and antiskyrmions by rotations of the magnetic moments at the edge of a rectangular slab. The skyrmions and antiskyrmions remain stable and do not annihilate each other.

Twisted bilayers of nodal superconductors were recently proposed as a promising platform to host superconducting phases that spontaneously break time-reversal symmetry. Here we extend this analysis to twisted multilayers, focusing on two high-symmetry stackings with alternating ($\pm \theta$) and constant ($\theta$) twist angles. In analogy to alternating-twist multilayer graphene, the former can be mapped to twisted bilayers with renormalized interlayer couplings, along with a remnant gapless monolayer when the number of layers $L$ is odd. In contrast, the latter exhibits physics beyond twisted bilayers, including the occurrence of “magic angles” characterized by cubic band crossings when $L\mathrm{mod}4=3$. Due to their power-law divergent density of states, such multilayers are highly susceptible to secondary instabilities. Within a BCS mean-field theory, defined in the continuum and on a lattice, we find that both stackings host chiral topological superconductivity in extended regions of their phase diagrams.

The hydrogen-rich ternary compounds under high pressure which rely on the synergistic effect of crystal structure and electronic property changes have a good prospect of realizing room temperature superconductivity. Here, we study the structure and superconductivity of the ternary Y-Ca-H system under high pressure using $abinitio$ calculations. We found four unprecedented ternary hydrides with clathrate hydrogen sublattice: $P\text{−}3m1\text{−}\mathrm{Y}{\mathrm{Ca}}_2{\mathrm{H}}_{18}, Fm\text{−}3m\text{−}{\mathrm{Y}}_3\mathrm{Ca}{\mathrm{H}}_{24}, P4/mmm\text{−}\mathrm{YCa}{\mathrm{H}}_{20}$, and $Fm\text{−}3m\text{−}\mathrm{Y}{\mathrm{Ca}}_3{\mathrm{H}}_{24}$ which are potential high-temperature superconductors. Strikingly, the superconducting transition temperature of ${\mathrm{Y}}_3\mathrm{Ca}{\mathrm{H}}_{24}$ was calculated to be 242–258 K at 150 GPa. The strong electron-phonon coupling and the high electron density of states of hydrogen at the Fermi level play important roles in high-temperature superconductivity. Further analysis suggests that the phonon softening in the mid-frequency region induced by Fermi surface nesting effectively enhances the electron-phonon coupling. We found that the appropriate stoichiometric ratio is crucial for the discovery of new hydrides in the Y-Ca-H system, which would provide ideas for exploring ternary hydrides.

We investigate non-Abelian statistics of Majorana-Kramers pairs (MKPs) in a network system of one-dimensional time-reversal invariant topological superconductors by using numerical simulations of braiding dynamics and examine the tolerance against various perturbations which may cause decoherence of MKPs. We, first, consider effects of a magnetic field which breaks time-reversal symmetry. In contrast to a naive expectation, the non-Abelian braiding of MKPs is robust against applied magnetic fields provided that the initial and final states of a braiding process are invariant under the combination of a time reversal and a mirror reflection, even when intermediate states break the combined symmetry. Second, we investigate the stability of non-Abelian braidings in the case with gate-induced inhomogeneous potentials at junctions between superconducting nanowires, which generally generate a non-Majorana nearly zero-energy Andreeev bound state at the junctions. It is found that the non-Majorana nearly zero-energy states interfere with MKPs, resulting in the failure of non-Abelian braidings, when the length scale of the inhomogeneous potentials is comparable to the coherence length of the superconductors.

Polarization dynamical response is a fundamental issue for both physics and functional device applications for ferroelectrics. The phase field model has been proved as an efficient and indispensable method to capture the polarization evolution behaviors. With the size of polar element reducing to be atomic scale, the underlying physics in the phase field model should be well clarified. Starting from the generalized many-body stochastic dynamics, we discuss the thermodynamics of the polarization dynamics simulated based on the phase field scheme. It is found that the presence of random force guarantees the thermodynamics of polarization system. The numerical simulations indicate that the thermal fluctuations induced by random force give rise to a different heat dissipation mechanism during the process of polarization dynamical responses, which is not taken into account in the conventional phase field simulations. In addition, the thermal fluctuations of random force are found to lead to the unexpected phase instability when considering the atomic-scale polarization dynamical behaviors, which is considered to be originated from the incompatibility between the free-energy functional and random force used in the current phase field model. If simply revising the free-energy functional to get rid of such contradiction, the possible phase instability can be eliminated, but it results in the underestimation of thermal fluctuations and the associated polarization dynamical behaviors. In our opinion, the viable solution is to reconstruct the potential field, making it be compatible with the thermal fluctuation induced by random force. Our discussion could help to provide hints for the development of multiscale modeling scheme in polarization dynamics based on a phase field model.

Utilizing first-principles and particle swarm optimization methods, we performed a systematic investigation of crystal structural stability and electrical properties of $A\mathrm{Ge}{X}_3$ compounds $(A=\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Rb},\mathrm{Cs};X=\mathrm{F},\mathrm{Cl},\mathrm{Br},\mathrm{I})$. Our work not only found the perovskite phases, but also discovered the post-perovskite, post-post-perovskite, and octahedra face-sharing structure phases, which are usually stable under high pressure, large strain, or exist in the inorganic–organic compound. These diverse structural phases provide abundant and promising properties. One striking phase is the $P{2}_1{2}_1{2}_1$ perovskite in ${\mathrm{KGeCl}}_3$ and ${\mathrm{KGeBr}}_3$, which possesses intrinsic small polar vortices and antivortices that may lead to a gyrotropic phase transition. The ferroelectric phase of $R3c$ $(\mathrm{LiGe}{X}_3, \mathrm{NaGe}{X}_3)$, $R3m$ $\left(\mathrm{CsGe}{X}_3\right)$ and $Pna{2}_1$ $(\mathrm{KGe}{X}_3, \mathrm{RbGe}{X}_3)$ were also found. The new $Pna{2}_1$ phase possesses both proper and hybrid improper polarization, and the latter is evidenced by two original energetic couplings: one coupling polarization with the antipolar distortion from Ge atoms and antipolar distortion from $A$-site atoms, and another coupling polarization with out-of-phase halide octahedral tilting, in-phase halide octahedral tilting, and antipolar distortion from Ge atoms. The diverse structural phases and electrical properties make Ge-based halide a promising ${ABX}_3$ structure family in ferroics and piezoelectrics.

Most observed phase separation phenomena in complex oxides occur in systems with chemical dopants or structural defects, and theories have established the strong connection between phase separation and the random distribution of chemical dopants. Recent experiments on fabricated high-quality oxide superlattices also confirmed that the phase separation is suppressed in the clean systems without chemical disorders. Thus far, phase separation in strongly correlated oxides without the need of chemical dopants or structural defects has not been fully demonstrated. Here, we have built chemically ordered hybrid superlattices using prototypical ${\mathrm{SrRuO}}_3$ and ${\mathrm{SrTiO}}_3$ perovskite oxides. Contrary to previous understandings, we observe phase separation of two magnetic phases with different spin easy axes. We elucidate this phenomenon through first-principles calculations that the hybrid superlattices have a spontaneous structural instability, leading to a coexistence of ferromagnetic and antiferromagnetic phases. Our findings provide an alternative pathway other than chemical doping to introduce phase separation in correlated oxides and imply that phase separation can exist in clean systems without the need of chemical disorders.

Recent experiments suggest that ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ has a two-component superconducting order parameter (OP). A two-component OP has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls—a possibility that would explain a number of experimental observations including the smallness of the signature of time reversal symmetry breaking at $T_{\mathrm{c}}$ and telegraph noise in critical current experiments. We use resonant ultrasound spectroscopy to perform ultrasound attenuation measurements across the superconducting $T_{\mathrm{c}}$ of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. We find that compressional sound attenuation increases by a factor of 7 immediately below $T_{\mathrm{c}}$, in sharp contrast with what is found in both conventional ($s$-wave) and high-$T_{\mathrm{c}}$ ($d$-wave) superconductors. Our observations are most consistent with the presence of domain walls that separate different configurations of the superconducting OP. The fact that we only observe an increase in sound attenuation for compressional strains, and not for shear strains, suggests an inhomogeneous superconducting state formed of two distinct, accidentally degenerate superconducting OPs that are not related to each other by symmetry. Whatever the mechanism, a factor of 7 increase in sound attenuation is a singular characteristic that must be reconciled with any potential theory of superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

The non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems, associated with a point gap on the complex energy plane, has attracted great theoretical and experimental interest. Much less is studied on the so-called second-order non-Hermitian skin effect, where the bulk does not support a point gap but localization at the corner still occurs. This work discovers a class of hybrid skin-topological modes as the second-order non-Hermitian skin effect without asymmetric couplings. Specifically, by only adding gain/loss to two-dimensional Chern insulators and so long as the gain/loss strength does not close the line gap, all the topological edge states are localized at one corner under the open boundary condition, with the bulk states extended. The resultant non-Hermitian Chern bands can be still topologically characterized by Chern numbers, whereas the hybrid skin-topological modes are understood via some auxiliary Hermitian systems that belong to either intrinsic or extrinsic second-order topological insulator phases. By proposing an innovative construction of auxiliary Hamiltonian, our generic route to hybrid skin-topological modes is further successfully extended to nonequilibrium topological systems with gain and loss, where the anomalous Floquet band topology is no longer captured by band Chern numbers. The extension thus leads to the intriguing finding of nonequilibrium hybrid skin-topological modes. In addition to offering a straightforward route to experimental realization of hybrid topological-skin effects, this study also opens up a promising perspective for the understanding of corner localization by revealing the synergy of three important concepts, namely, non-Hermitian topological insulator, second-order non-Hermitian skin effect, and second-order topological insulator.

Auxetic materials, with negative Poisson's ratio (NPR), exhibit enhanced fracture toughness and shear resistance, due to their unusual mechanical behavior. Although a considerable number of two-dimensional (2D) NPR materials have been predicted theoretically, most of these materials have only in-plane or out-of-plane NPR. In this paper, using first-principles calculations, we found that monolayer $\delta$-GeS and $\delta$-GeSe show fully auxetic behaviors with both in-plane and out-of-plane NPRs at the same time. Meanwhile, monolayer $\delta$-GeSe has a direct bandgap and strong absorption in the blue and violet ranges. Owing to the large spontaneous polarization and strong dipole interaction, they can maintain the ferrielectric properties even at room temperature. Further, they have a considerable piezoelectric coefficient about one order of magnitude larger than recently studied 2D $\mathrm{MoS}_2$ and $h$-BN, due to small elastic stiffness constants. The rare fully auxeticity combined with various properties of monolayer $\delta$-GeS and $\delta$-GeSe could lead to novel multifunctional applications.

Hybrid quantum dot structures are potential building blocks for spintronic devices and quantum logic gates, within which the understanding of many-body correlations is a prerequisite for implementing quantum information processing and generating controlled entanglement. Herein, we consider a hybrid tripartite quantum dot device, one of which is embedded directly between the source and drain electrodes, while the other two dots are side coupled to the first one. Modeling the system using the three-impurity Anderson model, we concentrate on the Ruderman-Kittel-Kasuya-Yosida interaction, the suppression of the Kondo behavior in the side dots, the destructive quantum interference, the gate-controlled quantum phase transitions, the Dicke effect, the ferromagnetic Kondo effect, and the thermodynamical properties in various parameter regimes using the numerical renormalization group method. Unified formulations are established, which are associated with the effective width of the zero-energy peak of the central dot without side dots, the central-side exchange coupling, as well the on-site electron-electron repulsion. We demonstrate that these formulas are well suitable for the non-, weak-, and strong-interacting cases.

A Thouless pump transports an integer amount of charge when pumping adiabatically around a singularity. We study the splitting of such a critical point into two separate critical points by adding a Hubbard interaction. Furthermore, we consider extensions to a spinful Rice-Mele model, namely, a staggered magnetic field or an Ising-type spin coupling, further reducing the spin symmetry. The resulting models additionally allow for the transport of a single charge in a two-component system of spinful fermions, whereas in the absence of interactions, zero or two charges are pumped. In the SU(2)-symmetric case, the ionic Hubbard model is visited once along pump cycles that enclose a single singularity. Adding a staggered magnetic field additionally transports an integer amount of spin while the Ising term realizes a pure charge pump. We employ real-time simulations in finite and infinite systems to calculate the adiabatic charge and spin transport, complemented by the analysis of gaps and the many-body polarization to confirm the adiabatic nature of the pump. The resulting charge pumps are expected to be measurable in finite-pumping speed experiments in ultracold atomic gases for which the $\mathrm{SU}\left(2\right)$ invariant version is the most promising path. We discuss the implications of our results for a related quantum-gas experiment by Walter et al. [arXiv:2204.06561].