We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity $s$-wave and odd-parity $p$-wave interactions. We find the solutions of the stable in-medium three-body cluster states such as the Cooper triple by solving the corresponding in-medium variational equations. We further feature a phase diagram consisting of the $s$- and $p$-wave Cooper pairing phases, and Cooper tripling phase, in a plane of $s$- and $p$-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both $s$- and $p$-wave interactions are moderately strong.

The unique nonreciprocal responses of superconductors, which stem from the Cooper pairs' quantum condensation, have been attracting attention. Recently, theories of the second-order nonlinear response in noncentrosymmetric superconductors were formulated based on the Bogoliubov–de Gennes theory. In this paper, we study the mechanism and condition for second-order optical responses of time-reversal symmetric superconductors. The numerical results show the characteristic photocurrent and second harmonic generation in the superconducting state. However, the superconductivity-induced nonlinear optical responses disappear under some conditions on pair potential. We show that the coexistence of intraband and interband pairing is necessary for the second-order superconducting optical responses. In addition, the superconducting Berry curvature factor, which is related to a component of Berry curvature in the superconducting state, is essential for the nonlinear responses. Thus, we derived the microscopic conditions where the superconducting nonlinear response appears.

Persistent spin textures (PSTs) in momentum space have the potential to enable spintronic devices which are currently limited by spin lifetimes in nonmagnetic spin-orbit coupled materials. We perform a first-principles study on the proustite mineral family, ${\mathrm{Ag}}_3{B\mathrm{Q}}_3$ (B = As, Sb; Q = S, Se), and show these chalcogenides exhibit nonsymmetry-protected PSTs, which we refer to as symmetry-assisted PSTs. Chemical substitution can be used to tune the PST quality and properties, e.g., spin lifetime, and we find that a Rashba anisotropy criterion correlates with the PST area and spin lifetime for two of the three proustites examined. Last, we show that a first-order effective SOC Hamiltonian, often used in two-dimensional systems, is insufficient to describe the PST state in all proustites, suggesting that higher order models are necessary to fully describe PSTs in bulk three-dimensional materials.

Persistent spin textures (PSTs) in solid-state materials arise from a unidirectional spin-orbit field in momentum space and offer a route to deliver long carrier spin lifetimes sought for future quantum microelectronic devices. Nonetheless, few three-dimensional materials are known to host PSTs owing to crystal symmetry and chemical requirements. There are even fewer examples demonstrated experimentally. Here we report that high-quality persistent spin textures can be obtained in the polar point groups containing an odd number of mirror operations. We use representation theory analysis and electronic structure calculations to formulate general discovery principles to identify PSTs hidden in known complex ternary layered and perovskite structures with large electric polarizations. We then show some of these materials exhibit PSTs without requiring any special crystalline symmetries. This finding removes the limitation imposed by mirror-symmetry protected PSTs that has limited compound discovery. Our general design approach enables the pursuit of persistent spin helices in materials exhibiting the $C_3$ _v crystal class adopted by many quantum materials exhibiting large Rashba coefficients.

Multipole decomposition method is a promising tool for investigation of radiating or scattering responses of electromagnetic sources or particles. It works even in the case of relatively complicated and compound scatterers like multilayer particles, clusters, or asymmetrical systems. Commonly, the radiation fields of point electric or magnetic sources are decomposed only into electric or magnetic dipole moments, while real sources can be described by a series of multipoles, including higher multipoles and toroidal moments. In this paper, we introduce the concept of modified multipoles describing real sources of electric, magnetic, and toroidal types. Using the analytical expressions of first-order multipoles, we discuss how they depend on the position of the center of radiation, as well as on the shift of the source, relative to the center of coordinates. We present results of multipoles for the sources with defects and asymmetry. The long-awaited question about distinguishing radiation patterns of electric and toroidal dipole moments in a far-field zone is discussed and solved in this paper. We show that radiation patterns of shifted electric and toroidal dipoles can be rotated to different angles relative to each other due to shifting. Moreover, we discuss modified anapoles. Our modified dipole approach will be useful for multipole analysis of complex systems in photonics such as nanoparticle clusters, metamaterials, and nanoantennas, as well as for better understanding issues of toroidal electrodynamics.

Inspired by the physics of rare-earth nickelates, we study the photoemission (PES) and resonant inelastic x-ray scattering (RIXS) spectra of a correlated electron system with two types of insulating sublattices. Sublattice A is characterized by a hybridization gap and a low-spin state, while sublattice B features a Mott gap and a local magnetic moment. We show how the coupling of these two qualitatively different insulating states affects the dynamics of photoinduced charge carriers and how the nonequilibrium states manifest themselves in the PES and RIXS signals. In particular, we find that charge carriers created on the B sublattice migrate to the A sublattice, where they contribute to the creation of in-gap states in the PES signal and to characteristic peaks in the nonequilibrium RIXS spectrum. While the contributions from the two sublattices cannot be easily distinguished in the local photoemission spectrum, the weights of the RIXS signals in the two-dimensional ${\omega }_{\text{in}}\text{−}{\omega }_{\text{out}}$ space provide information on the local state evolution on both sublattices.

Magnetic topological materials are a class of compounds with the underlying interplay of nontrivial band topology and magnetic spin configuration. Extensive interest has been aroused due to their application potential involved with an array of exotic quantum states. With angle-resolved photoemission spectroscopy and first-principles calculations, here we study the electronic properties of two magnetic Weyl semimetal candidates, PrAlSi and SmAlSi. Though the two compounds harbor distinct magnetic ground states (ferromagnetic and antiferromagnetic for PrAlSi and SmAlSi, respectively) and $4f$ shell fillings, we find that they share a quite analogous low-energy band structure. By measurements across the magnetic transitions, we further reveal that there is no evident evolution of the band structure in both compounds and the experimental spectra can be well reproduced by the nonmagnetic calculations, together suggesting a negligible effect of the magnetism on their electronic structures and a possibly weak coupling between the localized $4f$ electrons and the itinerant conduction electrons. Our results offer essential insights into the interactions between magnetism, electron correlations, and topological orders in the $R\mathrm{Al}X$ ($R$ = light rare earth and $X$ = Si or Ge) family.

Motivated by the fact that the idealized Kitaev chain toy model and the experimental semiconductor-superconductor Majorana nanowire can both host the Majorana zero modes, we theoretically investigate the question to what extent the two models are equivalent or similar, using the perspective of the corresponding dual spin models for both. We start with the duality between the Kitaev chain and the transverse-field XY spin model through the Jordan-Wigner transformation with the goal of establishing the connection between the Kitaev chain and the nanowire. By applying the Jordan-Wigner transformation to the nanowire, we find that the corresponding bosonic spin model is a generalized spin cluster model, containing 3- and 4-spin terms, with staggered couplings. By projecting out the upper band of the bare SM with higher energy, we obtain an effective low-energy spinless system from the spinful nanowire system deep in the topological regime. Finally, we establish the connection between the Kitaev chain and Majorana nanowire by showing that the spinless Kitaev chain can be viewed as the first-order approximation of the spinful Majorana nanowire deep in the topological regime.

Correlated oxides, such as ${\mathrm{BiMnO}}_3$ and ${\mathrm{LaMnO}}_3$, show a complex interplay of electronic correlations and crystal structure exhibiting multiple first-order phase transitions, some without a clear order parameter. The quantitative theoretical description of this temperature-dependent electronic-structural interplay in the vicinity of a Mott transition is still a challenge. Here we address this issue by simultaneously considering both structural and electronic degrees of freedom, within a self-consistent density functional theory with embedded dynamical mean field theory. Our results show the existence of novel electronic states characterized by the coexistence of insulating, semimetallic, and metallic orbitals. This state is in agreement with resonant x-ray scattering. We also show that electronic entropy plays a decisive role in both electronic and structural phase transitions. By self-consistent determination of both the electronic state and the corresponding crystal structure, we show that the temperature evolution of these phases can be quantitatively explained from first principles, thus demonstrating the predictive power of the theoretical method for both the structural and the electronic properties.

Layered $2H\text{−}T{X}_2$ with $T=\mathrm{Nb}$, Ta and $X=\mathrm{S}$, Se exhibit rich dimensionality effects on charge density wave (CDW) order and superconductivity, but comprehensive understanding of these correlated quantum phases in the two-dimensional limit of $2H\text{−}T{X}_2$ is still lacking, hindering their practical applications. Here, I calculate from first principles the phonon linewidth and bare susceptibility to study the origin of CDW formation in ${\mathrm{NbSe}}_2$, ${\mathrm{TaS}}_2$, ${\mathrm{TaSe}}_2$, and ${\mathrm{NbS}}_2$ monolayers, analyze their relative CDW strength, and evaluate electron-phonon superconductivity within the fully anisotropic Migdal-Eliashberg theory. A peaked linewidth of the longitudinal acoustic branch and no Fermi-surface nesting around ${\mathbf{q}}_{\mathrm{CDW}}$ indicate CDW instability driven by the wave-vector-dependent electron-phonon coupling. The $3\times 3$ CDW ground state favors a distinct hollow-centered clustering of transition-metal atoms, with larger distortion amplitude in ${\mathrm{NbSe}}_2$ and ${\mathrm{TaSe}}_2$ than in ${\mathrm{TaS}}_2$ and ${\mathrm{NbS}}_2$. Superconducting results of the monolayer CDW phase prove that strong spin-orbit coupling effects are dominant in determining the critical temperature $T_{\mathrm{c}}$ of each system via modifying both the strength and anisotropic extent of electron-phonon interactions. I also recapitulate measured opposite thickness dependencies of $T_{\mathrm{c}}$ in $\mathrm{Nb}{X}_2$ and $\mathrm{Ta}{X}_2$, and show that whether superconductivity is weakened or enhanced in monolayer limit relies on specific evolution of CDW-modulated Fermi-level density of states and electron-phonon matrix elements under reduced dimensionality. This work lays the foundation for applications of $2H$ group V transition-metal dichalcogenides in versatile nanoscale quantum devices.

We propose a physical witness for dynamically detecting topological phase transitions (TPTs) via an experimentally observable out-of-time-order correlation (OTOC). The distinguishable OTOC dynamics appears in the topological trivial and nontrivial phases due to the topological locality. In the long-time limit, the OTOC undergoes a zero-to-finite-value transition at the critical point of the TPTs. This transition is robust to the choices of the initial state of the system and the operators used in the OTOC. The proposed OTOC witness can be applied to systems with and without chiral symmetry, e.g., the lattices described by the Su-Schrieffer-Heeger model, Creutz model, and Haldane model. Moreover, our proposal, as a physical witness in real space, is still valid even in the presence of disorder. Our work fundamentally brings the OTOC into the realm of TPTs and offers the prospect of exploring topological physics with quantum correlations.

The bianisotropy of meta-atoms is usually associated with their nonlocal response and mutual coupling between electric and magnetic dipole moments induced by an incident field. In this Letter, we generalize the theory of bianisotropy beyond the dipole response to cases of arbitrary high-order multipole resonances. We demonstrate that bianisotropy is fully connected to the geometrical structure of meta-atoms and caused exclusively by the absence of their inversion symmetry, while the strength of the bianisotropy response grows normally with the size of a meta-atom. Applying a group theory analysis, we reveal the explicit criteria when the dipole approximation is enough for the correct description of bianisotropy and when accounting for higher-order multipoles is required. We consider a triangular prism as an illustrative example of a bianisotropic particle and show how accounting for higher-order multipoles prevents the violation of Onsager-Casimir conditions for kinetic coefficients appearing in the dipole approximation. The developed theory is an essential step toward a deeper insight into the scattering properties of nanoantennas and meta-atoms.

The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest-neighbor hopping subjected to external time-dependent perturbations. While in the first model the external drivings are realized by a continuous variation of the onsite energies, in the second one it is generated by deformations of a parabolic potential. We concentrate on the effects of the potential on the localization properties and investigate the statistics of the energy-level velocities and curvatures regarding their typical magnitudes and domain of agreement with the predictions of random matrix theory for the Gaussian orthogonal, unitary and symplectic ensembles. Moreover, the statistical properties of the avoided level crossings are investigated in terms of the corresponding Landau-Zener parameters. We find that the strength of the Landau-Zener transitions exhibit universal behavior which also imply universal single-particle dynamics for slow perturbations independent of the disorder and potential strength, the system size and the symmetry class. These results can be verified experimentally by measurements of single-particle energy spectra in quantum dots.

${\mathrm{Eu}}^{3+}$:${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystals are promising candidates for quantum memories because their nuclear spin coherence lifetime can be extended to 47 seconds at a particular magnetic field. Although an extended coherence lifetime of 6 hours can be achieved with a large number of dynamic decoupling sequences, these pulses will also introduce unwanted noise. To realize quantum storage with a lifetime of hours, it is necessary to quantitatively characterize the spin decoherence process of ${\mathrm{Eu}}^{3+}$ ions to guide the experimental efforts. In practice, a number of limiting factors could impose a limit on the achievable spin coherence lifetime, which includes the spin inhomogeneous broadening of the ${\mathrm{Eu}}^{3+}$ ensemble and the homogeneity and stability of the external magnetic field. Here, we provide a Monte Carlo simulation model of the nuclear spin decoherence process of ${\mathrm{Eu}}^{3+}$ ions in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystals, and these limiting factors are considered to provide an accurate prediction of the spin coherence lifetimes. This method is universal and can be applied to other rare-earth-ion-doped crystals.

We combine static magnetic susceptibility $\chi \left(T\right)$, muon-spin relaxation, and ${}^1\mathrm{H}$ nuclear magnetic resonance measurements to explore the spin dynamics in the disordered-induced quantum spin liquid candidate ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$. Inverse Laplace transform analysis of the ${}^1\mathrm{H}$ spin-lattice relaxation rate $1/T_1$ enables us to identify two characteristic temperatures $T_{\mathrm{g}}=110\mathrm{K}$ and $T^{*}=26\mathrm{K}$. Below $T_{\mathrm{g}}$, a slower $1/T_1^{\mathrm{slow}}$ component dictated by gapped excitations with a spin gap ${\mathrm{\Delta }}_h=30–38\mathrm{K}$ evolves distinctly from a faster $1/T_1^{\mathrm{fast}}$ component pertaining to gapless excitations. Furthermore, we observe a sub-Curie divergent $\chi \left(T\right)\propto T^{-0.68}$, a power-law dependent $1/T_1^{\mathrm{fast}}\propto T^{1.4}$, and a weakly activated $1/T_1^{\mathrm{slow}}\propto exp(-{\mathrm{\Delta }}_l/k_{\mathrm{B}}T)$ (${\mathrm{\Delta }}_l=3–6\mathrm{K}$) below $T^{*}=26\mathrm{K}$. All these features suggest the coexistence of a disordered spin-liquid state and spin singlets with spatially distributed gaps.

The anomalous Hall effect in high conductivity region is studied using a two-dimensional network model. We find that the off-diagonal conductivity comprises two parts: one which reflects the bulk properties as obtained by the Kubo formula and another which is sensitive to boundary conditions imposed on the network. In the fully coherent limit, the latter scales with the width of the conducting channel, while for real-world samples, it is controlled by the coherence length. It provides an alternative interpretation of the observed behavior in the clean limit which is otherwise attributed to the skew scattering. We highlight analogies to friction in viscous fluids responsible for Couette flow. In the present case, this quantum effect is governed by wave interference.

The robustness against local perturbations, as long as the symmetry of the system is preserved, is a distinctive feature of topological quantum states. Magnetic impurities and defects break time-reversal invariance and, consequently, time-reversal invariant (TRI) topological superconductors are fragile against this type of disorder. Nonmagnetic impurities, however, preserve time-reversal symmetry and one naively expects a TRI topological superconductor to persist in the presence of nonmagnetic impurities. In this work, we study the effect of nonmagnetic disorder on a TRI topological superconductor with extended $s$-wave pairing, which can be engineered at the interface of an Fe-based superconductor and a strongly spin-orbit coupled Rashba layer. We model two different types of nonmagnetic random disorder and analyze both the bulk density of states and edge state spectrum. Contrary to naive expectations, we find that the disorder strongly affects the topological phase by closing the energy gap, while trivial superconducting phases remain stable and fully gapped. The disorder phase diagram reveals a strong expansion of a nodal phase with increasing disorder. We further show the decay of the helical Majorana edge states in the topological phase and how they eventually disappear with increasing disorder. These results alter our understanding of effects of impurities and disorder on TRI topological phases and may help explain the difficulty of experimental observation of TRI topological superconductors.

Nonequilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying nonequilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of nonequilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing protocol based on excited-state VQE is NISQ-friendly, as it can successfully differentiate the MBL phase from thermal phases with relatively shallow quantum circuits, and it is also robust against the effect of quantum noises.

We performed a series of aging experiments with an inorganic glass (${\mathrm{As}}_2{\mathrm{Se}}_3$) at a temperature $T_2$ near the glass transition point $T_g$ by first relaxing it at $T_1$. The relaxations of Young's modulus were monitored, which were (almost if not ideally) exponential with $T_1$-dependent relaxation time τ, corroborating the Kovacs’ paradox in an inorganic glass. Associated with the divergence of τ, the quasiequilibrated Young's modulus $E_{\infty }$ does not converge either. An elastic model of relaxation time and a Mori-Tanaka analysis of $E_{\infty }$ lead to a similar estimate of the persistent memory of the history, illuminating ergodicity breaking within the accessible experimental time, as described in the Gardner transition theory. Experiments with different $T_2$ exhibit a critical temperature $T_p\sim T_g$, i.e., when $T_2>T_p$, both τ and $E_{\infty }$ converge. The results unveil a long-expected phenomenon that structural glass transition could be a zero-to-nonzero transition, manifested by a nonvanishing structural memory in aging when the temperature is below $T_p$ in the glass transition range. This demonstrates the existence of the ergodicity breaking deep in the glass state and $T_p$ could be the Gardner transition point of the structural glass.