The ground-state properties of the Hubbard model with attractive local pairing interactions are investigated in the framework of lattice density-functional theory. A remarkable correlation is revealed between the interaction-energy functional $W\left[\mathit{\eta }\right]$ corresponding to the Bloch-state occupation-number distribution ${\eta }_{\kappa \sigma }$ and the entropy $S\left[\mathit{\eta }\right]$ of a system of noninteracting fermions having the same ${\eta }_{\mathit{k}\sigma }$. The relation between $W\left[\mathit{\eta }\right]$ and $S\left[\mathit{\eta }\right]$ is shown to be approximately linear for a wide range of ground-state representable occupation-number distributions ${\eta }_{\mathit{k}\sigma }$. Taking advantage of this statistical analogy, a simple explicit ansatz for $W\left[\mathit{\eta }\right]$ of the attractive Hubbard model is proposed, which can be applied to arbitrary periodic systems. The accuracy of this approximation is demonstrated by calculating the main ground-state properties of the model on several 1D and 2D bipartite and nonbipartite lattices and by comparing the results with exact diagonalizations.

Quantum spin Hall (QSH) insulators exhibit spin-polarized conducting edge states that are topologically protected from backscattering and offer unique opportunities to address fundamental science questions and device applications. Finding viable materials that host such topological states, however, remains a continuing challenge. Here, by using in-depth first-principles theoretical modeling, we predict large band gap QSH insulators in the recently synthesized bottom-up two-dimensional $M{\mathrm{Si}}_2{Z}_4$ ($M$ = Mo or W and $Z$ = P or As) material family with $1T^{\prime }$ structure. A structural distortion in the $2H$ phase drives a band inversion between the metal (Mo/W) $d$ and $p$ states of P/As to realize spinless Dirac states without spin-orbit coupling. When spin-orbit coupling is included, a hybridization gap as large as $\sim 204$ meV opens up at the band-crossing points, realizing spin-polarized conducting edge states with nearly quantized spin Hall conductivity. We also show that the inverted band gap can be tuned with a vertical electric field, which drives a topological phase transition from the QSH to a trivial insulator with Rashba-like edge states. Our study identifies the two-dimensional $M{\mathrm{Si}}_2{Z}_4$ material family in the $1T^{\prime }$ structure as large band gap, tunable QSH insulators with protected spin-polarized edge states and large spin Hall conductivity.

We develop a reliable parameter-free analytic continuation method for quantum many-body calculations. Our method is based on a kernel grid, a causal spline, a regularization using the second-derivative roughness penalty, and the L-curve criterion. We also develop the L-curve averaged deviation to estimate the precision of our analytic continuation. To deal with statistically obtained data more efficiently, we further develop a bootstrap-averaged analytic continuation method. In the test using the exact imaginary-frequency Green's function with added statistical error, our method produces the spectral function that converges systematically to the exact one as the statistical error decreases. As an application, we simulate the two-orbital Hubbard model for various electron numbers with the dynamical-mean field theory in the imaginary time and obtain the real-frequency self-energy with our analytic continuation method, clearly identifying a non-Fermi-liquid behavior as the electron number approaches the half filling from the quarter filling. Our analytic continuation can be used widely, and it will facilitate drawing clear conclusions from imaginary-time quantum many-body calculations.

Thouless pumping is a mechanism to perform the topologically protected transport of particles by adiabatically modulating the Hamiltonian. The transported current is a topological invariant that is intimately related to the integer quantum Hall effect. Most of the previous works focus on topological pumping in linear and square lattices. In this Letter, we theoretically propose a mechanism to perform topological pumping in arrays of spin chains with complex geometries. To achieve this, we consider an array where the spin chains are coupled through their edges, which allows us to split the populations to generate superpositions of spin excitations in different spin chains. We show that due to the topological protection, the quantum superpositions can be transported through the array against the effect of disorder. This approach will open another avenue to transport excitations and correlated states with potential applications in quantum technologies and information processing. Our ideas can be realized in state-of-the-art quantum simulators such as cold atoms and superconducting qubit arrays.

Like the twisting control in magic-angle twisted bilayer graphene, the stacking control is another mechanical approach to manipulate the fundamental properties of solids, especially the van der Waals materials. We explore the stacking-induced magnetic frustration and the spiral spin liquid on a multilayer triangular lattice antiferromagnet where the system is built from ABC stacking with competing intralayer and interlayers couplings. By combining the nematic bond theory and the self-consistent Gaussian approximation, we establish the phase diagram for this ABC-stacked multilayer magnet. It is shown that the system supports a wide regime of spiral spin liquid with multiple degenerate spiral lines in the reciprocal space, separating the low-temperature spiral order and the high-temperature featureless paramagnet. The transition to the spiral order from the spiral spin liquid regime is first order. We further show that the spiral-spin-liquid behavior persists even with small perturbations such as further neighbor intralayer exchanges. The connection to the ABC-stacked magnets, the effects of Ising or planar spin anisotropy, and the outlook on the stacking-engineered quantum magnets are discussed.

Phonons are an ideal platform for realizing stable spinless two-dimensional (2D) Dirac points because they have a bosonic nature and hard-to-break time-reversal symmetry. It should be noted that the twofold degenerate nodal points in the phonon dispersions of almost all reported 2D materials are misclassified as “Dirac points” owing to a historical issue. The correct name for these twofold degenerate nodal points should be “Weyl” because 2D phononic systems are essentially spinless and because each twofold degenerate point is described by a Weyl model in two dimensions. To date, reports of fourfold degenerate Dirac point phonons in 2D materials are lacking. In this paper, we searched through all 80 layer groups (LGs) and discovered that Dirac phonons can be realized in 7 of the 80 LGs. Moreover, the Dirac points in the phonon dispersions of 2D materials can be divided into essential and accidental degenerate points, which appear at high-symmetry points and on high-symmetry lines, respectively. Guided by symmetry analysis, we identified the presence of Dirac phonons in several 2D material candidates with six LGs. This work offers a method for identifying Dirac phonons in 2D and proposes 2D material candidates for realizing Dirac phonons.

Inspired by the discovery and fascinating properties of kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A$= K, Rb, Cs), we investigate the superconductivity and topological properties of the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$-prototype kagome materials $\mathrm{Cs}{M}_3{\mathrm{Te}}_5$ ($M$=Ti, Zr, Hf) using first-principles calculations. The calculated results of formation energy and phonon dispersion indicate that this family of kagome materials are stable and may be synthesized in experiments. By analytically solving the Allen-Dynes-modified McMillan formula, the superconducting critical temperatures for ${\mathrm{CsTi}}_3{\mathrm{Te}}_5, {\mathrm{CsZr}}_3{\mathrm{Te}}_5$, and ${\mathrm{CsHf}}_3{\mathrm{Te}}_5$ are predicted as 8.02, 5.47, and 3.51 K, respectively. The electron-phonon couplings are dominated by the coupling between the in-plane atomic vibrational modes and the in-plane electronic orbitals. In addition, the ${\mathrm{CsZr}}_3{\mathrm{Te}}_5$ and ${\mathrm{CsHf}}_3{\mathrm{Te}}_5$ can be categorized as ${\mathbb{Z}}_2$ topological metals according to the calculations of topological invariant and surface states. Such coexistence of superconductivity and nontrivial topological properties in ${\mathrm{CsZr}}_3{\mathrm{Te}}_5$ and ${\mathrm{CsHf}}_3{\mathrm{Te}}_5$ are beneficial to study the interaction between superconductivity and nontrivial band character.

A space-time crystal is defined as a quantum-mechanical system with both spatial and temporal periodicity. Such a system can be described by the Floquet-Bloch (FB) theory. We first formulate a semiclassical theory by constructing a wave packet through the superposition of the FB wave functions, and we derive the equations of motion of FB electrons subjected to slowly varying external fields (not to be confused with the fast-changing Floquet drive), revealing behaviors similar to ordinary Bloch electrons but with quantities modified in the Floquet context. Specifically, we study the local magnetic moment due to the self-rotation of the wave packet, a contribution to total magnetization from the Berry curvature in $\mathbf{k}$-space, and the polarization of a fully occupied FB band. Based on the semiclassical theory, we can also show the fingerprint of the energy flow in such an energy-nonconserved system. We then discuss the density matrix of a FB system attached to a thermal bath, which allows us to investigate quantities involving many electrons in the noninteracting limit. As an application, we calculate the intrinsic current response in an oblique space-time metal showing the nonequilibrium nature of the FB system. The current response can also be related to the acoustoelectric effect. Overall, we develop a systematic approach for studying space-time crystals, and we provide a powerful tool to explore the electronic properties of this exotic system with coupled space and time.

Obtaining an accurate theoretical description of the emergent phenomena in oxide heterostructures is a major challenge. Recently, intriguing paramagnetic spin and pinned orbital moments have been discovered by x-ray magnetic circular dichroism measurements at the Cu $L_{2,3}$ edge of a tetragonal $\mathrm{CuO}/{\mathrm{SrTiO}}_3$ heterostructure. Using first-principles calculations, we propose a scenario that explains both types of moments, based on the formation of oxygen vacancies in the ${\mathrm{TiO}}_2$ interface layer. We show the emergence of a paramagnetic two-dimensional electron gas hosted in the interface CuO layer. It is invisible at the Ti $L_{2,3}$ edge since the valence of the Ti atoms remains unchanged. Strong structural distortions breaking both the local and global fourfold rotation $C_4$ symmetries at the interface lead to the in-plane pinning of the Cu orbital moment close to the vacancy. Our results, and in particular the pinning of the orbital moment, may have implications for other systems, especially monoxide/dioxide interfaces with similar metal-oxygen bond length and weak spin-orbit coupling.

Orbital ordering (OO) or charge ordering (CO) in $e_g^1$ compounds like $R{\mathrm{MnO}}_3$ (R = rare-earth element), $R{\mathrm{NiO}}_3$, and ${\mathrm{CaFeO}}_3$ makes them attractive functional materials. Despite belonging to the $e_g^1$ family, ${\mathrm{SrFeO}}_3$ is metallic and free from OO and CO, which may limit its technological potential. Here, through first-principles calculations, we propose a rational design of OO and CO insulating ${\mathrm{SrFeO}}_3$ by superlattice strategy and strain engineering. With a systematical investigation of the interplay among Jahn-Teller distortion related to OO, breathing distortion associated with CO, strain, octahedral rotations, and cation ordering, we reveal that cation ordering in ${\mathrm{SrFeO}}_3/{\mathrm{ABO}}_3$ superlattices not only is capable to stabilize Jahn-Teller and breathing distortions, but is also indispensable in triggering metal-insulator transition by the collaboration with Jahn-Teller or breathing distortion, leading to ferromagnetic insulating ${\mathrm{SrFeO}}_3$. Owing to the different sensitivity of Jahn-Teller and breathing distortions to strain, purposeful design of OO or CO phase and even as multiferroics coexisting ferroelectric and ferromagnetic orders can be realized by tuning the relative stability of CO and OO phases by strain engineering. The coupled charge, orbital, spin, and ferroelectricity degrees of freedom make ${\mathrm{SrFeO}}_3/{\mathrm{ABO}}_3$ superlattices appealing for desired applications.

We consider magic-angle graphene in the doping regime around charge neutrality, and we study the connection between a recently proposed intervalley coherent insulator at zero doping and the neighboring superconducting domes. The magic-angle graphene continuum model has an emergent U(1) valley-charge conservation symmetry and an emergent SU(2) symmetry corresponding to opposite spin rotations in the two valleys. The intervalley coherent insulator spontaneously breaks both these emergent symmetries, and as a result has four Goldstone modes that couple to doped charge carriers. We derive the effective interaction mediated by the Goldstone modes, and we study its role in electron pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction, which is attractive in spin-triplet pairing channels and repulsive in spin-singlet channels. From a weak-coupling BCS calculation, we find the leading superconducting instability in the $p$-wave channel.

We study the quantum nonlinear planar Hall effect in bilayer graphene under a steady in-plane magnetic field. When time-reversal symmetry is broken by the magnetic field, a charge current occurs in the second-order response to an external electric field as a result of the Berry curvature dipole in momentum space. We show that a nonlinear planar Hall effect originating from the anomalous velocity is caused by an orbital effect of an in-plane magnetic field on electrons in bilayer graphene in the complete absence of spin-orbit coupling. Taking into account the symmetry analysis, we derive the dominant dependence of the Berry curvature dipole moment on the magnetic field components. Moreover, we illustrate how to control and modulate the Berry curvature dipole with an external planar magnetic field, gate voltage, and Fermi energy.

Nonzero spin polarization occurs in nonmagnetic materials induced by spin-orbital coupling when inversion symmetry is broken. Understanding the origin of spin polarization is essential for finding effective methods of manipulating the electron spin. Recently, nontrivial Dirac node arcs with a novel spin texture have been reported in a tetradymite family $M_2{\text{Te}}_{2}X$ (with $M=\text{Ti}$, Zr, or Hf and $X=\text{P}$ or As) and have potential applications in spintronics. Here, combining spin- and angle-resolved photoemission spectroscopy and first-principles calculations, we have unambiguously distinguished the spin-polarized topological surface states from the bulk continuum states in ${\text{Zr}}_2{\text{Te}}_2\text{P}$, and report that surface resonance Rashba-type spin splittings and spin-momentum-layer locked bulk states exist along with the Dirac node arcs in reciprocal space in adjacent energy ranges. Our work shows the importance of resonance and hybridization between surface and bulk states to their electronic spin textures and provides a platform for developing spintronics devices.

The interaction among nontrivial topology, symmetry breaking orders, and strong electron correlation could generate many exotic physical phenomena. Recently, charge-density wave (CDW) orders and the Kondo effect are reported to occur in some of the $Ln\mathrm{Sb}\mathrm{Te}$ compounds, which are suggested to be either topological insulators or topological semimetals. Here we perform optical spectroscopic measurements on four of the $Ln\mathrm{Sb}\mathrm{Te}$ $(Ln=\mathrm{La}, \mathrm{Ce}, \mathrm{Sm}, \mathrm{Gd})$ compounds in order to investigate their exact electronic ground states. Metallic responses are commonly observed in all of the four compounds, despite their different transport behaviors. Furthermore, We observe some temperature-dependent excitations in the midinfrared region which are most likely to stem from CDW gaps. There is one such gap of about 452 meV in LaSbTe, one about 471 meV in CeSbTe, and two around 374 and 480 meV in GdSbTe, but none in SmSbTe, which is inconsistent with their highly similar electronic structures. Additionally, the presence of a Kondo hybridization gap is a bit too weak to be clearly revealed in our measured temperature range. Our results provide more detailed information on the $Ln\mathrm{Sb}\mathrm{Te}$ family, which helps to understand the underlying physics of these systems and inspires more related explorations.

We present multiscale dynamical simulations of voltage-induced insulator-to-metal transitions in the double-exchange model, a canonical example of itinerant magnets and correlated electron systems. By combining the nonequilibrium Green's function method with large-scale Landau-Lifshitz-Gilbert dynamics, we show that the transition from an antiferromagnetic insulator to the low-resistance state is initiated by the nucleation of a thin ferromagnetic conducting layer at the anode. The metal-insulator interface separating the two phases is then driven toward the opposite electrode by the applied voltage, giving rise to a growing metallic region. We further show that the initial transformation kinetics is well described by the Kolmogorov-Avrami-Ishibashi model with an effective spatial dimension that depends on the applied voltage. Implications of our findings for the resistive switching in colossal magnetoresistant materials are also discussed.

We study the thermalizing properties of the mass-deformed Sachdev-Ye-Kitaev model, in a regime of parameters where the eigenstates are ergodically extended over just portions of the full Fock space, as an all-to-all toy model of many-body localization (MBL). Our numerical results strongly support the hypothesis that, although considerably delayed, thermalization is still present in this regime. Our results add to recent studies indicating that MBL should be interpreted as a strict Fock-space localization.

Fröhlich condensation is a room-temperature nonequilibrium phenomenon which is expected to occur in many physical and biological systems. Although predicted theoretically a half century ago, the nature of such condensation remains elusive. In this Letter, we derive a full quantum theory of Fröhlich condensation from the Wu-Austin Hamiltonian and present an analytical proof that a second-order phase transition induced by nonequilibrium and nonlinearity emerges in the large-$D$ limit with and without decorrelation approximation. This critical behavior cannot be witnessed if external sources are treated classically. We show that the phase transition is accompanied by large fluctuations in the statistical distribution of condensate phonons and that the Mandel-$Q$ factor which characterizes fluctuations becomes negative in the limit of excessive external energy input. In contrast with the cold atom equilibrium Bose-Einstein condensation (BEC), the Fröhlich condensate is a result of the nonequilibrium driving where the pump plays a role of setting the number of particles, and the medium plays a role of setting the temperature. Hence, BEC can either arise by reducing the medium temperature at fixed pump (equilibrium case), or by increasing the pump at fixed medium temperature (nonequilibrium case).

We study the Loschmidt echo in the quenched two-dimensional $p$-wave topological superconductor. We find that if this superconductor is quenched out of the critical point separating its topological and nontopological phases into either of the two gapful phases, its Loschmidt echo features singularities occurring periodically in time where the second derivative of the Loschmidt echo over time diverges logarithmically. Conversely, we give arguments towards $s$-wave superconductors not having singularities in their Loschmidt echo regardless of the quench. We also demonstrate that the conventional mean-field theory calculates classical echo instead of its quantum counterpart, and show how it should be modified to capture the full quantum Loschmidt echo.

Two-dimensional higher-order topological insulators can display a number of exotic phenomena, such as half-integer charges localized at both corners and disclination defects. In this paper, we analyze these phenomena, focusing on the paradigmatic example of the quadrupole insulator with $C_4$ rotation symmetry, and present a topological field theory description of the mixed geometry-charge responses. Our theory provides a unified description of the corner and disclination charges in terms of a physical geometry (which encodes disclinations), and an effective geometry (which encodes corners). We extend this analysis to interacting systems, and predict the response of fractional quadrupole insulators, which exhibit charge $e/2(2k+1)$ bound to corners and disclinations.

The chiral magnetoelectric compound ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ is investigated through temperature-dependent synchrotron-based powder x-ray diffraction and x-ray absorption spectroscopy between 15 and 300 K. Our work provides direct evidence for the exchange-striction in the material around the concomitant onset point of collinear antiferromagnetic and the magnetoelectric phases. The x-ray absorption near edge spectra and x-ray photoelectron spectra show that the sample consists of both ${\mathrm{Ni}}^{2+}$ and ${\mathrm{Ni}}^{3+}$ ions in the lattice. The ionic state of Ni is found to be quite robust, and it is largely independent of the preparation route. Additionally, a minority ${\mathrm{Te}}^{4+}$ state is found to coexist with the majority ${\mathrm{Te}}^{6+}$ state, which may arise from the charge disproportionation between Ni and Te ions (${\mathrm{Ni}}^{2+} + {\mathrm{Te}}^{6+}\iff {\mathrm{Ni}}^{3+} + {\mathrm{Te}}^{4+}$). The observed mixed valency of Ni is also confirmed by the total paramagnetic moment (${\mu }_{\text{eff}}$) per Ni atom in the system. This mixed valency in the metal ions and the exchange-striction may be attributed to the observed magnetoelectric effect in the system.