We study the Hubbard model on the square lattice coupled in addition to the optical Su-Schrieffer-Heeger (SSH) phonons, using the singular-mode functional renormalization group method. At half filling and in the absence of the Hubbard interaction $U$, we find the degenerate spin-density-wave–charge-density-wave–$s$-wave-superconductivity state at smaller electron-phonon coupling strength $\lambda$ and higher phonon frequency $\omega$, and the valence bond solid (VBS) state at larger $\lambda$ and lower $\omega$. After switching on a positive $U$, the VBS state is suppressed, while the spin-density wave (SDW) state is enhanced. At finite doping, the SSH phonon is found to favor $s$-wave superconductivity (sSC) at $U=0$. With increasing positive $U$, we find $d$-wave superconductivity (dSC) and incommensurate SDW states. In a narrow window of moderate $U$ and $\lambda$, we also find the incommensurate VBS state. The sSC and dSC here can be naturally related to the charge-density wave (CDW) and SDW fluctuations, both of which can be triggered by the SSH phonons. In contrast, the repulsive interaction $U$ enhances SDW but suppresses CDW fluctuations. Our results at half filling are consistent with quantum Monte Carlo (QMC) and provide insights at finite doping where QMC may suffer from the minus sign problem.

Spin gapless semiconductors exhibit a finite band gap for one spin channel and a closed gap for another spin channel, and they have emerged as a new state of magnetic materials with a great potential for spintronic applications. The first experimental evidence for spin gapless semiconducting behavior was observed in an inverse Heusler compound ${\mathrm{Mn}}_2\mathrm{CoAl}$. Here, we report a detailed investigation of the crystal structure and anomalous Hall effect in ${\mathrm{Mn}}_2\mathrm{CoAl}$ using experimental and theoretical studies. The analysis of the high-resolution synchrotron x-ray diffraction data shows antisite disorder between Mn and Al atoms within the inverse Heusler structure. The temperature-dependent resistivity shows semiconducting behavior and follows Mooij's criteria for disordered metal. The scaling behavior of the anomalous Hall resistivity suggests that the anomalous Hall effect in ${\mathrm{Mn}}_2\mathrm{CoAl}$ is primarily governed by an intrinsic mechanism due to the Berry curvature in momentum space. The experimental intrinsic anomalous Hall conductivity (AHC) is found to be $\sim 35$ S/cm, which is considerably larger than the theoretically predicted value for ordered ${\mathrm{Mn}}_2\mathrm{CoAl}$. Our first-principles calculations conclude that the antisite disorder between Mn and Al atoms enhances the Berry curvature and hence the value of intrinsic AHC, which is in very good agreement with the experiment.

We derive the effective theories for quantum Hall droplets with attractive interaction among the constituent particles. In the absence of confining potentials, such droplets are defined by their freely moving interfaces (or boundaries) with the vacuum. We demonstrate that the effective theories take forms like string theories. Generalization to interfaces between different quantum Hall liquids is discussed.

How to achieve half-metallicity is always a central topic in spintronics and the polarity-tunable half-metallicity is particularly interesting for spin manipulation. In this work, motivated by the intrinsic ferromagnetism in the monolayer electride ${\mathrm{LaBr}}_2$, based on density functional theory calculations, we investigate the electronic and magnetic properties of bilayer ${\mathrm{LaBr}}_2$, with an aim to search for polarity-tunable half-metallicity. We first find that the antiferromagnetic interlayer coupling state is the ground state and the band structure is spin degenerate, with an indirect band gap of 0.454 eV. By applying a vertical electric field, spin splitting occurs and when the electric field is strong enough ($\ge 0.33$ V/Å), half-metallicity can be achieved. More interestingly, the spin polarity of the half-metallicity can be tuned by reversing the electric field direction. It originates from the spatial separation of the two spin channels in both the valence band and conduction band and their localization at different layers. Based on the polarity-tunable half-metallicity under vertical electric field, a magnetic tunnel junction based on bilayer ${\mathrm{LaBr}}_2$ is designed and the ON/OFF switching can be achived by applying parallel or anti-parallel vertical electric fields in the two leads, which leads to giant tunnel magnetoresistance up to $1\times {10}^6$. The findings suggest new potential of ${\mathrm{LaBr}}_2$, and more generally, $A$-type antiferromagnets of application in spintronic devices.

A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.

We prove that invisible bands associated with zeros of the single-particle Green's function exist ubiquitously at topological interfaces of two-dimensional Chern insulators, dual to the chiral edge/domain-wall modes. We verify this statement in a repulsive Hubbard model with a topological flat band, using real-space dynamical mean-field theory to study the domain walls of its ferromagnetic ground state. Moreover, our numerical results show that the chiral modes are split into branches due to the interaction and that the branches are connected by invisible flat bands. Our work provides deeper insight into interacting topological systems.

The dynamics of atoms plays a key role in governing various dynamical and transport properties of glasses. However, it remains elusive which structural features (if any) control atom dynamics in glasses. Here, based on million-atom molecular dynamics simulations and classification-based machine learning, we extract a needle in a haystack by identifying a local, nonintuitive structural signature (a revised version of the recently developed softness metric) that governs glass dynamics. We do so by investigating the ion mobility in sodium silicate glasses—a realistic, archetypal glass—finding that the sodium ion mobility is largely encoded in its initial softness, wherein softer Na atoms exhibit higher mobility. Importantly, our approach allows us to interpret the machine-learned softness metric and thus elucidate the atomistic origin of the ion mobility. Namely, we find that Na mobility is anticorrelated with the local density of defect oxygen neighbors that are located between the nearest two coordination shells. This local packing order offers a potential path to develop glass formulations with tailored dynamical properties. Finally, we demonstrate that the softness is strongly anticorrelated with the activation energy for Na atom reorganization.

The interplay between magnons and phonons and its influences on magnon dissipation have attracted widespread attentions. Whereas the previous theoretical works were usually restricted to the interactions between low-frequency magnons and acoustic phonons in the long-wavelength region, in the present work we go beyond this limit and investigate the magnon relaxation in a two-dimensional ferromagnet, a monolayer ${\mathrm{CrI}}_3$, through magnon-phonon scattering channels mediated by the variation of the exchange strength resulting from all-wavelength acoustic phonons as well as the optical ones. With a precise description of the magnon and phonon Bloch states from first principles, we evaluate the magnon relaxation rate due to these exchange-mediated magnon-phonon scatterings and reveal rich features in its momentum dependence, which reflects nicely the role of the associated phonons with in-plane atomic vibrations. The magnon-number-conserving scattering is found to be orders of magnitude stronger than the magnon-number-nonconserving scattering due to the weak anisotropic exchange coupling or dipole-dipole interaction. Our first-principles-based approach provides a better solution for the quantitative evaluation of the magnon dissipation by phonons.

Dissipative time crystals can appear in spin systems, when the $Z_2$ symmetry of the Hamiltonian is broken by the environment, and the square of total spin operator $S^2$ is conserved. In this paper, we relax the latter condition and show that time-translation-symmetry-breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. We engineer an ad hoc Lindbladian using power-law-decaying spin operators and show that time-translation-symmetry breaking appears when the decay exponent obeys $0<\eta \le 1$. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points. We study the phase diagram and the magnetization dynamics in the mean-field approximation. We prove that this approximation is quantitatively accurate, when $0<\eta <1$ and the thermodynamic limit is taken, because the system does not develop sizable quantum fluctuations, if the Gaussian approximation is considered.

The spin-dependent scattering process in a system of a topological insulator and a quantum dot is studied. The unitary scattering process is viewed as a gate transformation applied to an initial state of two electrons. Due to the randomness imposed through the impurities and alloying-induced effects of band parameters, the formalism of the random unitary gates is implemented. For quantifying entanglement in the system, we explored concurrence and ensemble-averaged Rényi entropy. We found that an applied external magnetic field leads to long-range entanglement on distances much larger than the confinement length. We showed that topological features of itinerant electrons sustain the formation of robust long-distance entanglement, which survives even in the presence of strong disorder.

Using the one-dimensional Hubbard model, which is commonly used for describing, e.g., high-$T_c$ superconducting cuprates, we study high-harmonic generation (HHG) from doped, correlated materials. Doping is modeled by changing the number of electrons in the lattice from the conventional half-filling case. For relatively small Hubbard $U$, i.e., small electron-electron correlation, we find little to no effect of doping on the dynamics and the HHG spectra. For increasing $U$ the degree of doping has a marked effect on the dynamics and spectra. We explain these findings through the quasiparticle-based doublon-holon picture. The dynamics are separated into two types, first, doublon and holon movement, and, second, doublon-holon pair creation and annihilation. Doping results in all configurations containing doublons or holons. Those quasiparticles can move at no extra cost in energy regardless of the correlation level. This motion at no energy cost increases the high-harmonic gain for low- and medium-harmonic orders. We discuss that in the high-$U$ limit, antiferromagnetic ordering becomes increasingly unlikely with increasing doping rates and explain an associated drop in the high-order harmonics relative to the case of half-filling.

The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron and hole densities are tuned from the trivial to the quantum spin Hall insulator regime. We show that the transport properties of the system in the time-reversal symmetry broken phase are consistent with recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum transport study on a Corbino disk where the bulk and edge contributions to the conductance can be separated. We show that the edge becomes smoothly conducting and the bulk is always insulating when one tunes the system from the trivial to the quantum spin Hall insulator phase, providing unambiguous transport signatures of the time-reversal symmetry broken phase.

It has been proposed that band-inverted electron-hole bilayers support a phase transition from an insulating phase with spontaneously broken time-reversal symmetry to a quantum spin Hall insulator phase as a function of increasing electron and hole densities. Here we show that in the presence of proximity-induced superconductivity, it is possible to realize Majorana zero modes in the time-reversal symmetry broken phase in the absence of magnetic field. We develop an effective low-energy theory for the system in the presence of a time-reversal symmetry-breaking order parameter to obtain analytically the Majorana zero modes and we find good agreement between the numerical and analytical results in the limit of weakly broken time-reversal symmetry. We show that the Majorana zero modes can be detected in superconductor/time-reversal symmetry broken insulator/superconductor Josephson junctions through the measurement of a $4\pi$ Josephson current. Finally, we demonstrate that the Majorana fusion-rule detection is feasible by utilizing the gate voltage dependence of the spontaneous time-reversal symmetry breaking order parameter.

We present a comprehensive study surface plasmon polariton (SPP) propagation on planar metallic waveguides under a dressing field. We perform a set of analytical calculations of the periodic time-dependent Schrödinger equation to study the interaction of an intense electromagnetic field with a metallic system. We model the strong light coupling to the metallic system using a nonperturbative procedure. In this paper, we show that, by introducing Floquet theory into the dressed metal, the behavior of the Floquet states are similar to the phase-modulated signals in the communication system. This will reveal a new perspective on the underlying science in an intricate, dressed quantum system. Furthermore, we examine the impurity scattering effects on charge transport in disordered plasmonic metals using the generalized Floquet-Fermi golden rule and provide a novel approach to diminish the losses in plasmonic materials using the dressing field. To gauge the effectiveness of our results, we introduce a figure of merit to compare the performance of plasmonic metals, subjective to a dressing field. The calculated dressed SPP characteristics suggest that high-efficiency SPP propagation can be achieved in practice. Our findings open up new directions for state-of-the-art nanoplasmonic devices.

The recent discovery of magnetic Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ opens up new avenues for research into the interactions between topological orders, magnetism, and electronic correlations. Motivated by the observations of a large anomalous Hall effect because of large Berry curvature, we investigate another Berry curvature-induced phenomenon, namely the anomalous thermal Hall effect in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. We study it with and without strain, using a Wannier tight-binding Hamiltonian derived from first-principles density functional theory calculations. We first identify this material as a tilted type-I Weyl semimetal based on the band-structure calculation. Within the quasiclassical framework of Boltzmann transport theory, a giant anomalous thermal Hall signal appears due to the presence of large Berry curvature. Surprisingly, the thermal Hall current changes and even undergoes a sign-reversal upon varying the chemical potential. Furthermore, applying about 13 GPa stress, an enhancement as large as 33% in the conductivity is observed; however, the tilt vanishes along the path connecting the Weyl nodes. In addition, we have confirmed the validity of the Wiedemann-Franz law in this system for anomalous transports. We propose specific observable signatures that can be directly tested in experiments.

We introduce a class of singular connections as an alternative to the Berry connection for any family of quantum states defined over a parameter space. We find a natural application of the singular connection in the context of transition dipoles between two bands. We find that the shift vector is nothing but the difference between the singular connection and the connection induced from the Berry connections of involved bands; the gauge invariance of the shift vector is transparent from this expression. We show, using singular connections, that the topological invariant in two dimensions associated with optical transitions between the two bands can be computed, by means of this connection, by algebraically counting the points in the zero locus of a transition dipole matrix element of the two bands involved. It follows that this invariant provides a natural topological lower bound on the number of momenta in the Brillouin zone for which an electron cannot be excited from one Bloch band to the other by absorbing a photon.