Dirac point plays a crucial role in regulating electronic properties of topological semimetals. In two dimensions, the manipulation of Dirac points can spur a transition from Dirac semimetal through semi-Dirac phase to a gapped phase. Across such a so-called Lifshitz transition, we find that the quantum interference corrections to the conductivity $\delta {\sigma }_{xx}$ and $\delta {\sigma }_{yy}$ are always negative, giving rise to a weak localization behavior. The ratio $\delta {\sigma }_{xx}/\delta {\sigma }_{yy}$ undergoes a transition from linear to parabolic dependence on the merging parameter across the Lifshitz transition, which leads to a crossover of the temperature dependence of the inverse inelastic scattering time $1/{\tau }_{\varepsilon }$ from $\sim T$ to $\sim Tln(T_0/T)$. This fingerprint behavior can be readily tested experimentally through merging Dirac points in two-dimensional lattices. This work presents an alternative perspective to understand weak localization through Lifshitz transition.

The properties of mobile impurities in quantum magnets are fundamental for our understanding of strongly correlated materials and may play a key role in the physics of high-temperature superconductivity. Hereby, the motion of hole-like defects through an antiferromagnet has been of particular importance. It creates magnetic frustrations that lead to the formation of a quasiparticle, whose complex structure continues to pose substantial challenges to theory and numerical simulations. In this article, we develop a nonperturbative theoretical approach to describe the microscopic properties of such magnetic polarons. Based on the self-consistent Born approximation, which is provenly accurate in the strong-coupling regime, we obtain a complete description of the polaron wave function by solving a set of Dyson-like equations that permit to compute relevant spin-hole correlation functions. We apply this new method to analyze the spatial structure of magnetic polarons in the strongly interacting regime and find qualitative differences from predictions of previously applied truncation schemes. Our calculations reveal a remarkably high spatial symmetry of the polaronic magnetization cloud and a surprising misalignment between its orientation and the polaron crystal momentum. The developed framework opens up an approach to the microscopic properties of doped quantum magnets and will enable detailed analyses of ongoing experiments based on cold-atom quantum simulations of the Fermi-Hubbard model.

We numerically study the evolution of spectral correlations in the entanglement Hamiltonian (EH) of noninteracting fermions in the Aubry-André-Harper (AAH) model. We analyze the time evolution of the EH spectrum in a nonequilibrium setting by studying several quantities: spectral distribution, level statistics, entanglement entropy, and spectral form factor (SFF) in the context of the delocalization-localization transition in the AAH model. It is observed that the SFF of the entanglement spectrum in the delocalized phase and at the phase-transition point evolves in three time intervals. We make a systematic study of the emergence of these three timescales for various initial states and find that the number of time intervals remains 3 unless the Hamiltonian is tuned in the localized phase or when the initial state is maximally entangled, when there is a featureless time evolution. We find a broad direct correlation between the entanglement entropy and the length of the ramp of the SFF. We also find that in the delocalized phase the spectral correlations are stronger in the center of the spectrum and grow progressively weaker as more and more of the spectrum is considered.

The unconventional behaviors observed in twisted bilayer graphene (TBG) at special “magic angles” characterized by the vanishing Fermi velocity make TBG an intriguing platform for the study of correlated phenomena. Here, on the basis of an effective continuum model, we propose an analytic expression of the Fermi velocity based on which we demonstrate that the first magic angle of TBG is independent of the corrugation effect. We also correlate analytically the Dirac cone splitting of the biased TBG to the external electric field, twist angle, and corrugation effect. The biased TBGs exhibit unusual plasmonic responses. In the long-wavelength limit, the plasmon frequency is nearly independent of the carrier density but can be tuned by the bias voltage.

We explore the transition to a charge-disproportionated insulating phase in a five-orbital cubic tight-binding model applicable to transition-metal perovskites with a formal $d^4$ occupation of the transition-metal cation, such as ferrates or manganites. We use dynamical mean-field theory to obtain the phase diagram as a function of the average local Coulomb repulsion $U$ and the Hund's coupling $J$. The main structure of the phase diagram follows from the zero bandwidth (atomic) limit and represents the competition between high-spin and low-spin homogeneous and an inhomogeneous charge-disproportionated state. This results in two distinct insulating phases: the standard homogeneous Mott insulator and the inhomogeneous charge-disproportionated insulator, recently also termed Hund's insulator. We characterize the unconventional nature of this Hund's insulating state. Our results are consistent with previous studies of two- and three-orbital models applicable to isolated $t_{2g}$ and $e_g$ subshells, respectively, with the added complexity of the low-spin/high-spin transition. We also test the applicability of an effective two-orbital $\left(e_g\text{−}\mathrm{only}\right)$ model with disordered $S=3/2t_{2g}$ core spins. Our results show that the overall features of the phase diagram in the high-spin region are well described by this simplified two-orbital model, but also that the spectral features exhibit pronounced differences compared to the full five-orbital description.

Two indicators of finite-temperature topological properties based on the Uhlmann connection, one generalizing the Wilson loop to the Uhlmann-Wilson loop and the other generalizing the Berry phase to the Uhlmann phase, are constructed explicitly for a time-reversal invariant topological insulators with a $Z_2$ index. While the phases of the eigenvalues of the Wilson loop reflect the $Z_2$ index of the model at zero temperature, it is found that the signature from the Uhlmann-Wilson loop gradually fades away as temperature increases. On the other hand, the Berry phase exhibits quantization due to the underlying holonomy group. The Uhlmann phase retains the quantization at finite temperatures and serves as an indicator of topological properties. A phase diagram showing where jumps of the Uhlmann phase can be found is presented. By modifying the model to allow higher winding numbers, finite-temperature topological regimes sandwiched between trivial regimes at high and low temperatures may emerge.

We propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in $(1+1)$ dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude $E_0$ and frequency $\mathrm{\Omega }$, with a period determined by the Stückelberg phase, (2) the cutoff order of HHG is determined by $2e{E}_0/\hslash {\mathrm{\Omega }}^2$, with $e$ being the electron charge, and that (3) noninteger harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter $\gamma =(\mathrm{\Delta }/2)\mathrm{\Omega }/e{E}_0$, with $\mathrm{\Delta }$ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

Topological lasers are a new class of lasers that seek to exploit the special properties of topological states of light. A typical limiting factor in their performance is the existence of nontopological states with quality factors comparable to the desired topological states. We show theoretically that by distributing uniform gain and loss on two sublattices of a two-dimensional higher-order topological insulator (HOTI) lattice, single-mode lasing based on topological corner states can be sustained over a wide range of pump strengths. This behavior stems from the parity/time-reversal breaking of the topological corner states, which supplies them with more effective gain than the edge and bulk states, rather than through localized pumping of the domain corners. These results point to opportunities for exploiting non-Hermitian phenomena and designing compact high performance topological lasers.

Kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) exhibit superconductivity at 0.9–2.5 K and charge-density wave (CDW) at 78–103 K. Key electronic states associated with the CDW and superconductivity remain elusive. Here, we investigate low-energy excitations of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ by angle-resolved photoemission spectroscopy. We found an energy gap of 50–70 meV at the Dirac-crossing points of linearly dispersive bands, pointing to an importance of spin-orbit coupling. We also found a signature of strongly Fermi-surface and momentum-dependent CDW gap characterized by the larger energy gap of maximally 70 meV for a band forming a saddle point around the $M$ point, the smaller (0–18 meV) gap for a band forming massive Dirac cones and a zero gap at the $\mathrm{\Gamma }/A$-centered electron pocket. The observed highly anisotropic CDW gap which is enhanced around the $M$ point signifies an importance of scattering channel connecting the saddle points, laying foundation for understanding the nature of CDW and superconductivity in $A{\mathrm{V}}_3{\mathrm{Sb}}_5$.

Realizations of some topological phases in two-dimensional systems rely on the challenge of jointly incorporating spin-orbit and magnetic exchange interactions. Here, we predict the formation and control of a fully valley-polarized quantum anomalous Hall effect in bilayer graphene, by separately imprinting spin-orbit and magnetic proximity effects in different layers. This results in varying spin splittings for the conduction and valence bands, which gives rise to a topological gap at a single Dirac cone. The topological phase can be controlled by a gate voltage and switched between valleys by reversing the sign of the exchange interaction. By performing quantum transport calculations in disordered systems, the chirality and resilience of the valley-polarized edge state are demonstrated. Our findings provide a promising route to engineer a topological phase that could enable low-power electronic devices and valleytronic applications as well as putting forward layer-dependent proximity effects in bilayer graphene as a way to create versatile topological states of matter.

We study the high-frequency Hall conductivity in a two-dimensional model of conduction electrons coupled to a background magnetic skyrmion texture via an effective Hund's coupling term. For an ordered skyrmion crystal, a Kubo formula calculation using the basis of skyrmion crystal Chern bands reveals a resonant Hall response at a frequency set by the Hund's coupling: $\hslash {\omega }_{\mathrm{res}}\approx J_H$. A complementary real-space Kubo formula calculation for an isolated skyrmion in a box reveals a similar resonant Hall response. A linear relation between the area under the Hall resonant curve and the skyrmion density is discovered numerically and is further elucidated using a gradient expansion which is valid for smooth textures and a local approximation based on a spin-trimer calculation. We point out the issue of distinguishing this skyrmion contribution from a similar feature arising from spin-orbit interactions, as demonstrated in a model for Rashba spin-orbit coupled electrons in a collinear ferromagnet, which is analogous to the difficulty of unambiguously separating the dc topological Hall effect from the anomalous Hall effect. The resonant feature in the high-frequency topological Hall effect is proposed to provide a potentially useful local optical signature of skyrmions via probes such as scanning magneto-optical Kerr microscopy.

We study the possibility of complex tensor ($d$-wave) superconducting order in three-dimensional semimetals with chiral spin-1/2 triple-point fermions, which have an effective orbital angular momentum of $L=1$ arising from a crossing of three bands. Retaining the first three lowest order terms in momentum and assuming rotational symmetry we show that the resulting mean-field $d$-wave ground state breaks time-reversal symmetry, but then depends crucially on the coefficients of the two quadratic terms in the Hamiltonian. The phase diagram at a finite chemical potential displays both the “cyclic” and the “ferromagnetic” superconducting states, distinguished by the average value of the magnetization; in the former state it is minimal (zero), whereas in the latter it is maximal (two). In both states we find mini Bogoliubov-Fermi surfaces in the quasiparticle spectrum, conforming to recent general arguments.

We present a micromagnetic formulation for modeling the magnetization dynamics and thermal equilibrium in ferrimagnetic materials at low and elevated temperatures. The formulation is based on a mean-field approximation (MFA). In this formulation, the ferrimagnet is described micromagnetically by two coupled sublattices with corresponding interactions, including inter- and intrasublattice micromagnetic exchange as well as four-spin interactions described as an intersublattice molecular field with a cubic dependence of the magnetization. The MFA is used to derive a Landau-Lifshitz-Bloch type equation for ferrimagnetic material, including cases with a ferromagnetic-antiferromagnetic phase transitions. For validation, the results obtained via the presented model are compared with recent experimental data for phase transitions in FeRh.

It remains highly controversial whether long-distance spin transport or only Joule heating without spin transport exists in the disordered magnetic amorphous ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (a-YIG). Here, we carefully check and analyze the origin of the observed electrical signals in the Py/a-YIG/Pt-based nonlocal spin-transport experiments with both horizontal and vertical geometries, based on the ferromagnetic resonance (FMR)-induced spin pumping and inverse spin Hall effect. In all lateral nonlocal devices with a distance from 2.0 μm to 200 nm and vertical structures with a $\ge \text{40-nm-thick}$ a-YIG spacer layer, the spin-current-induced direct voltage peak signal is absent under FMR conditions, indicating that a-YIG does not possess long-distance spin transport. Furthermore, we demonstrate that a weak spin-torque FMR voltage signal, which gradually reduces to zero with increasing a-YIG thickness in the vertical geometry, is attributed to the leaked spin rectification voltage generated in the Py layer due to the electric leakage between the top Pt layer and the bottom Py layer through the pinhole defects in the thin middle a-YIG layer. Additionally, we find an improvement of the interfacial spin-mixing conductance due to spin accumulation in the interface of a-YIG/Py, which can significantly enhance spin-orbit torque efficiency in the ferromagnet/heavy metal systems with a disordered magnetic a-YIG buffer layer.

We investigate the steady-state phases of the dissipative spin-1/2 $J_1\text{−}{J}_2$ XYZ model on a two-dimensional square lattice. We show the next-nearest-neighboring interaction plays a crucial role in determining the steady-state properties. By means of the Gutzwiller mean-field (MF) factorization, we find the emergence of antiferromagnetic (AFM) steady-state phases. The existence of such AFM steady-state phases in thermodynamic limit is confirmed by cluster mean-field (CMF) analysis. Moreover, we find evidence of the limit cycle phase through the largest quantum Lyapunov exponent in small cluster and check the stability of the oscillation by calculating the averaged oscillation amplitude up to $4\times 4$ CMF approximation.

Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\alpha \text{−}{\mathrm{RuCl}}_3$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed.