The nontrivial topology of materials has been one of the keys for breaking through to a new stage of electronics involving phenomena such as topologically protected quantum spin Hall (QSH) states and quantum anomalous Hall (QAH) states. In this work, we study the Kane-Mele model with next-nearest-neighbor Rashba spin-orbit coupling (SOC), which accurately describes the QSH effect of two-dimensional group IV A materials. By investigating electronic structures with different SOCs and Zeeman fields, we obtain various phase transitions and plot rich phase diagrams where a time-reversal-symmetry-broken QSH insulator and three types of QAH insulators are identified based on calculations of topological invariants, including total and spin Chern numbers and Wannier function centers. In addition, the edge modes and spin texture within the bulk gap are also nontrivial. Based on the results of the model, we also study a real QSH material, stanene, with a large bulk gap and propose a scheme based on its transport properties to design a spin-resolved filter.

We study the optical absorption spectrum of a doped two-dimensional semiconductor in the spin-valley polarized limit. In this configuration, the carriers in the Fermi sea are indistinguishable from one of the two carriers forming the exciton. Most notably, this indistinguishability requires the three-body trion state to have $p$-wave symmetry. To explore the consequences of this, we evaluate the system's optical properties within a polaron description, which can interpolate from the low-density limit, where the relevant excitations are few-body bound states, to higher-density many-body states. In the parameter regime where the trion is bound, we demonstrate that the spectrum is characterized by an attractive quasiparticle branch, a repulsive branch, and a many-body continuum, and we evaluate the doping dependence of the corresponding energies and spectral weights. In particular, at low doping we find that the oscillator strength of the attractive branch scales with the square of the Fermi energy as a result of the trion's $p$-wave symmetry. Upon increasing density, we find that the orbital character of the states associated with these branches interchanges. We compare our results with previous investigations of the scenario where the Fermi sea involves carriers distinguishable from those in the exciton, for which the trion ground state is $s$ wave.

We report a computational search for three-dimensional bulk ferromagnetic semiconductors based on itinerant Stoner physics. Stoner-based ferromagnetic semiconductors require an unusual combination of high band edge density of states and moderate transport effective mass. Nonetheless, several potential materials are found. We identify arsenopyrites, exemplified by FeAsS, as materials that, with suitable doping, exhibit ferromagnetic semiconducting behavior for both $n$- and $p$-type dopants. The existence of a material that becomes ferromagnetic for both $p$ and $n$ types may enable device concepts, for example, ferromagnetic $p-n$ junction devices.

We report on an optically probed ferromagnetic resonance experiment which elucidates the magnon-exciton coupling at the interface between a magnetic thin film and an atomically thin semiconductor. Our approach allies the long-lived magnons hosted in a film of yttrium iron garnet (YIG) to strongly bound excitons in a flake of a transition metal dichalcogenide, ${\mathrm{MoSe}}_2$. The magnons induce on the excitons a dynamical valley Zeeman effect ruled by interfacial exchange interactions. This nascent class of hybrid system suggests new opportunities for information transduction between microwave and optical regions.

Isolated nonmagnetic substitutional defect ions experience huge coupled electric magnetic interaction in the single-phase multiferroic ${\mathrm{BiFeO}}_3$. In the ferroelectric state above the magnetic Néel temperature $T_N$, the electric environment generates a single symmetric electric field gradient (EFG) parallel to the electric polarization direction. Below $T_N$, a distinct magnetic interaction arises, monitored by the probe nuclei via their magnetic moment. Two magnetic environments arise, given by the relative angle of the local magnetic moment within its easy magnetic plane with respect to the EFG orientation. The angle between field gradient orientation and magnetic field direction is the most stable fitting parameter. The magnetic interaction concomitantly increases the EFG dramatically which reflects an outstandingly large local magnetoelectric coupling. In the set of best fits, two different electric environments form concurrently with two distinctly different local magnetic fields. The magnetic ordering in ${\mathrm{BiFeO}}_3$ thus completely distorts the electric environment of the nonmagnetic probe nucleus. The implications for the local effect of dopants in ${\mathrm{BiFeO}}_3$ are discussed. A third probe environment arising independent of temperature is identified and associated with an iron vacancy.

The introduction of non-Hermiticity to topological systems profoundly modifies their topological properties, leading to unprecedented phenomena beyond the descriptions of Bloch band theory, e.g., the breakdown of the conventional bulk-boundary correspondence. However, the comprehensive interplay between band topology and non-Hermiticity remains elusive. Here, based on a non-Hermitian Su-Schrieffer-Heeger model, we demonstrate that in the non-Hermitian topological systems, band topology and non-Hermiticity interplay by competing with each other, exhibiting a transition from symmetry dominance to non-Hermitian dominance. The former is featured with two edge states separately distributed at the two ends of the Su-Schrieffer-Heeger chain, similar to their Hermitian counterparts. In the latter, however, driven by non-Hermiticity, the two edge states become localized toward the same chain end, exhibiting the non-Hermitian skin effect. We find that such a transition is a universal behavior in the non-Hermitian systems, which is responsible for the breakdown of the conventional bulk-boundary correspondence and is the key factor to understanding the non-Hermitian topological properties. Furthermore, it is shown that this transition can be modified by the mode coupling between the edge states. As a comparison, we propose a non-Hermitian square-root Su-Schrieffer-Heeger model, where the edge states do not couple with each other and the mode coupling effect can be deactivated. Our work explicitly reveals the interplay between band topology and non-Hermiticity, which lays the foundation for the studies of non-Hermitian topological physics.

We investigate the microscopic dynamics at the initial stage of photoinduced phase transitions in tetrathiafulvalene-$p$-chloranil by exact diagonalization. We first show that the one-dimensional extended Peierls-Hubbard model exhibits a neutral phase with small ionicity and negligible dimerization and an ionic phase with moderate ionicity and dimerization. Aside from these phases, we find a doubly ionized phase with strong dimerization that we call the “dipole” phase. These ground-state phases are characterized by various order parameters and the Zak phase, which is relevant to electronic polarization. We further explore the microscopic dynamics of the three phases triggered by short monocycle optical pulses. The electronic order parameters and lattice displacement suggest that the neutral-ionic, ionic-neutral, and dipole-ionic transitions are induced. Furthermore, clear spectroscopic changes are observed in the time-dependent spectral density and pump-probe conductivity. A detailed analysis of the spectroscopy demonstrates the generation of coherent charge-transfer strings via multiphoton absorption and the crucial roles of the excited states and the metastable ground state at the new lattice position for the ultrafast dynamics.

Local magnetic properties of the ${\mathrm{Mn}}_5{\mathrm{Ge}}_3{\mathrm{C}}_x$(001) epitaxial films grown on Ge(111) with a nominal carbon concentration $0⩽x⩽0.85$ have been studied by means of ${}^{55}\mathrm{Mn}$ nuclear magnetic resonance (NMR). The NMR spectra were recorded from the demagnetized films and from the films fully magnetized along the $c$ direction as well as in the hexagonal $c$ plane. The data unambiguously show a synchronized carbon penetration of the crystal lattice ($D{8}_8$ structure, Nowotny phase, space group $P{6}_3/mcm$), occupying every second $2\left(b\right)$ void located within the chain of $\mathrm{Mn}\left[6\right(g\left)\right]$ octahedra and setting the limit for the carbon uptake into the ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ lattice at $x=0.5$. Moreover, the NMR data indicate that the chains of carbon-filled voids are correlated also in plane. Eventually, for the end concentration of $x=0.5$, a highly ordered superstructure is proposed, responsible for the observed two magnetically inequivalent positions within the $\mathrm{Mn}\left[4\right(d\left)\right]$ sublattice.

Motivated by the lack of direct evidence with inelastic neutron scattering of the well documented bound state of Heisenberg ferromagnets, we use the time-dependent thermal density matrix renormalization group algorithm to study the temperature dependence of the dynamical spin structure factor of Heisenberg ferromagnetic spin chains. For spin 1/2, we show that the bound state appears as a well defined excitation with significant spectral weight in the temperature range $J/12\lesssim T\lesssim J/3$, pointing to the possibility of detecting it with inelastic neutron scattering near $k=\pi$ provided the temperature is neither too low nor too high—at low temperature, the spectral weight only grows as $T^{3/2}$ and, at high temperature, the bound state peak merges with the two-magnon continuum. For spin 1, the situation is more subtle because the bound state with two neighboring spin flips competes with an antibound state with two spin flips on the same site. As a consequence, the relative spectral weight of the bound state is smaller than for spin 1/2 and a weak resonance due to the antibound state appears in the continuum. A clearer signature of the bound state (antibound state) can be obtained if a negative (positive) biquadratic interaction is present.

We first show the realization of exceptional points in a non-Hermitian superconducting system based on a conventional superconductor and then demonstrate that, surprisingly, the system hosts odd-frequency pairing, solely generated by the non-Hermiticity. While there is a coexistence of even- and odd-frequency pairs under general conditions, we find that the even-frequency term vanishes at the exceptional degeneracies, leaving only odd-frequency pairing. This exceptional odd-frequency pairing is directly given by the imaginary part of the eigenvalues at the exceptional points and can be measured from the spectral function. Our results thus put forward non-Hermitian systems as a powerful platform to realize odd-frequency superconducting pairing.

The celebrated variational path integral approach to the polaron problem shows remarkable discrepancies with diagrammatic Monte Carlo (DiagMC) for the Bogoliubov-Fröhlich Hamiltonian which describes an impurity weakly coupled to a Bose condensed atomic gas. It has been shown both by a renormalization group approach and by the method of correlated Gaussian wave functions that the model has a subtle UV divergence caused by quantum fluctuations, which are not captured within Feynman's approach. In this work we address the issues with Feynman's approach and show that by extending the model action to a more general form, and by considering higher-order corrections beyond the Jensen-Feynman inequality, a good agreement with DiagMC can be obtained.

Magnetocrystalline anisotropy (MCA) energy and the anisotropy of the orbital magnetic moment (AOM), relations between them, and methods of their calculation are investigated for the (001) fcc Co film and $\mathrm{Co}/X$ bilayers ($X=\mathrm{Pd}$ and Pt), using a realistic tight-binding model. The relations derived by Bruno [Phys. Rev. B 39, 865 (1989)] and van der Laan [J. Phys.: Condens. Matter 10, 3239 (1998)], including the AOM of Co only, are found to give largely incorrect mean values of the MCA energy but reproduce its oscillatory variation versus the Co thickness, with scaling factors needed for the bilayers. The presently proposed extension of the Bruno relation, with the AOM of both Co and Pd or Pt included, predicts the correct sign of the MCA energy for both bilayers and reproduces its magnitude and oscillation pattern very well, without extra scaling, for the Co/Pd bilayer, though this relation is not satisfied locally, by the MCA and AOM layer terms. A similarly extended van der Laan relation fails to reproduce the MCA energy, its sign, and the oscillation pattern, and largely overestimates its magnitude. For all investigated systems, the Co orbital moment oscillates versus the Co thickness with the 2 monolayer (ML) period for the out-of-plane direction of magnetization and the 5 ML period for the in-plane direction while the oscillations of the Pd and Pt orbital moments are more complex and similar for both magnetization directions. The exact and approximate MCA energies obtained with the force theorem and the perturbation theory (PT), respectively, are close to each other for the Co film and the Co/Pd bilayer. For the Co/Pt bilayer, only the mean value of the MCA energy is well approximated by the PT while its oscillation amplitude is overestimated a few times due to the large SOC in Pt. It is also shown that the MCA energy includes the intraband term, usually neglected, but, in fact, finite and vital for systems without the inversion symmetry as its magnitude is comparable to that of the interband term for the Co/Pd bilayer.

We investigate thermal transport in square ice, a two-dimensional analog of spin ice, exploring the role played by emergent magnetic monopoles in transporting energy. Using kinetic Monte Carlo simulations based on energy-preserving extensions of single-spin-flip dynamics, we explicitly compute the (longitudinal) thermal conductivity $\kappa$ over a broad range of temperatures. We use two methods to determine $\kappa$: a measurement of the energy current between thermal baths at the boundaries, and the Green-Kubo formula, yielding quantitatively consistent values for the thermal conductivity. We interpret these results in terms of transport of energy by diffusion of magnetic monopoles. We relate the thermal diffusivity $\kappa /C$, where $C$ is the heat capacity, to the diffusion constant of an isolated monopole, showing that the subdiffusive motion of the monopole implies $\kappa /C$ vanishes at zero temperature. Finally, we discuss the implications of these results for thermal transport in three-dimensional spin ice, in spin-ice materials such as ${\mathrm{Dy}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, and outline some open questions for thermal transport in highly frustrated magnets.

We investigate the effect of thermal fluctuations on the two-particle spectral function for a disordered $s$-wave superconductor in two dimensions, focusing on the evolution of the collective amplitude and phase modes. We find three main effects of thermal fluctuations: (1) the phase mode is softened with increasing temperature, reflecting the decrease of superfluid stiffness; (2) remarkably, the nondispersive collective amplitude modes at finite energy near $\mathbf{q}=[0,0]$ and $\mathbf{q}=[\pi ,\pi ]$ survive even in the presence of thermal fluctuations in the disordered superconductor; and (3) the scattering of the thermally excited fermionic quasiparticles leads to low-energy incoherent spectral weight that forms a strongly momentum-dependent background halo around the phase and amplitude collective modes and broadens them. Due to momentum and energy conservation constraints, this halo has a boundary which disperses linearly at low momenta and shows a strong dip near the $[\pi ,\pi ]$ point in the Brillouin zone.

At large commensurate angles, twisted bilayer graphene which holds even parity under sublattice exchange exhibits a tiny gap. Here, we point out a way to tune this tiny gap into a large gap. We start from comprehensive understanding of the physical origin of gap opening by density functional theory calculations. We reveal that the effective interlayer hopping, intralayer charge-density wave, or interlayer charge imbalance favors a gap. Then, on the basis of tight-binding calculations, we suggest that a periodic transverse inhomogeneous pressure, which can tune interlayer hoppings in specific regions of the moi$\acute{\mathrm{r}}$e supercell, may open a gap of over 100 meV, which is further confirmed by first-principles calculations. Our results provide a theoretical guidance for experiments to open a large gap in twisted bilayer graphene.

We discuss multipartitions of the gapped ground states of $(2+1)$-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to show that such multipartitions can be achieved by using what we call vertex states in $(1+1)$-dimensional conformal field theory: these are a type of state used to define an interaction vertex in string field theory and can be thought of as a proper generalization of conformal boundary states. This approach allows an explicit construction of the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a nontrivial distribution of the spectrum of the partially transposed density matrix. For reflected entropy, we test the recent claim that states the difference between reflected entropy and mutual information is given, once short-range correlations are properly removed, by $(c/3)ln2$ where $c$ is the central charge of the topological liquid that measures ungappable edge degrees of freedom. As specific examples, we consider topological chiral $p$-wave superconductors and Chern insulators. We also study a specific lattice-fermion model realizing Chern insulator phases and calculate the correlation measures numerically, both in its gapped phases and at critical points separating them.