The quantum spin Hall effect is conventionally thought to require a strong spin-orbit coupling, producing an effective spin-dependent magnetic field. However, spin currents can also be present without transport of spins, for example, in spin-waves or skyrmions. In this paper, we show that topological skyrmionic spin textures can be used to realize a quantum spin Hall effect. From basic arguments relating to the single-valuedness of the wave function, we deduce that loop integrals of the derivative of the Hamiltonian must have a spectrum that is integer multiples of $2\pi$. By relating this to the spin current, we form a new quantity called the quantized spin current which obeys a precise quantization rule. This allows us to derive a quantum spin Hall effect, which we illustrate with an example of a spin-1 Bose-Einstein condensate.

We propose possible high-temperature superconductivity (SC) with singlet $s^{\pm }$-wave pairing symmetry in the single-orbital Hubbard model on the square-octagon lattice with only nearest-neighbor hopping terms. Three different approaches are engaged to treat with the interacting model for different coupling strengths, which yield consistent results for the $s^{\pm }$ pairing symmetry. We propose octagraphene, i.e., a monolayer of carbon atoms arranged into this lattice, as a possible material realization of this model. Our variational Monte Carlo study for the material with realistic coupling strength yields a pairing strength comparable with the cuprates, implying a similar superconducting critical temperature between the two families. This study also applies to other materials with similar lattice structure.

We theoretically study the Josephson current in Ising superconductor–half-metal–Ising superconductor junctions. By solving the Bogoliubov–de Gennes equations, the Josephson currents contributed by the discrete Andreev levels and the continuous spectrum are obtained. For very short junctions, because the direct tunneling of the Cooper pair dominates the Josephson current, the current-phase difference relation is independent of the magnetization direction, which is the same as the conventional superconductor-ferromagnet-superconductor junctions. On the other hand, when the length of the half-metal is similar to or greater than the superconducting coherence length, the spin-triplet Josephson effect occurs and dominates the Josephson current. In this case, the current-phase difference relations show the strong magnetoanisotropic behaviors with the period $\pi$. When the magnetization direction points to the $\pm z$ directions, the current is zero regardless of the phase difference. However, the current has a large value when the magnetization direction is parallel to the junction plane, which leads to a perfect switch effect of the Josephson current. Furthermore, we find that the long junctions can host both the 0 state and $\pi$ state, and the $0\text{−}\pi$ transitions can be achieved with the change of the magnetization direction. The physical origins of the switch effect and $0\text{−}\pi$ transitions are interpreted from the perspectives of the spin-triplet Andreev reflection, the Ising pairing order parameter and the Ginzburg-Landau type of free energy. In addition, the influences of the chemical potential, the magnetization magnitude, and the strength of the Ising spin-orbit coupling on the switch effect and $0\text{−}\pi$ transitions are also investigated. Furthermore, the two-dimensional Josephson junctions are also investigated and we show that the spin-triplet Josephson effect can exist always. These results provide a convenient way to control the Josephson critical current and to adjust the junctions between the 0 state and $\pi$ state by only rotating one magnetization.

We present a method to considerably improve the numerical performance for solving Eliashberg-type coupled equations on the imaginary axis. Instead of the standard practice of introducing a hard numerical cutoff for treating the infinite summations involved, our scheme allows for the efficient calculation of such sums extended formally up to infinity. The method is first benchmarked with isotropic Migdal-Eliashberg theory calculations and subsequently applied to the solution of the full-bandwidth, multiband, and anisotropic equations focusing on the $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$ interface as a case study. Compared to the standard procedure, we reach similarly well converged results with less than one fifth of the number of frequencies for the anisotropic case, while for the isotropic set of equations we spare approximately ninety percent of the complexity. Since our proposed approximations are very general, our numerical scheme opens the possibility of studying the superconducting properties of a wide range of materials at ultralow temperatures.

We construct a one-dimensional local spin Hamiltonian with an intrinsically nonlocal, and therefore anomalous, global ${\mathbb{Z}}_2$ symmetry. The model is closely related to the quantum Ising model in a transverse magnetic field, and contains a parameter that can be tuned to spontaneously break the nonlocal ${\mathbb{Z}}_2$ symmetry. The Hamiltonian is constructed to capture the unconventional properties of the domain walls in the symmetry-broken phase. Using uniform matrix product states, we obtain the phase diagram that results from condensing the domain walls. We find that the complete phase diagram includes a gapless phase that is separated from the ordered ferromagnetic phase by a Berezinskii-Kosterlitz-Thouless transition, and from the ordered antiferromagnetic phase by a first-order phase transition.

Renewed interest in the homogeneous electron gas (HEG) has been stimulated by recent accurate simulations of it over a wide range of densities and temperatures. Those data, combined with known theoretical limits, have led to analytical representations of the free energy. Such a representation is, at least in principle, the complete HEG equation of state. The initial objective here is to establish that the two best representations [“corrKSDT,” Phys. Rev. Lett. 112, 076403 (2014), Phys. Rev. Lett. 120, 076401 (2018), and “GDB” Phys. Rev. Lett. 119, 135001 (2017)] of the simulation data and constraints are effectively the same in both functional form and accuracy of representation. The second objective is to disclose and delineate a significant difficulty. Despite their expected accuracy for the free energy, the underlying functional form is not adequate for derived thermodynamic properties. As an example, the specific heats obtained from the representations exhibit anomalies suggesting the need first for additional simulation data in critical regimes, then for refined fitting functions. The existing representations are, however, almost certainly adequate for applications based on the free energy alone (e.g., density-functional theory for warm dense matter). The third objective is to show that, despite their inability to provide a complete thermodynamic description of the HEG, the best analytical representations do provide a fully adequate exchange-correlation local density approximation for free-energy density-functional calculations.

The critical properties of the ${\mathrm{QED}}_3$ Gross-Neveu-Yukawa (GNY) model in 2 + 1 dimensions with $N$ flavors of two-component Dirac fermions are computed to first order in the $1/N$ expansion. For the specific case of $N=2$, the critical point is conjectured to be dual to the Néel-to-valence-bond-solid (VBS) deconfined critical point of quantum antiferromagnets on the square lattice. It is found that Aslamazov-Larkin diagrams, missed by previous $\epsilon$- and $1/N$-expansion studies with four-component fermions, give important contributions to the scaling dimensions of various operators. With the inclusion of these diagrams, the resummed scaling dimensions of the adjoint fermion bilinear and scalar field at the ${\mathrm{QED}}_3$ GNY critical point are in reasonable agreement with numerical studies of the Néel-to-VBS transition, in support of the duality conjecture.

The carrier dynamics and electronic structures of type-II Weyl semimetal candidates ${\mathrm{MoTe}}_2$ and ${\mathrm{WTe}}_2$ have been investigated by using temperature-dependent optical conductivity $\left[\sigma \right(\omega \left)\right]$ spectra. Two kinds of Drude peaks (narrow and broad) have been separately observed. The width of the broad Drude peak increases with elevating temperature above the Debye temperature of about 130 K in the same way as those of normal metals, on the other hand, the narrow Drude peak becomes visible below 80 K and the width is rapidly suppressed with decreasing temperature. Because the temperature dependence of the narrow Drude peak is similar to that of a type-I Weyl semimetal TaAs, it was concluded to originate from Dirac carriers of Weyl bands. The result suggests that the conductance has the contribution of two kinds of carriers, normal semimetallic and Dirac carriers, and this observation is evidence of the type-II Weyl semimetals ${\mathrm{MoTe}}_2$ and ${\mathrm{WTe}}_2$. The obtained carrier mass of the semimetallic bands and the interband transition spectra suggest the weak electron correlation effect in both materials.

Contribution of a $d$ electron to ferroelectricity of type-II multiferroics causes strong magnetoelectric coupling and distinguishes them from the conventional type-I multiferroics. However, their therein polarization is too small because the ferroelectricity is merely a derivative from the magnetic order. Here we report a class of multiferroic materials, monolayer $\mathrm{VO}{X}_2$ ($X=\mathrm{Cl}$, Br, and I), which combine the advantages of type-I and type-II multiferroics. Both ferroelectricity and magnetism arise from the same V cation, where the filled $d$ orbital is perpendicular to an a priori ferroelectric polarization and thus poses no hindrance to ferroelectricity, indicating a violation of the usual $d^0$ rule. This makes the combination of large polarizations and strong magnetoelectric coupling possible. Our findings not only add new ferromagnetic-ferroelectric multiferroics, but also point to a unique mechanism to engineer multiferroics.

We present a complete all-electron density functional theory/ab initio study of structural and electronic properties at pure In(111) and Cd-doped In(111) surfaces, enabling a deep analysis of the electric field gradient (EFG) in these systems. We explained, from first-principles, results of previously performed key time-differential perturbed γ-γ angular correlations experiments [W. Körner et al., Phys. Rev. Lett. 49, 1735 (1982)] on ${}^{111}\mathrm{In}$ isotopes (which decay to ${}^{111}\mathrm{Cd}$ impurity probe-atoms) deposited onto the In(111) surface of thin films under ultrahigh vacuum, adding inactive indium layer by layer, carefully designed to determine the EFG at different depths from the surface. We confirmed the existence of only two hyperfine interactions, one related with ${}^{111}\mathrm{Cd}$ probes localized at the two more superficial In sites (${\mathrm{HFI}}^{\mathrm{S}}$), and the other related with probes localized in any of the other inequivalent In sites existing from the surface towards the bulk (${\mathrm{HFI}}^{\mathrm{B}}$). In the case of ${\mathrm{HFI}}^{\mathrm{S}}$, $V_{33}$ is oriented normal to the (111) surface, and for ${\mathrm{HFI}}^{\mathrm{B}}$ we found a $V_{33}$ orientation parallel to the [001] axis and coincident with the orientation predicted for both the pure and Cd-doped In bulk (not determined experimentally at present), enabling us to confirm the experimental assignment of ${\mathrm{HFI}}^{\mathrm{B}}$. The axial symmetry that the EFG has in pure and Cd-doped In bulk systems is broken when the surface is generated and is recovered as the probe (In or Cd, respectively) goes deeper from the surface into the bulk. We separated the structural and electronic effects and their sources in the pure and Cd-doped In(111) surface. For the Cd-doped systems we confirm the experimental ratio $|V_{33}^S/V_{33}^B|\approx 4$, showing that light structural modifications have in important impact on the Cd $p$-states distribution, which governs the $V_{33}$ behavior. Finally, from the combination of the predicted $V_{33}$ for the Cd-doped systems as a function of the depth of the Cd localization from the surface with the experimental fractions of ${\mathrm{HFI}}^{\mathrm{S}}$ and ${\mathrm{HFI}}^{\mathrm{B}}$, we demonstrated that a single 3-Å active monolayer was enough to explain the origin of these fractions (in discrepancy with the previous interpretation of the experiments), proposing a deposition rate for the inactive In layers, in agreement with the experimental fraction evolution as a function of inactive In deposition.

Recently, β-Te [atomically two-dimensional (2D) tellurium] with rectangular crystal structure has been synthesized successfully on highly oriented pyrolytic graphite substrates by using molecular beam epitaxy [Z. Zhu et al., Phys. Rev. Lett. 119, 106101 (2017); Chen et al., Nanoscale 9, 15945 (2017)]. It has been found to possess remarkable properties such as ultralow lattice thermal conductivity and high thermoelectric efficiency. Based on first-principles calculations, we study the thermal expansion and thermodynamic properties of the experimental phase monolayer β-Te, using the quasiharmonic approach. It is found that β-Te shows large positive thermal expansion at elevated temperature, while the linear thermal expansion coefficient is negative along the $a$ direction at very low temperature. The linear thermal expansion coefficient along the $b$ direction is ${4.9\times 10}^{-5}{\mathrm{K}}^{-1}$ at 500 K, which is considerably large in 2D materials. β-Te exhibits strong in-plane anisotropy, including thermal expansion, 2D elastic moduli, and Poisson's ratios. However, the elastic moduli, Poisson's ratios and the in-plane anisotropy are weakened with increasing temperature, and the variations are dominated by the generalized mode Grüneisen parameters.

Perturbation theory is an indispensable tool in quantum mechanics and electrodynamics that handles weak effects on particle motion or fields. However, its extension to plasmons involving complex motion of both particles and fields remained challenging. We show that this challenge can be mastered if electron motion obeys the laws of hydrodynamics, as recently confirmed in experiments with ultraclean heterostructures. We present a unified approach to evaluate corrections to plasmon spectra induced by carrier drift, magnetic field, scattering, viscosity, and Berry curvature. The developed theory enables us to resolve the long-standing stability problem for direct current in confined two-dimensional electron systems against self-excitation of plasmons. We show that arbitrarily weak current in the absence of dissipation is unstable provided the structure lacks mirror symmetry. On the contrary, we find that in extended periodic systems—plasmonic crystals—weak carrier drift is always stable. Instead, this drift induces anomalous Doppler shift, which can be both below and higher than its value in uniform systems.

We study the loading of electrons into a quantum dot with dynamically controlled tunnel barriers. We introduce a method to measure tunneling rates for individual discrete states and to identify their relaxation paths. Exponential selectivity of the tunnel coupling enables loading into specific quantum dot states by tuning independently energy and rates. While for the single-electron case orbital relaxation leads to fast transition into the ground state, for electron pairs triplet-to-singlet relaxation is suppressed by long spin-flip times. This enables the fast gate-controlled initialization of either a singlet or a triplet electron pair state in a quantum dot with broad potential applications in quantum technologies.

We theoretically analyze the nonlinear anomalous Nernst effect as the second-order response of temperature gradient by using the semiclassical framework of electron dynamics. We find that a nonlinear current can be generated transverse to the applied temperature gradient in time-reversal-symmetry materials with broken inversion symmetry. This effect has a quantum origin arising from the Berry curvature of states near the Fermi surface. We discuss the nonlinear Nernst effect in transition metal dichalcogenides (TMDCs) under the application of uniaxial strain. In particular, we predict that under fixed chemical potential in TMDCs, the nonlinear Nernst current exhibits a transition from $T^{-2}$ temperature dependence in low temperature regime to a linear $T$ dependence in high temperature.

The rare-earth nitride ferromagnetic semiconductors owe their varying magnetic properties to the progressive filling of the $4f$ shell across the series. Recent electrical transport measurements on samarium nitride, including the observation of superconductivity, have been understood in terms of a contribution from a $4f$ transport channel. Band structure calculations generally locate an empty majority-spin $4f$ band within the conduction band although over a wide range of possible energies. Here we report optical reflection and transmission measurements on samarium nitride from 0.01 to 4 eV that demonstrate clearly that the $4f$ band forms the bottom of the conduction band. Results at the lowest energies show no free carrier absorption, indicating a semiconducting ground state, and support earlier conclusions based on transport measurements.

In this work we propose to simulate many-body thermodynamics of infinite-size quantum lattice models in one, two, and three dimensions, in terms of few-body models of only O(10) sites, which we coin as quantum entanglement simulators (QES's). The QES is described by a temperature-independent Hamiltonian, with the boundary interactions optimized by the tensor network methods to mimic the entanglement between the bulk and environment in a finite-size canonical ensemble. The reduced density matrix of the physical bulk then gives that of the infinite-size canonical ensemble under interest. We show that the QES can, for instance, accurately simulate varieties of many-body phenomena, including finite-temperature crossover and algebraic excitations of the one-dimensional spin liquid, the phase transitions and low-temperature physics of the two- and three-dimensional antiferromagnets, and the crossovers of the two-dimensional topological system. Our work provides an efficient way to explore the thermodynamics of intractable quantum many-body systems with easily accessible systems.

In this study, the metal-insulator transition in the square-lattice Hubbard model at half-filling is revisited in relation to the DOS and spectral functions by means of the ladder dual fermion approximation (LDFA). For this purpose, a new expression of the two-body Green's function in the form of resolvents is proposed, which provides tractable and efficient means to calculate the local vertex function with the Lanczos exact diagonalization (ED) method. This makes it possible to use the Lanczos ED method as a solver of the effective impurity Anderson model for LDFA, opening up the way to access low temperatures for these perturbative extensions of the dynamical mean-field theory and to obtain accurate DOS and spectral functions on the real frequency axis by a new variant of the maximum entropy method. It is found that for $U\le 3.5t$, as temperature decreases, the pseudogap formation due to antiferromagnetic correlations in the quasiparticle peak of the spectral function occurs at the $X$ point $[\mathit{k}=(\pi ,0\left)\right]$, spreads through the Fermi surface and ends at the $M_2$ point $[\mathit{k}=(\pi /2,\pi /2\left)\right]$. The almost simultaneous creation of the pseudogap and the loss of the Fermi liquid feature is consistent with that expected in the Slater regime. Although the pseudogap still appears in the quasi-particle-like single peak for $U\ge 4.0t$, the Fermi-liquid feature is partially lost on the Fermi surface already at higher temperatures as expected in the Mott-Heisenberg regime, in which local spins are preformed at high temperatures. A sharp crossover from a pseudogap phase to a Mott insulator at finite $U^{*}\approx 4.7t$ is found to occur below the temperature of the pseudogap formation similar to a previous study with the nonlinear $\sigma$ model approach.