In extended Kitaev models on the honeycomb lattice, off-diagonal interactions (e.g., the $\mathrm{\Gamma },{\mathrm{\Gamma }}^{\prime }$ terms) can give rise to non-Kitaev quantum spin liquids and several magnetically ordered phases. In the present paper, we dope holes to the system and study the resultant $t\text{−}K\text{−}\mathrm{\Gamma }\text{−}{\mathrm{\Gamma }}^{\prime }$ model using mean-field theory. The interplay between the charge and spin degrees of freedom results in a rich phase diagram. Similar to doped cuprates, superconductors, pseudogap phases, Fermi liquid, strange metal and paramagnetic phase are generated. What is different is that, we obtain more than one superconducting phase (including a topological one) and more than one pseudogap phase no matter what the original spin state is. The Chern number of the topological superconductor is either $\nu =\pm 2$ or $\nu =\pm 1$, depending on the ratio $\mathrm{\Gamma }/\left|K\right|$ in the spin channel. We further find that an intermediate in-plane magnetic field can slightly enlarge the size of the topological superconducting phase.

We have investigated thermoelectric properties of the antiferromagnetic semimetal $\mathrm{Fe}{\mathrm{Ge}}_2$. As temperature decreases from 340 K, the Seebeck coefficient takes a maximum around the Néel temperature and then decreases to show a sign change from positive to negative <50 K. When a strong magnetic field is applied perpendicular to the sample plane, the sign change disappears, and the positive Seebeck coefficient is observed in the whole temperature range. This large magneto-Seebeck effect is anisotropic since the Seebeck coefficient is insensitive to in-plane magnetic fields. Based on the Mott formula, we discuss the origins for this anisotropic magneto-Seebeck effect.

We implement a self-consistent Hartree-Fock approximation based on a microscopic model in real space, which allows us to consider the interplay between the Hubbard and the extended Coulomb interaction in twisted bilayer graphene at the magic angle. These two interactions tend to favor different symmetry-breaking patterns, therefore having complementary roles in the regimes where one or the other dominates. We show that, for sufficiently large values of the on-site Hubbard repulsion, magic angle graphene has an antiferromagnetic ground state at the charge neutrality point, while at half filling of the lowest valence band the state becomes fully spin-polarized. In general, a suitable screening of the extended Coulomb interaction is required to observe the magnetic state in either case, as otherwise the instabilities take place in the charge sector, preferentially in the form of time-reversal, chiral, or valley symmetry breaking.

We have investigated the temperature- and field-variation of electronic state for the Dirac semimetal of ${\mathrm{EuMnBi}}_2$ by means of optical spectroscopy and theoretical calculation. The optical conductivity spectra show a clear Drude peak in the paramagnetic phase, which gradually diminishes in the Mn-$3d$ antiferromagnetic phase with decreasing temperature. Meanwhile, the absorption peaks due to the interband transition grow at low temperatures, resulting in a pseudogap feature with an energy scale of 0.07 eV. The analysis of Drude weight shows that the Drude response is nearly governed by the Dirac electrons at low temperatures. On the contrary, both the antiferromagnetic transition and spin reorientation of Eu-$4f$ moment do not significantly change the spectra except the moderate variation of Drude weight. As a comparison, we have also investigated the charge dynamics for ${\mathrm{EuZnBi}}_2$, which is an analog without the Mn-$3d$ antiferromagnetic ordering. In ${\mathrm{EuZnBi}}_2$, the optical conductivity spectra do not show the pseudogap structure, but show an intense Drude peak at all temperatures. Combined with the results of ab initio calculation, in ${\mathrm{EuMnBi}}_2$, it is likely that the reconstruction of electronic state driven by the Mn-$3d$ antiferromagnetic ordering causes the Dirac semimetallic state with tiny hole pockets, wherein electronic states other than the Dirac band are nearly gapped-out from the Fermi level.

We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the data. By testing our method with an exactly calculable model and applying it to practical dynamical mean-field calculations, we find that intermediate-frequency behaviors of Green's functions are determined solely by causality, and noncausal statistical errors are removed very efficiently. Furthermore, we demonstrate that numerical calculations of the physical branch of the Luttinger-Ward functional can be stabilized by ensuring causality of the noninteracting Green's function. Our method and findings provide a basis for improving stability and efficiency of numerical simulations of quantum many-body systems.

We study the superfluid response and localization dynamics from static and mobile impurities. The superfluidity is formed in the rung-Mott phase of a bosonic ladder model producing spin-Meissner currents induced by a $\mathbb{U}\left(1\right)$ gauge field or a uniform magnetic field. Impurities are described through two-state systems, which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to a classical Ising symmetry for static and mobile impurities associated to the inversion symmetry of the two legs of the ladder. From the decoupled rungs limit, we also identify a local ${\mathbb{Z}}_2$ gauge theory for mobile impurities. The properties of the system are studied from an effective quantum spin model including the possibility of four-body coupling in the limit of a strong interaction between bosons and impurities. Through analytical approaches and numerical exact diagonalization, we study the superfluid currents both in the weakly-coupled and strongly-coupled rungs limits for the bosons. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the two-peak random potential. In the strongly disordered situation, through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a Néel state.

We consider quantum spin ice in a temperature regime in which its response is dominated by the coherent motion of a dilute gas of monopoles through an incoherent spin background, taken to be quasistatic on the relevant timescales. The latter introduces well-known blocked directions that we find sufficient to reduce the coherent propagation of monopoles to quantum diffusion. This result is robust against disorder, as a direct consequence of the ground-state degeneracy, which disrupts the quantum interference processes needed for weak localization. Moreover, recent work [Tomasello et al., Phys. Rev. Lett. 123, 067204 (2019)] has shown that the monopole hopping amplitudes are roughly bimodal: for $\approx 1/3$ of the flippable spins surrounding a monopole, these amplitudes are extremely small. We exploit this structure to construct a theory of quantum monopole motion in spin ice. In the limit where the slow hopping terms are set to zero, the monopole wave functions appear to be fractal; we explain this observation via mapping to quantum percolation on trees. The fractal, nonergodic nature of monopole wave functions manifests itself in the low-frequency behavior of monopole spectral functions, and is consistent with experimental observations.

A novel spin orientation mechanism—dynamic electron spin polarization—has been recently suggested in Phys. Rev. Lett. 125, 156801 (2020). It takes place for unpolarized optical excitation in weak magnetic fields of the order of a few millitesla. In this paper we demonstrate experimentally and theoretically that the dynamic electron spin polarization degree changes sign as a function of time, strength of the applied magnetic field, and its direction. The studies are performed on indirect band-gap (In,Al)As/AlAs quantum dots and their results are explained in the framework of a theoretical model developed for our experimental setting.

For zigzag nanoribbons of transition metal dichalcogenides (TMDCs), experiments show a band gap with different gap size at the Mo edges, while theoretical models often predict metallic edges. Such an inconsistency could be attributed to the inadequate understanding of the possible mechanisms of edge reconstructions. Here, we revisit the mechanisms of different edge reconstructions along the Mo edge of $\mathrm{Mo}{X}_2$ ($X=\mathrm{Se}$, S) zigzag nanoribbons by first-principles calculations. We demonstrate that the valency of $\frac{1}{3}$ edge Mo increases to 5+ with $X$ adatom reconstruction, or all edge Mo decreases to 3+ with a Mo trimer reconstruction. Based on these Mo valence reconstructions, thermodynamically stable reconstructions are proposed for the Mo edge in $6\times$ and $4\times$ periodicities, which are comparable with the recent experimental observation of a small energy gap (of 0.36 eV) at the Mo edge of zigzag $\mathrm{Mo}{\mathrm{Se}}_2$ nanoribbons. The edge Mo valency reconstruction leads to quasi-one-dimensional Peierls distortion and charge- and spin-density waves at the edge. These findings should be applicable to other TMDCs.

We study the electronic structures of chiral Eshelby-twisted van der Waals atomic layers with a particular focus on a chiral twisted graphite (CTG), a graphene stack with a constant twist angle $\theta$ between successive layers. We show that each CTG can host infinitely many resonant states which arise from the interaction between the degenerate monolayer states of the constituent layers. Each resonant state has a screw rotational symmetry, and may have a smaller reduced Brillouin zone than other nonresonant states in the same structure. And each CTG can have the resonant states with up to four different screw symmetries. We derive the energies and wave functions of the resonant states in a universal form of a one-dimensional chain regardless of $\theta$, and show that these states exhibit a clear optical selection rule for circularly polarized light. Finally, we discuss the uniqueness and existence of the exact center of the lattice and the self-similarity of the wave amplitudes of the resonant states.

Understanding the intricate interplay between multiple electronic phases in quantum materials such as charge density wave (CDW), superconducting, and metallic phases is a challenging issue. Systematic introduction of pressure is one approach that has been used to probe this interplay. However, the influence of pressure together with the intricate interaction between electronic and lattice degrees of freedom can trigger complex structural evolution and distribution of various electronic phases at the atomic scale, the characterization of which demands high spatial resolution. We investigate the atomic-scale response of the charge density waves and the underlying atomic lattice in $1T\text{−}\mathrm{Ta}{\mathrm{S}}_2$ after exposure to hydrostatic pressure. High-resolution transmission electron microscopy images show that the CDW order parameter reacts with an elasticlike strain response to pressure-induced stacking faults and dislocations in the lattice. This is characterized by a proliferation of phase defects including CDW dislocations, discommensurations, and domain walls. Our results evidence the importance of pressure-induced lattice deformations and defects in modulating, stabilizing, or destroying electronic phases at the atomic scale.

The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In particular, fractional Chern insulators in bands with Chern number $\left|C\right|>1$ can demonstrate richer physical properties than continuum Landau level states and have recently been detected in experiments. Motivated by this, we examine the stability of fractional Chern insulators with higher Chern number in the Hofstadter model, using large-scale infinite density matrix renormalization group (iDMRG) simulations on a thin cylinder. We confirm the existence of fractional states in bands with Chern numbers $C=1,2,3,4,5$ at the filling fractions predicted by the generalized Jain series [Phys. Rev. Lett. 115, 126401 (2015)]. Moreover, we discuss their metal-to-insulator phase transitions, as well as the subtleties in distinguishing between physical and numerical stability. Finally, we comment on the relative suitability of fractional Chern insulators in higher Chern number bands for proposed modern applications.

We present a detailed theoretical description of the influence of the spin accumulation in metallic Fermi leads on the Kondo effect in systems such as quantum dots and Kondo alloys. We discuss an interplay of the spin accumulation, magnetic field, and ferromagnetic leads spin polarization on the Kondo spin-dependent densities of states, conductance, and resistance. It has been shown that the presence of the above-mentioned factors by breaking the spin symmetry leads to the suppression of the Kondo effect. However, for appropriately selected parameter values, these effects can compensate each other, which may lead to the restoration of the Kondo effect in the analyzed systems. We also address some recent experiments related to the spin current in the Kondo alloys.

The energy bands of non-Hermitian systems exhibit nontrivial topological features that arise from the complex nature of the energy spectrum. Under periodic boundary conditions (PBCs), the energy spectrum describes rather generally closed loops in complex plane, characterized by integer nonzero winding numbers. Such nontrivial winding provides the topological signature of the non-Hermitian skin effect (NHSE), i.e., the macroscopic condensation of bulk states at the lattice edges under open boundary conditions (OBCs). In spite of the great relevance of band winding in the non-Hermitian topological band theory and the related NHSE, most of current results rely on tight-binding models of non-Hermitian systems, while exact Bloch wave function analysis of the NHSE and related topological band theory is still lacking. While tight-binding models can correctly describe narrow-band electronic states with a relatively weak degree non-Hermiticity, they are not suited to describe high-energy wide-band electronic states and/or regimes corresponding to strong non-Hermiticity. Here we consider the single-particle continuous Schrödinger equation in a periodic potential, in which non-Hermiticity is introduced by an imaginary vector potential in the equation, and show that the NHSE is ubiquitous under OBC and characterized by a nonvanishing integer winding number, even though the energy spectrum under PBC always comprises an open curve, corresponding to high-energy electronic states. We also show that the interior of the PBC energy spectrum corresponds to the complex eigenenergies sustaining localized (edge) states under semi-infinite boundary conditions.

Atomic and electronic structure investigations of the substitutional ${\mathrm{Au}}_2\mathrm{Sn}$ surface alloy formed on Au(111) are presented. Low energy electron diffraction and scanning tunneling microscopy (STM) reveal a structure with a local $\sqrt{3}\times \sqrt{3}$ periodicity with a superimposed modulation resulting in a $26\times \sqrt{3}$ unit cell. STM images show a striped structure that resembles the herringbone reconstruction of clean Au(111), but with a longer periodicity compared to the $22\times \sqrt{3}$ unit cell of clean Au(111). Angle-resolved photoelectron spectroscopy data along the high-symmetry lines $\overline{\mathrm{\Gamma }}-{\overline{K}}^{\prime }-{\overline{M}}^{\prime }$ and $\overline{\mathrm{\Gamma }}-{\overline{M}}^{\prime }-{\overline{\mathrm{\Gamma }}}^{\prime }$ of a $\sqrt{3}\times \sqrt{3}$ surface Brillouin zone show two bands from the ${\mathrm{Au}}_2\mathrm{Sn}$ surface alloy layer. The experimental bands are compared to the calculated band structure of the local $\sqrt{3}\times \sqrt{3}$ periodicity. Most of the experimental band dispersions are qualitatively reproduced by the theoretical band structure including a spin split of one of the alloy bands. However, our detailed data reveal a band split, not present in the calculated bands of the $\sqrt{3}\times \sqrt{3}$ model, which is a consequence of the striped atomic structure of the ${\mathrm{Au}}_2\mathrm{Sn}$ surface alloy.

We investigate diffusive nanowire-based structures with two normal terminals on the sides and a central superconducting island in the middle, which is either grounded or floating. Using a semiclassical calculation we demonstrate that both device layouts permit a quantitative measurement of the energy dependent subgap thermal conductance $G_{\mathrm{th}}$ from the spectral density of the current noise. In the floating case this goal is achieved without the need to contact the superconductor provided the device is asymmetric, which may be attractive from the experimental point of view. In addition, we observe that the shot noise in the floating case is sensitive to a well-known effect of nonequilibrium suppression and bistability of the superconducting gap. Our calculations are directly applicable to the multimode case and can serve as a starting point to understand the shot noise response in an open one-dimensional Majorana device.

The helical state is a fundamental prerequisite for many spintronics applications and Majorana zero mode engineering in nanoscopic semiconductors. Its existence in quasi-one-dimensional nanowires was predicted to be detectable as a characteristic reentrant behavior in the conductance, which in a typical two-terminal architecture may be difficult to distinguish from other possible phenomena such as Fabry-Perot oscillations. Here we present an alternative method of helical gap detection free of the mentioned ambiguity, based on the nonlocal conductance measurements in a three-terminal junction. We find that the interplay between the spin-orbit coupling and the perpendicular magnetic field leads to a spin-dependent trajectory of electrons and as a consequence a preferential injection of electrons in one of the arms. This causes a remarkable enhancement of nonlocal conductance in the helical gap regime. We show that this phenomenon can be also used to detect the topological superconducting phase when the junction is partially proximitized by an s-wave superconductor.

We investigate the optical activity of tilted nodal loop semimetals. We calculate the full conductivity matrix for a band structure containing a nodal loop with possible tilt in the $x\text{−}y$ plane, which allows us to study the Kerr rotation and ellipticity both for a thin film and a bulk material. We find signatures in the Kerr signal that give direct information about the tilt velocity and direction, the radius of the nodal loop, and the internal chemical potential of the system. These findings should serve as a guide to understanding optical measurements of nodal loop semimetals and as an additional tool to characterize them.