An efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal $L$ sums in spherical-harmonic expansions, so that fast convergence in single-$L$ sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients $A_L$ that define RSM can be calculated once for a fixed structure and speed up the whole self-consistent-field procedure. The accuracy and rapid convergence properties are confirmed using two analytic models, including the Coulomb potential and energy. We then implement the full-potential RSM using the Green's function Korringa-Kohn-Rostoker (KKR) method for real applications and compare the results with other first-principle methods and experimental data, showing that they are equally as accurate.

The ground states encode the information of the topological phases of a 2-dimensional system, which makes them crucial in determining the associated topological quantum field theory (TQFT). Most numerical methods for detecting the TQFT relied on the use of minimum entanglement states (MESs), extracting the anyon mutual statistics and self statistics via overlaps and/or the entanglement spectra. The MESs are the eigenstates of the Wilson loop operators, and are labeled by the anyons corresponding to their eigenvalues. Here we revisit the definition of the Wilson loop operators and MESs. We derive the modular transformation of the ground states purely from the Wilson loop algebra, and as a result, the modular $S$ and $T$ matrices naturally show up in the overlap of MESs. Importantly, we show that due to the phase degree of freedom of the Wilson loop operators, the MES-anyon assignment is not unique. This ambiguity obstructs our attempt to detect the topological order, that is, there exist different TQFTs that cannot be distinguished solely by the overlap of MESs. In this paper, we provide the upper limit of the information one may obtain from the overlap of MESs without other additional structure. Finally, we show that if the phase is enriched by rotational symmetry, there may be additional TQFT information that can be extracted from overlap of MESs.

We use the first-principles and effective Hamiltonian methods to study the electronic structure and magnetic properties of a recently synthesized layered antiferromagnetic square-net topological semimetal ${\mathrm{EuZnSb}}_2$ [Phys. Rev. Res. 2, 033462 (2020)]. The main message of the paper is that effects of small changes in the band structure produced by the magnetic ordering and changes in the orientation of the Néel vector are amplified in such transport properties as the spin Hall conductivity. We predict that the effects of the broken symmetry introduced by the ordering of the Néel vector, being very weak in the bulk, are pronounced in the surface electronic dispersion, suggesting that surface probes may be more suited to measure them. The coexistence of the magnetism with many other competing phases make this material interesting and possibly useful for quantum spintronics applications.

The scattering theory of low-energy (slow) electrons has been developed by Evans and Mills [Phys. Rev. B 5, 4126 (1972)]. The formalism is merely based on the electrostatic Coulomb interaction of the scattering electrons with the charge-density fluctuations above the surface and can describe most of the interesting features observed in the high-resolution electron energy-loss spectroscopy experiments. Here we extend this theory by including the spin-orbit coupling in the scattering process. We discuss the impact of this interaction on the scattering cross section. In particular, we discuss cases in which a spin-polarized electron beam is scattered from nonmagnetic surfaces with a strong spin-orbit coupling. We show that under some assumptions one can derive an expression for the scattering cross section, which can be used for numerical calculations of the spin-polarized spectra recorded by spin-polarized high-resolution electron energy-loss spectroscopy experiments.

Adiabatic and periodic variation of the lattice parameters can make it possible to transport charge through a system even without net external electric or magnetic fields, known as Thouless charge pumping. The amount of charge pumped in a cycle is quantized and entirely determined by the system's topology, which is robust against perturbations such as disorder and interactions. However, coupling to the environment may play a vital role in topological transport in many-body systems. We study the topological Thouless pumping, where the charge carriers interact with local optical phonons. The semiclassical multitrajectory Ehrenfest method is employed to treat the phonon trajectories classically and charge carriers quantum mechanically. We find a breakdown of the quantized charge transport in the presence of phonons. It happens for any finite electron-phonon coupling strength at the resonance condition when the pumping frequency matches the phonon frequency, and it takes finite phonon coupling strength away from the resonance. Moreover, there exist parameter regimes with nonquantized negative and positive charge transport. The modified effective pumping path due to electron-phonon coupling accurately explains the underlying physics. In the large coupling regime where the pumping disappears, the phonons are found to eliminate the staggering of the on-site potentials, which is necessary for the pumping protocol. Finally, we present a stability diagram of quantized pumping as a function of the time period of pumping and phonon coupling strength.

A measurement-based quantum feedback protocol is developed for spin-state initialization in a gate-defined double quantum dot spin qubit coupled to a superconducting cavity. The protocol improves qubit state initialization as it is able to robustly prepare the spin in shorter time and reach a higher fidelity, which can be preset. Being able to preset the fidelity aimed at is a highly desired feature enabling qubit initialization to be more deterministic. The protocol developed herein is also effective at high temperatures, which is critical for the current efforts toward scaling up the number of qubits in quantum computers.

We consider two distant spin qubits in quantum dots, both coupled to a two-dimensional topological ferromagnet hosting chiral magnon edge states at the boundary. The chiral magnon is used to mediate entanglement between the spin qubits, realizing a fundamental building block of scalable quantum computing architectures: a long-distance two-qubit gate. Previous proposals for long-distance coupling with magnons involved off-resonant coupling, where the detuning of the spin-qubit frequency from the magnonic band edge provides protection against spontaneous relaxation. The topological magnon mode, on the other hand, lies in between two magnonic bands far away from any bulk magnon resonances, facilitating strong and highly tuneable coupling between the two spin qubits. Even though the coupling between the qubit and the chiral magnon is resonant for a wide range of qubit splittings, we find that the magnon-induced qubit relaxation is vastly suppressed if the coupling between the qubit and the ferromagnet is antiferromagnetic. A fast and high-fidelity long-distance coupling protocol is presented capable of achieving spin-qubit entanglement over micrometer distances with $1\mathrm{MHz}$ gate speed and up to $99.9\%$ fidelities. The resulting spin-qubit entanglement may be used as a probe for the long-sought detection of topological edge magnons.

The two orbital Hubbard model, with the electrons additionally coupled to a complex magnetic background, arises in the pyrochlore molybdates. The background involves local moments Hund's coupled to the electrons, driving double exchange ferromagnetism, and antiferromagnetic (AF) tendency arising from competing superexchange. The key scales include the Hubbard repulsion and the superexchange, both of which can be tuned in these materials. They control the phase transition from a ferromagnetic metal to a spin-glass metal and then to a spin-glass (Mott) insulator. We provide a comprehensive description of the ground state of this model using an unrestricted Hartree-Fock scheme implemented via a simulated annealing procedure and establish the metal-insulator transition line for varying Hubbard interaction and superexchange. The electrons see an effective disorder, due to orbital frustration, already in the ferromagnetic phase. The disorder is further enhanced by antiferromagnetic coupling and the resulting magnetic disorder. As a result, increasing AF coupling shifts the metal-insulator transition to lower Hubbard interaction and gives it an additional “Anderson” character. We provide detailed results on the magnetic and orbital correlations, the density of states, and the optical conductivity.

We report density functional theory plus exact diagonalization of the multiorbital Anderson impurity model calculations for the Co adatom on the top of a Cu(001) surface. For the Co atom $d$-shell occupation $n_d\approx 8$, a singlet many-body ground state and Kondo resonance are found, when the spin-orbit coupling is included in the calculations. The differential conductance is evaluated in good agreement with the scanning tunneling microscopy measurements. The results illustrate the essential role which the spin-orbit coupling is playing in the formation of a Kondo singlet for the multiorbital impurity in low dimensions.

Antiferromagnetic (AFM) transitions of birefringent Dirac fermions created by a Y-shaped Kekulé distortion in graphene are investigated by mean-field theory and determinant quantum Monte Carlo simulations. We show that the quantum critical point can be continuously tuned by the bond-modulation strength, and the universality of the quantum criticality remains in the Gross-Neveu-Heisenberg class. The critical interaction scales with the geometric average of the two velocities of the birefringent Dirac cones, and decreases monotonically between the uniform and completely depleted limits. Since the AFM critical interaction can be tuned to very small values, antiferromagnetism may emerge automatically, realizing the long-sought magnetism in graphene. These results enrich our understanding of the semimetal-AFM transitions in Dirac-fermion systems, and open a route to achieve magnetism in graphene.

We performed a materials investigation into the properties of the THz conductivity spectra in the ternary alloy ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{(1-x)}{\mathrm{Se}}_x\right)}_3$ as a function of selenium fraction, $x$, and temperature. We find that the reduction in crystalline anharmonicity caused by the preferential ordering of the $x=1/3$ phase of ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{(1-x)}{\mathrm{Se}}_x\right)}_3$results in the prominent $E_u^1$phonon (occurring between 1.5 and 1.9 THz) red-shifting on cooling less than the binary ${\mathrm{Bi}}_2{\mathrm{Te}}_3$and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$samples. We also find that the $E_u^1$phonon couples to an electronic continuum at low temperatures ($T⩽40\mathrm{K}$), regardless of ${\mathrm{Bi}}_2{\left({\mathrm{Te}}_{(1-x)}{\mathrm{Se}}_x\right)}_3$stoichiometry or the Hall mobility of the topological insulator crystal. These results highlight the role that these optical modes play in the electronic and thermal transport within this ternary alloy and pave the way for exploring the interesting phonon dynamics within these topological insulator and thermoelectric materials.

Quantum Hall–superconductor heterostructures provide possible platforms for intrinsically fault-tolerant quantum computing. Motivated by several recent experiments that successfully integrated these phases, we investigate transport through a proximitized integer quantum Hall edge—paying particular attention to the impact of vortices in the superconductor. By examining the downstream conductance, we identify regimes in which subgap vortex levels mediate Andreev processes that would otherwise be frozen out in a vortex-free setup. Moreover, we show that at finite temperature, and in the limit of a large number of vortices, the downstream conductance can average to zero, indicating that the superconductor effectively behaves like a normal contact. Our results highlight the importance of considering vortices when using transport measurements to study superconducting correlations in quantum Hall–superconductor hybrids.

We propose a mechanism to explain the quantum anomalous Hall (QAH) effect and the electric-field-induced topological phase transition in AB-stacked $\mathrm{MoTe}{}_2/\mathrm{WSe}{}_2$ moiré heterobilayers at $\nu =1$ hole filling. We suggest that the Chern band of the QAH state is generated from an intrinsic band inversion composed of the highest two moiré hole bands with opposite valley numbers and a gap opening induced by two Coulomb-interaction-driven magnetic orders. These magnetic orders, including an in-plane ${120}^{\circ }$-Néel order and an in-plane ferromagnetic order, interact with moiré bands via corresponding in-plane exchange fields. The Néel order ensures the insulating gap, the ferromagnetic order induces the nonzero Chern number, and both orders contribute to time-reversal symmetry breaking. The Néel order is acquired from the Hartree-Fock exchange interaction and the formation of ferromagnetic order is attributed to interlayer-exciton condensation and exciton ferromagnetism. The exciton ferromagnetism can be demonstrated by excitonic Bose-Hubbard physics and Berezinskii-Kosterlitz-Thouless transition. In low electric fields, the equilibrium state is a Mott-insulator state. At a certain electric field, a correlated insulating state composed of the hole-occupied band and the exciton condensate becomes the thermodynamically stable phase and the topological phase transition occurs as the ferromagnetic order emerges. The consistency between the present theory and experimental observations is discussed. Experimental observations, including the spin-polarized/valley-coherent nature of the QAH state, the absence of charge gap closure at the topological phase transition, the canted spin texture, and the insulator-to-metal transition are interpreted by the mechanism.

The control of thermal fluxes—magnitude and direction—in mesoscale and nanoscale electronic circuits can be achieved by means of heat rectification using thermal diodes in two-terminal systems. The rectification coefficient $\mathcal{R}$, given by the ratio of forward and backward heat fluxes, varies with the design of the diode and the working conditions under which the system operates. A value of $\mathcal{R}\ll 1$ or $\mathcal{R}\gg 1$ is a signature of high heat rectification performance, but current solutions allowing such ranges necessitate rather complex designs. Here, we propose a simple solution: the use of a superconductor-insulator-superconductor (SIS) junction under an applied fast oscillating (THz range) voltage as the control of the heat flow direction and magnitude can be done by tuning the initial value of the superconducting phase. Our theoretical model, based on the Green functions formalism and coherent transport theory, shows a possible sharp rise of the heat rectification coefficient with values up to $\mathcal{R}\approx 500$ beyond the adiabatic regime. The influence of quantum coherent effects on heat rectification in the SIS junction is highlighted.

We theoretically study the Coulomb drag in graphene when there is a temperature difference between the layers. Within the degenerate limit for equal layer densities, we find that this can lead to significant deviations from the usual quadratic temperature dependence of the drag resistivity. The exact behavior depends strongly on the phase space available for intraband scattering, and is not symmetrical when the temperatures of the layers are interchanged. In particular, when one layer is at a much higher temperature $T$ than the other, the drag resistivity behaves as ${\rho }_D\sim T/d^5$, where $d$ is the interlayer separation. The magnitude of the drag in this limit is always larger when the active layer is at the higher temperature.

The effect of light on the properties of ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ superlattices is studied using first-principles calculations in their paraelectric phase $p$ as well as in the, $c, r$, and $aa$ phases that are defined by polarization lying along the [001], $\left[11v\right]$, and [110] directions, respectively. While the $r$ phase is the ground state in dark conditions, illumination triggers a rotation of the polarization towards the out-of-plane direction, which results in the $r$ phase transforming into a $c$ phase at a large concentration of photoexcited carriers. We further reveal that a space charge region of free carriers builds up at the interface under illumination, implying that these superlattices can be thought as acting as $p-i-n$ junctions under light. These free charges screen the polarization discontinuity at the interface, effectively reducing the electrostatic depolarizing field.

Helium (He) is the most inert noble gas at ambient conditions. It was predicted to adopt a hexagonal close packed structure ($P{6}_3/mmc$) and remains in the insulating phase up to 32 TPa. In contrast, lithium (Li) is one of the most reactive metals at zero pressure, while its cubic high-pressure phase ($Fd\overline{3}m$) is a weak metallic electride above 475 GPa. Strikingly, computations predict a stable compound of ${\mathrm{Li}}_5{\mathrm{He}}_2$ ($R\overline{3}m$) by mixing $Fd\overline{3}m$ Li with $P{6}_3/mmc$ He above 700 GPa from ab initio evolutionary searches. The presence of helium promotes the lattice transformation from $Fd\overline{3}m$ Li to $Pm\overline{3}m$ Li, and turns the three-dimensional distributed interstitial electrons into the mixture of zero- and two-dimensional anionic electrons. This significantly increases the degree of metallization at the Fermi level; consequently, the coupling of conductive anionic electrons with the Li-dominated vibrations is the key factor to the formation of superconducting electride ${\mathrm{Li}}_5{\mathrm{He}}_2$ with a transition temperature up to 26 K, dynamically stable to pressures down to 210 GPa.

We report on studies of charge carrier plasmon excitations in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ by transmission electron energy-loss spectroscopy. In particular, we present results on the plasmon dispersion and its width as a function of momentum transfer. The dispersion can be qualitatively explained in the framework of random phase approximation calculations, using an unrenormalized tight-binding band structure. The constant long-wavelength width of the plasmon indicates that it is caused by a decay into interband transitions and not by quantum critical fluctuations. The results from these studies on a prototypical correlated metal system show that the long-wavelength plasmon excitations near 1 eV are caused by resilient quasiparticles and are not influenced by correlation effects.

Studies of topological bands and their associated low-dimensional boundary modes have largely focused on linear systems. This work reports robust dynamical features of three-dimensional (3D) nonlinear systems in connection with intriguing topological bands in 3D. Specifically, for a 3D setting of coupled rock-paper-scissors cycles governed by the antisymmetric Lotka-Volterra equation (ALVE) that is inherently nonlinear, we unveil distinct characteristics and robustness of surface-polarized masses and analyze them in connection with the dynamics and topological bands of the linearized Lotka-Volterra equation. Our results show that insights learned from Weyl semimetal phases with type-I and type-II Weyl singularities based on a linearized version of the ALVE are still remarkably useful, even though the system dynamics is far beyond the linear regime. This work indicates the relevance and importance of the concept of topological boundary modes in analyzing high-dimensional nonlinear systems and hopes to stimulate further topological studies where various topological gapless phases of matter may emerge in higher-dimensional nonlinear systems.