Gapless Weyl semimetals (WSMs) are a novel class of topological materials that host massless Weyl fermions as their low-energy excitations. When the Weyl cone is tilted, the Lorentz invariance is broken and the Lifshitz transition drives the system from type-I WSMs into type-II WSMs. Here, based on the lattice model, we perform a systematic numerical study of the effect of on-site disorder on the diagonal magnetoconductivity in tilted WSMs. We use the self-consistent Born approximation to calculate the disorder-induced self-energy and then apply the Kubo-Streda formula to calculate the diagonal magnetoconductivity. For the transverse magnetoconductivity ${\sigma }_{xx}$, the disorder is found to exhibit distinct effects in the quantum limit regime and in the quantum oscillation regime of type-I WSMs, which could be understood from Einstein's relationship. With strong disorder, ${\sigma }_{xx}$ shows a linear relation with the inverse magnetic field $\frac{1}{B}$, which exhibits certain robustness to both the Fermi energy and the Weyl cone tilting. For the longitudinal magnetoconductivity ${\sigma }_{zz}$, the strong disorder can break the positive magnetoconductivity as well as the Shubnikov–de Haas oscillations. By analyzing the spectral function, we find that the chiral anomaly is still preserved at strong disorder even when the Weyl cone is overtilted, as there is no gap opening around the Weyl nodes. The implications of our results for experiments are discussed.

We theoretically study the modification of the energy spectrum of long-wavelength acoustic phonons due to the electron-phonon interaction in a three-dimensional topological Weyl semimetal under the influence of quantizing magnetic fields. We find that the dispersion and attenuation of phonons show striking oscillatory behaviors when varying the magnetic field at low temperatures. These oscillations are distinct when the Fermi energy is in different energy regimes. Moreover, the van Hove singularity of the Weyl spectrum can manifest as a transition between different oscillation patterns when increasing the magnetic field. These phonon behaviors could provide testable fingerprints of the Fermi-surface morphology and relativistic feature of the Weyl semimetal.

Majorana modes, typically arising at the edges of one-dimensional topological superconductors, are considered to be a promising candidate for encoding nonlocal qubits in fault-tolerant quantum computing. Here we exploit the two-dimensional geometry of Majorana corner modes in second-order topological superconductors to establish measurement-only quantum computation. It is shown that eight Majorana corner modes emerge when such systems are periodically driven, through which two nonlocal logical qubits and one nonlocal ancilla qubit can be constructed. Quantum gate operations can then be implemented by a designed series of parity measurements of topologically protected Majorana corner modes, accomplished via Mach-Zehnder type interference in the conductance between different corners of a second-order topological superconductor. Our theoretical proposal represents a scenario in which topologically protected single- and two-qubit gate operations can be carried out in a minimal setup, thus potentially establishing an efficient and low-cost building block for Majorana-based qubit architectures.

We analyze the influence of dimerization on the topological phases of a Rashba nanowire proximitized to a superconducting substrate. We find that periodic alternations of the hopping integral and spin-orbit coupling can lead to band inversion, inducing a transition to the topologically nontrivial superconducting phase that hosts Majorana zero-energy modes. This “dimerization-induced topological superconductivity” completely repels the topological phase of the uniform nanowire, whenever they happen to overlap. We provide an analytical justification for this puzzling behavior based on symmetry and parity considerations, and discuss feasible spectroscopic methods for its observation. We also test stability of the topological superconducting phases against electrostatic disorder.

The magnetodynamic properties of a square thin-film micromagnet ($2\mu \mathrm{m}\times 2\mu \mathrm{m}\times 16\mathrm{nm}$) with a flux-closure magnetic ground state were investigated by micromagnetic simulations. The system was excited with an applied magnetic field, displacing the vortex core sufficiently far from its equilibrium position to result in a nonlinear relaxation upon removal of the field. We find that creation of edge topological defects leads to exchange explosions and periodic emission of short-wavelength spin waves emanating from these defects. The exchange explosions of the edge topological defects are investigated and explained in terms of vortex/antivortex creation and the formation of a Bloch point. This finding could prove useful to the development of nanoscale devices for periodic generation of high-frequency microwave radiation.

The one-dimensional (1D) Rashba effect has become quite important due to its key role in basic science to realize exotic electronic phenomena, such as Majorana bound states. Similar to the two-dimensional or three dimensional systems, the modulation of Rashba effect in 1D matrix is the kernel of spintronics for manipulating electron spin. Herein, by investigating the effects of transverse and vertical external electric field (EEF) on the Rashba spin splitting and magnetic anisotropy energy (MAE) in a type of highly flexible 1D system (Gd-adsorbed zigzag graphene nanoribbons) from first principles, we found that the Rashba spin splitting in such 1D system can be effectively regulated by the transverse EEF. Moreover, perpendicular magnetic anisotropy holds with either transverse or vertical EEF applied, despite obvious modulation of the MAE contributions in $k$ space as well as the Rashba spin splitting. The modulation mechanism is further analyzed from the orbital-decomposed band structures and spin density for Gd-zigzag graphene nanoribbons (ZGNRs) at different electric-field values. It is found the modulation of $\mathrm{Gd}5d_{x^2-y^2},d_{xy}$ by C $p_z$ orbitals of edge states is the key to manipulating the magnetic anisotropy, which even plays a decisive role in modifying the Rashba spin splitting in such 1D nanoribbon system. The MAE and 1D Rashba spin splitting are expected to be controlled through modifying the edge states in such systems via EEF or other means. Our study introduces a strategy to manipulate Rashba spin splitting by edge states and provides insight into the magnetic anisotropy in 1D Rashba system, which would revitalize further research in ZGNR-based systems within the spintronics and exotic electronic phenomena.

The appearance of unconventional superconductivity near heavy-fermion quantum critical points (QCPs) motivates investigation of pairing correlations close to a “beyond Landau” Kondo-destruction QCP. We focus on a two-Anderson-impurity cluster in which Kondo destruction is induced by a pseudogap in the conduction-electron density of states. Analysis via continuous-time quantum Monte Carlo and the numerical renormalization group reveals a previously unstudied QCP that both displays the critical-local moment fluctuations characteristic of Kondo destruction and leads to a strongly enhanced singlet-pairing susceptibility. Our results provide insights into the mechanism for superconductivity in quantum critical metals.

We discuss the effects of exponential fragmentation of the Hilbert space on phase transitions in the context of coupled ferromagnetic Ising models in arbitrary dimension with special emphasis on the one-dimensional case. We show that the dynamics generated by quantum fluctuations is bounded within spatial partitions of the system and weak mixing of these partitions caused by global transverse fields leads to a zero temperature phase with ordering in the local product of both Ising copies but no long-range order in either species. This leads to a natural connection with the Ashkin-Teller universality class for general lattices. We confirm this for the periodic chain using quantum Monte Carlo simulations. We also point out that our treatment provides an explanation for pseudo-first-order behavior seen in the Binder cumulants of the classical frustrated $J_1-J_2$ Ising model and the $q=4$ Potts model in two dimensions.

A common path to superconducting spintronics, Majorana fermions, and topologically protected quantum computing relies on spin-triplet superconductivity. While naturally occurring spin-triplet pairing is elusive, and even common spin-triplet candidates, such as ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, support alternative explanations, proximity effects in heterostructures can overcome these limitations. It is expected that robust spin-triplet superconductivity in magnetic junctions should rely on highly spin-polarized magnets or complex magnetic multilayers. Instead, we predict that the interplay of interfacial spin-orbit coupling and the barrier strength in simple magnetic junctions, with only a small spin polarization and $s$-wave superconductors, can lead to nearly complete spin-triplet superconducting proximity effects. This peculiar behavior arises from an effective perfect transparency: interfacial spin-orbit coupling counteracts the native potential barrier for states of a given spin and wave vector. We show that the enhanced spin-triplet regime is characterized by a huge increase in conductance magnetoanisotropy, orders of magnitude larger than in the normal state.

As we reach the end of Moore's law, digital logic uses irreversible logic gates whose energy consumption has been scaled toward a lower limit. Reversible logic gates can provide a dramatic energy-efficient alternative, but rely on reversible dynamics. Here, we introduce a set of superconducting reversible gates that are powered alone by the inertia of the digital input states, contrasting existing adiabatic prototypes which are powered by an external adiabatic drive. The classic model of an inertia-powered reversible gate uses ballistic particles which scatter in two dimensions, where the digital state is represented by the particle path. Our ballistic gates use as the bit state the topological charge (polarity) of a fluxon moving along a long Josephson junction (LJJ) such that the particle path is confined to one dimension. The fundamental structures of our reversible fluxon logic (RFL) are one-bit gates which consist of two LJJs connected by a circuit interface that comprises three large-capacitor Josephson junctions (JJs). Numerical simulations show how a fluxon approaching the interface under its own inertia converts its energy to an oscillating evanescent field, from which in turn a new fluxon is generated in the other LJJ. We find that this resonant forward scattering of a fluxon across the interface requires large capacitances of the interface JJs because they enable a conversion between bound-evanescent and traveling fluxon states (without external power). Importantly, depending on the circuit parameters, the new fluxon may have either the original or the inverted polarity, and these two processes constitute the fundamental identity and not operations of the logic. Based on these one-bit RFL gates, we design and study a related two-bit RFL gate which shows that fluxons can exhibit conditional polarity change. Energy efficiency is accomplished because only a small fraction of the fluxon energy is transferred to modes other than the intended fluxon. Simulations show that over $97\%$ of the total fluxon energy is preserved during gate operations, in contrast to irreversible gates where the entire bit energy is consumed in bit switching. To provide insight into these phenomena, we analyze the one-bit gate circuits with a collective-coordinate model which describes the field in each LJJ as a combination of fluxon and mirror antifluxon. This allows us to reduce the many-junction circuit (the three interface JJs and the many JJs approximating the LJJs, solved numerically) to that of two coupled degrees of freedom that each represent a particle. The evolution of the reduced model agrees quantitatively with the full circuit simulations and validates the use of the mirror-fluxon ansatz. Parameter tolerances are calculated for the proposed circuits and indicate that RFL gates can be manufactured and tested.

Cross-sectional scanning tunneling microscopy (X-STM) is used to experimentally study the influence of isovalent Bi atoms on the electronic structure of InP. We map the spatial pattern of the Bi impurity state, which originates from Bi atoms down to the sixth layer below the surface, in topographic, filled-state X-STM images on the natural $\left\{110\right\}$ cleavage planes. The Bi impurity state has a highly anisotropic bowtielike structure and extends over several lattice sites. These Bi-induced charge redistributions extend along the $〈110〉$ directions, which define the bowtielike structures we observe. Local tight-binding calculations reproduce the experimentally observed spatial structure of the Bi impurity state. In addition, the influence of the Bi atoms on the electronic structure is investigated in scanning tunneling spectroscopy measurements. These measurements show that Bi induces a resonant state in the valence band, which shifts the band edge toward higher energies. Furthermore, we show that the energetic position of the Bi-induced resonance and its influence on the onset of the valence band edge depend crucially on the position of the Bi atoms relative to the cleavage plane.

We investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromagnetic insulators, which is the magnonic analog of the inverse spin-galvanic effect of electrons. We derive a linear-response theory of a temperature-gradient-induced spin polarization for collinear and noncollinear antiferromagnets, which comprises both extrinsic and intrinsic contributions. We apply our theory to several noncentrosymmetric antiferromagnetic insulators, i.e., to a one-dimensional antiferromagnetic spin chain, a single layer of kagome noncollinear antiferromagnet, e.g., ${\text{KFe}}_3{\left(\text{OH}\right)}_6{\left({\text{SO}}_4\right)}_2$, and a noncollinear breathing pyrochlore antiferromagnet, e.g., ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$. The shapes of our numerically evaluated response tensors agree with those implied by the magnetic symmetry. Assuming a realistic temperature gradient of $10\text{K/mm}$, we find two-dimensional spin densities of up to $\sim {10}^6\hslash /{\text{cm}}^2$ and three-dimensional bulk spin densities of up to $\sim {10}^{14}\hslash /{\text{cm}}^3$, encouraging an experimental detection.

Nuclear spin-1/2 lattices where each spin has a small effective number of interacting neighbors represent a particular challenge for first-principles calculations of free induction decays (FIDs) observed by nuclear magnetic resonance. The challenge originates from the fact that these lattices are far from the limit where classical spin simulations perform well. Here we use the recently developed method of hybrid quantum-classical simulations to compute nuclear FIDs for ${}^{29}\mathrm{Si}$-enriched silicon and fluorapatite. In these solids, the small effective number of interacting neighbors is either due to the partition of the lattice into pairs of strongly coupled spins (silicon), or due to the partition into strongly coupled chains (fluorapatite). We find a very good overall agreement between the hybrid simulation results and the experiments. In addition, we introduce an extension of the hybrid method, which we call the method of coupled quantum clusters. It is tested on ${}^{29}\mathrm{Si}$-enriched silicon and found to exhibit excellent performance.

While antiferromagnetic skyrmions display appealing properties, their lateral expansion in the high-velocity regime hinders their potential for applications. In this work, we study the impact of spin Hall torque, spin transfer torque, and topological torque on the velocity-current relation of antiferromagnetic skyrmions with the aim of reducing this deformation. Using a combination of micromagnetic simulations and analytical derivations, we demonstrate that the lateral expansion of the antiferromagnetic skyrmion is reminiscent of the well-known Lorentz contraction identified in one-dimensional antiferromagnetic domain walls. We also show that in the flow regime the lateral expansion is accompanied by a progressive saturation of the skyrmion velocity when driven by spin Hall and topological torques. This saturation occurs at much smaller velocities when driven by the topological torque, while the lateral expansion is reduced, preventing the skyrmion size from diverging at large current densities. We extend this study toward synthetic antiferromagnets, where the weaker antiferromagnetic exchange leads to much larger lateral expansion at smaller current densities in all cases. This study suggests that a compromise must be made between skyrmion velocity and lateral expansion during the device design. In this respect, exploiting the topological torque could lead to better control of the skyrmion velocity in antiferromagnetic racetracks.

Here, we present an analytical and numerical model describing the magnetization dynamics in MgO-based spin-torque nano-oscillators with an in-plane magnetized polarizer and an out-of-plane free layer. We introduce the spin-transfer torque asymmetry by considering the cosine angular dependence of the magnetoresistance between the two magnetic layers in the stack. For the analytical solution, dynamics are determined by assuming a circular precession trajectory around the direction perpendicular to the plane, as set by the effective field, and calculating the energy integral over a single precession period. In a more realistic approach, we include the bias dependence of the tunnel magnetoresistance, which is assumed empirically to be a piecewise linear function of the applied voltage. The dynamical states are found by solving the stability condition for the Jacobian matrix for out-of-plane static states. We find that the bias dependence of the tunnel magnetoresistance, which is an inseparable effect in every tunnel junction, exhibits drastic impact on the spin-torque nano-oscillator phase diagram, mainly by increasing the critical current for dynamics and quenching the oscillations at high currents. The results are in good agreement with our experimental data published elsewhere.

We revisit the problem of the spectra of two holes in a ${\mathrm{CuO}}_2$ layer, modeled as a $\mathrm{Cu}\text{−}3d^8$ impurity with full multiplet structure coupled to a full O-$2p$ band as an approximation to the local electronic structure of a hole-doped cuprate. Unlike previous studies that treated the O band as a featureless bath, we describe it with a realistic tight-binding model. While our results are in qualitative agreement with previous work, we find considerable quantitative changes when using the proper O-$2p$ band structure. We also find that (i) the ligand O-$2p$ orbitals play an essential role, within this impurity model; (ii) the three-orbital Emery model provides an accurate description for the subspace with ${}^{1}A_1$ symmetry, which includes the ground state in the relevant region of the phase diagram; (iii) this ground state has only $\sim 50\%$ overlap with a Zhang-Rice singlet; (iv) there are other low-energy states, in subspaces with different symmetries, that are absent from the three-orbital Emery model and its one-band descendants. These states play an important role in describing the elementary excitations of doped cuprates.

A point charge near the surface of a topological insulator (TI) with broken time-reversal symmetry is predicted to generate an image magnetic charge in addition to an image electric charge. We use scanning tunneling spectroscopy to study the image potential states (IPSs) of the topological semimetal Sb(111) surface. We observe five IPSs with discrete energy levels that are well described by a one-dimensional model. The spatial variation of the IPS energies and lifetimes near surface step edges shows the first local signature of resonant interband scattering between IPSs, which suggests that image charges too may interact. Our work motivates the exploration of the TI surface geometry necessary to realize and manipulate a magnetic charge.

The spin relaxation in the D'yakonov-Perel' mechanism is theoretically studied in a symmetric double-quantum-well structure (DQWS) with an intersubband spin-orbit interaction (SOI) due to the local structural inversion asymmetry and the linear-in-wave-number Dresselhaus SOI. It is found that the spin relaxation rate induced by the intersubband SOI exhibits a suppression with $\omega {\tau }_p$ in the Lorentzian form of ${\left(1+{\omega }^2{\tau }_p^2\right)}^{-1}$, where $\hslash \omega$ is the intersubband energy separation and ${\tau }_p$ is the momentum relaxation time. The present Lorentzian suppression leads to a crossover with increasing $\omega {\tau }_p$ from the D'yakonov-Perel'-type relaxation (the spin relaxation time ${\tau }_s\propto {\tau }_p^{-1}$) to the Elliott–Yafet-type relaxation (${\tau }_s\propto {\tau }_p$). It is also shown that the spin relaxation rate in the presence of both the linear Dresselhaus SOI and the intersubband SOI is isotropic with respect to the in-plane spin direction in the present DQWS in contrast to a single quantum well exhibiting an in-plane anisotropy.

Electron energy loss spectroscopy in the low-loss regime is widely used to access to the screening of the Coulomb potential as a function of the momentum transfer. This screening is strongly reduced for low-dimensional materials and this spectroscopy is a technique of choice to study the resulting quantum confinement. Time-dependent density-functional theory within an ab initio formalism is particularly suited to simulate angular-resolved electron energy loss spectra, taking benefit from the reciprocal space description. For an isolated object, the standard procedure based on the supercell approach dramatically fails for the out-of-plane optical response of the surface and we have proposed a scheme called Selected-$G$ [N. Tancogne-Dejean, C. Giorgetti, and V. Véniard, Phys. Rev. B 92, 245308 (2015)], leading to a slab potential. In this paper, we show that the standard procedure also affects the in-plane components of the EEL spectra. Applying the Selected-$G$ procedure, we show that the full expression of the slab potential is crucial to describe slabs of finite thickness. We compare our formalism to other cutoff procedures, and show that if they provide spectra with the correct spectral weight, allowing the good description of plasmon dispersion, the amplitude of the peaks depends on the choice of the supercell. Our results, which provide spectra independent of vacuum, will have a strong impact on the calculation of properties such as quasiparticle corrections.