We numerically investigate the electronic transport properties (i.e., electron tunneling and Andreev reflection) of a topological superconductor composed of a magnetic topological insulator and superconductors. A phase diagram is provided to distinguish various topological phases and their corresponding distinct Majorana edge modes. When superconductors are proximity coupled with the top and bottom surfaces of a magnetic topological insulator thin film, a quantum phase transition from topological insulator to quantum anomalous Hall effect passes through the regime possessing both chiral and helical edge modes. The hallmark feature is that the coefficient of electron tunneling is quantized to be $5/4$ and the remaining scattering processes exhibit an identical probability with a magnitude of $1/4$ in the coexisting states with a Chern number of $\mathcal{N}=\pm 1$. When the superconductors are proximity coupled with a nonmagnetic topological insulator thin film, we find that the perfectly quantized electron tunneling or crossed Andreev reflection can alternately appear via tuning the chemical potential.

In a recent paper [Phys. Rev. B 97, 075135 (2018)], Menezes et al. analyze the topological behavior of an effective bosonic model defined on the Lieb lattice in the presence of an electromagnetic field. In this context, the authors claim to have found an atypical quantum Hall effect for the quasiparticles. However, some inconsistencies related to the treatment of the propagator jeopardize the main result in this system.

Through numerical simulations, we demonstrate the combination of ptychography and atomic electron tomography as an effective method for low dose imaging of individual low-Z atoms in three dimensions. After generating noisy diffraction patterns with multislice simulations of an aberration-corrected scanning transmission electron microscope through a 5-nm zinc-oxide nanoparticle, we have achieved three-dimensional (3D) imaging of individual zinc and oxygen atoms and their defects by performing tomography on ptychographic projections. The methodology has also been simulated in 2D materials, resolving individual sulfur atoms in vertical $\mathrm{W}{\mathrm{S}}_2/\mathrm{WS}{\mathrm{e}}_2$ van der Waals heterostructure with a low total electron dose where annular-dark-field images fail to resolve. We envision that the development of this method could be instrumental in studying the precise 3D atomic structures of radiation sensitive systems and low-$Z$ atomic structures such as 2D heterostructures, catalysts, functional oxides, and glasses.

Many positive electrode materials in lithium ion batteries include transition metals, which are difficult to describe by electronic structure methods like density functional theory (DFT) due to the presence of multiple oxidation states. A prominent example is the lithium manganese oxide spinel ${\mathrm{Li}}_x{\mathrm{Mn}}_2{\mathrm{O}}_4$ with $0\le x\le 2$. While DFT, employing the local hybrid functional PBE0r, provides a reliable description, the need for extended computer simulations of large structural models remains a significant challenge. Here, we close this gap by constructing a DFT-based high-dimensional neural network potential (HDNNP) providing accurate energies and forces at a fraction of the computational costs. As different oxidation states and the resulting Jahn-Teller distortions represent a new level of complexity for HDNNPs, the potential is carefully validated by performing x-ray diffraction experiments. We demonstrate that the HDNNP provides atomic level details and is able to predict a series of properties like the lattice parameters and expansion with increasing Li content or temperature, the orthorhombic to cubic transition, the lithium diffusion barrier, and the phonon frequencies. We show that for understanding these properties access to large time and length scales as enabled by the HDNNP is essential to close the gap between theory and experiment.

Amorphous carbon (a-C) materials have diverse interesting and useful properties, but the understanding of their atomic-scale structures is still incomplete. Here, we report on extensive atomistic simulations of the deposition and growth of a-C films, describing interatomic interactions using a machine learning (ML) based Gaussian approximation potential model. We expand widely on our initial work [M. A. Caro et al., Phys. Rev. Lett. 120, 166101 (2018)] by now considering a broad range of incident ion energies, thus modeling samples that span the entire range from low-density ($s{p}^2$-rich) to high-density ($s{p}^3$-rich, “diamondlike”) amorphous forms of carbon. Two different mechanisms are observed in these simulations, depending on the impact energy: low-energy impacts induce $sp$- and $s{p}^2$-dominated growth directly around the impact site, whereas high-energy impacts induce peening. Furthermore, we propose and apply a scheme for computing the anisotropic elastic properties of the a-C films. Our work provides fundamental insight into this intriguing class of disordered solids, as well as a conceptual and methodological blueprint for simulating the atomic-scale deposition of other materials with ML driven molecular dynamics.

The electronic structure of a vortex line trapped by a planar defect in a type-II superconductor is analyzed within the quasiclassical approach of the Bogoliubov–de Gennes theory. The normal reflection of electrons and holes at the defect plane results in the topological transition in the spectrum and formation of a type of quasiparticle state skipping or gliding along the defect. This topological transition appears to be a hallmark of the initial stage of the crossover from the Abrikosov to the Josephson vortex type revealed in the specific behavior of the quantized quasiparticle levels and density of states. The increase in the resulting hard and soft gaps affects the vortex mobility along the defect plane and the splitting of the zero-bias anomaly in the tunneling spectral characteristics.

To efficiently manipulate magnetism is a key physical issue for modern condensed matter physics, which is also crucial for magnetic functional applications. Most previous relevant studies rely on the tuning of spin texture, while the spin orientation is often negligible. As an exception, spin-orbit coupled $J_{\mathrm{eff}}$ states of $4d/5d$ electrons provide an ideal platform for emergent quantum effects. However, many expectations have not been realized due to the complexities of real materials. Thus the pursuit for more ideal $J_{\mathrm{eff}}$ states remains ongoing. Here a near-ideal $J_{\mathrm{eff}}=3/2$ Mott-insulating phase is predicted in the family of hexachloro niobates, which avoid some common drawbacks of perovskite oxides. The local magnetic moment is nearly compensated between spin and orbital components, rendering exotic recessive magnetism. More interestingly, the electronic structure and magnetism can be strongly tuned by rotating spin axis, which is rare but crucial for spintronic applications.

The competition between the ferromagnetic exchange interaction and antisymmetric Dzyaloshinskii-Moriya interaction can stabilize a helical phase or support the formation of skyrmions. In thin films of chiral magnets, the current density can be large enough to unpin the helical phase and reveal its nontrivial dynamics. We theoretically study the dynamics of the helical phase under spin-transfer torques that reveal distinct orientation processes, driven by topological defects in the bulk or induced by edges, limited by instabilities at higher currents. Our experiments confirm the possibility of on-demand switching the helical orientation by current pulses. This helical orientation might serve as a novel order parameter in future spintronics applications.

In vibration-transit theory of liquid dynamics, the atomic motion consists of two contributions: First-principles vibrational motion in a $3N$-dimensional liquid potential energy valley, plus transits, which operate to move the atoms between valleys. In one time step, when an atom crosses the intersection between two valleys, moving a very small distance, the atom's equilibrium position moves the very large distance between the equilibrium positions of two neighboring valleys. A figure showing this simultaneous two-part motion is presented early in this paper. We recognize the motion of the equilibrium position as the transit motion, and we verify that this motion can be observed and measured. We present a collection of single-atom transit-motion profile graphs extracted from molecular dynamics liquid trajectories. These graphs confirm that vibrations plus transit motions constitute nearly the entire liquid atomic motion. While the transit motion is never fully resolved on the liquid trajectory, it is by definition fully resolved on the trajectory of equilibrium positions. The transit contribution to thermodynamics is calibrated via two adjustable parameters in the transit partition function. The transit contribution to the liquid thermal energy is graphed and discussed. The condensed-matter atomic motion theory of thermodynamic functions for crystals and liquids is outlined with particular attention to recent developments in the equation-of-state program.

Considering coupling to a microstructured bath as a relaxation mechanism in a periodically driven dissipative Haldane model, we establish that the system may be tuned to a stroboscopic topological steady state at all finite temperatures. The amplitude and frequency of the periodic drive is so chosen that the Floquet Hamiltonian describing the Haldane model at stroboscopic instants of time in the unitary situation is topologically nontrivial. We establish that in the stroboscopic steady state, the system reaches a thermal state of the Floquet Hamiltonian at a controlled temperature. Further, it is observed that even with a coupling to a bath, remarkably a Chern insulator can indeed be prepared in a Chern nontrivial pure steady state which is expected to exhibit a stroboscopic bulk-boundary correspondence. Using the nonuniqueness of the macroscopic bulk electric polarization of a Chern insulator in its topological phase, we propose a generalized Chern invariant that reflects the topology of out-of-equilibrium many-body stroboscopic states of the Haldane model even in a dissipative ambience. The generalized topology of dynamical Chern insulators being dependent on single-particle correlations is expected to manifest in experiments probing many-body quantum observables.

Electronic phase transitions such as insulator-metal transitions are common in strongly correlated systems. Here, using a combination of thermodynamic linear-stability analysis and phase-field simulations and employing ${\mathrm{VO}}_2$ as a prototypical example, we predict that an insulator-metal transition driven by photoexcitation may involve an intermediate, modulated charge density state with a temperature-dependent characteristic wavelength. It is shown that such an intermediate two-phase electronic state is formed through a spinodal mechanism and that its formation can be generic for insulator-metal transitions driven by fast stimuli. This transient electronic phase separation is expected to stimulate future experimental and computational efforts.

We study the electronic structure of single crystal $1T-{\mathrm{TiSe}}_2$ using temperature ($T$)-dependent soft x-ray photoemission spectroscopy (PES) and natural circular dichroism (NCD) across the charge-density-wave (CDW) transition at $T_{\mathrm{cdw}}\sim 200$ K. We investigate detailed changes in energy positions and widths of the Ti $2p$ and Se $3d$ core-level spectra across $T_{\mathrm{cdw}}$. The Ti $2p-3d$-resonant PES shows a clear Ti $3d$ character two-hole correlation satellite in the valence band. A Cini-Sawatzky analysis indicates an effective attractive two-hole Coulomb interaction energy $U_{dd}$ =−1.3 eV. This attractive Coulomb energy is significantly larger than the known energy scale of excitonic correlations ($<$ 100 meV) in $1T-{\mathrm{TiSe}}_2$. On-resonant $T$-dependent measurements indicate that the strongly hybridized Ti $3d$-Se $4p$ bands show increased hybridization in the CDW phase. On-resonant valence band spectra show a finite, possibly experimental geometry-related NCD of the states at and near the Fermi level which do not show $T$ dependence across $T_{\mathrm{cdw}}$. Given the presence of excitonic effects and the periodic lattice distortion, our results suggest that theoretical models need to take into account the attractive Coulomb interaction and hybridization changes for a complete understanding of the CDW in $1T-{\mathrm{TiSe}}_2$.

An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region and a suppression in the composite ordered phase. The doping-dependent phase diagram shows that the composite ordered state can be stabilized in the doped Mott regime, if conventional electronic orders are suppressed by frustration. While antiferro-orbital order dominates the filling range $2\lesssim n\le 3$ and ferro-orbital order dominates the strongly interacting region for $1\lesssim n<2$, we find superconductivity with a remarkably high $T_c$ around $n=1.5$ (quarter filling). Also in the doped system, there is a close connection between the orbital-freezing crossover and superconductivity.

We consider a system consisting of two tunnel-coupled two-dimensional topological insulators proximitized by a top and bottom superconductor with a phase difference of $\pi$ between them. We show that this system exhibits a time-reversal invariant second-order topological superconducting phase characterized by the presence of a Kramers pair of Majorana corner states at all four corners of a rectangular sample. We furthermore investigate the effect of a weak time-reversal symmetry breaking perturbation and show that an in-plane Zeeman field leads to an even richer phase diagram exhibiting two nonequivalent phases with two Majorana corner states per corner as well as an intermediate phase with only one Majorana corner state per corner. We derive our results analytically from continuum models describing our system. In addition, we also provide independent numerical confirmation of the resulting phases using discretized lattice representations of the models, which allows us to demonstrate the robustness of the topological phases and the Majorana corner states against parameter variations and potential disorder.

Quantum-dot-based spin-photon interfaces are highly sought systems to implement deterministic photon-photon gates as well as to generate photonic cluster states. This requires mastering the technological challenge of fully controlling the coupling of a charged quantum dot to a cavity mode. Here, we report on a set of technological and experimental developments that allows doing so. The first ingredient consists in combining the in situ lithography technique, which allows a deterministic spatial and spectral coupling of the emitter to a pillar cavity mode, with a preidentification of the quantum dot charge states, using spectral fingerprints. The second ingredient relies on the design of an asymmetric tunneling barrier to inject the carrier in the quantum dot and an optical control of the charge occupation probability. We show that we can ensure both a high occupation probability of the charge in the quantum dot, reaching $91\pm 1\%$, and an optimal coupling to the cavity mode, resulting in a single-photon source combining a highly polarized brightness of $33\pm 5\%$ with both a high purity $(g^{\left(2\right)}\left(0\right)=1.6\pm 0.4\%)$ and indistinguishability ($97\pm 0.4\%$) of the single photons.

We discuss the feasibility of measurement-based braiding in semiconductor-superconductor (SM-SC) heterostructures in the so-called quasi-Majorana regime—the topologically-trivial regime characterized by robust zero-bias conductance peaks (ZBCPs) that are due to partially-separated Andreev bound states (ps-ABSs). These low energy ABSs consist of component Majorana bound states (also called quasi-Majorana modes) that are spatially separated by a length scale smaller than the length of the system, in contrast with the Majorana zero modes (MZMs) emerging in the topological regime, which are separated by the length of the wire. In the quasi-Majorana regime, the ZBCPs appear to be robust to various perturbations as long as the energy splitting of the ps-ABS is less than the typical width ${\epsilon }_w$ of the low-energy conductance peaks (${\epsilon }_w\sim 10–20\mu \text{eV}$). However, the feasibility of measurement-based braiding depends on a different, much smaller, energy scale ${\epsilon }_m\sim 0.1\mu \text{eV}$. This energy scale is given by the typical fermion parity-dependent ground state energy shift due to virtual electron transfer between the SM-SC system and a quantum dot used for parity measurements. In this paper we show that it is possible to prepare the SM-SC system in the quasi-Majorana regime with energy splittings below the ${\epsilon }_m$ threshold, so that measurement-based braiding is possible in principle. However, despite the apparent robustness of the corresponding ZBCPs, ps-ABSs are in reality topologically unprotected. Starting with ps-ABSs with energy below ${\epsilon }_m$, we identify the maximum amplitudes of different types of (local) perturbations that are consistent with perturbation-induced energy splittings not exceeding the ${\epsilon }_m$ limit. We argue that measurements generating perturbations larger than the threshold amplitudes appropriate for ${\epsilon }_m$ cannot realize measurement-based braiding in SM-SC heterostructures in the quasi-Majorana regime. We find that, if possible at all, quantum computation using measurement-based braiding in the quasi-Majorana regime would be plagued with errors introduced by the measurement processes themselves, while such errors are significantly less likely in a scheme involving topological MZMs.

We present and discuss the methodology for modeling $4f$ photoemission spectra, $4f$ photoelectron diffraction (PED) patterns, and magnetic dichroism effects for rare-earth-based materials. Using PED and magnetic dichroism in photoemission, we explore the electronic and magnetic properties of the near-surface region of the valence-fluctuating material ${\mathrm{EuIr}}_2{\mathrm{Si}}_2$. For the Eu-terminated surface, we found that the topmost Eu layer is divalent and exhibits a ferromagnetic order below 10 K. The valency of the next Eu layer, that is the fifth atomic layer, is about 2.8 at low temperature that is close to the valency in the bulk. The properties of the Si-terminated surface are drastically different. The first subsurface Eu layer (fourth atomic layer below the surface) behaves divalently and orders ferromagnetically below 48 K. Experimental data indicate, however, that there is an admixture of trivalent Eu in this layer, resulting in its valency of about 2.1. The next deeper lying Eu layer (eighth atomic layer below the surface) behaves mixed valently, but the estimated valency of 2.4 is notably lower than the value in the bulk. The presented approach and obtained results create a background for further studies of exotic surface properties of $4f$-based materials, and allow us to derive information related to valency and magnetism of individual rare-earth layers in a rather extended area near the surface.

We formulate the chiral vortical effect (CVE) and its generalization called generalized vortical effect using the semiclassical theory of wave packet dynamics. We take the spin-vorticity coupling into account and calculate the transport charge current by subtracting the magnetization one from the Noether local one. We find that the transport charge current in the CVE always vanishes in relativistic chiral fermions. This result implies that it cannot be observed in transport experiments in condensed matter systems such as Dirac/Weyl semimetals with the pseudo-Lorentz symmetry. We also demonstrate that the anisotropic CVE can be observed in nonrelativistic systems that belong to the point groups $D_n,C_n(n=2,3,4,6)$, and $C_1$, such as $n$-type tellurium.

The integer quantum Hall states at fillings $\nu =0$ and $\left|\nu \right|=1$ in monolayer graphene have drawn much attention as they are generated by electron-electron interactions. Here we explore aspects of the $\nu =0$ and $\left|\nu \right|=1$ quantum Hall states relevant for experimental samples. In particular, we study the effects of finite extent and finite temperature on the $\nu =0$ state and finite temperature for the $\nu =1$ state. For the $\nu =0$ state we consider the situation in which the bulk is a canted antiferromagnet and use parameters consistent with measurements of the bulk gap to study the edge states in tilted magnetic fields in order to compare with experiment [A. F. Young et al., Nature (London) 505, 528 (2014)]. When spatial modulation of the order parameters is taken into account, we find that for graphene placed on boron nitride, the gap at the edge closes for magnetic fields comparable to those in experiment, giving rise to edge conduction with $G\sim 2e^2/h$ while the bulk gap remains almost unchanged. We also study the transition into the ordered state at finite temperature and field. We determine the scaling of critical temperatures as a function of magnetic field $B$ and distance to the zero-field critical point and find sublinear scaling with magnetic field for weak and intermediate strength interactions, and $\sqrt{B}$ scaling at the coupling associated with the zero-field quantum critical point. We also predict that critical temperatures for $\nu =0$ states should be an order of magnitude higher than those for $\left|\nu \right|=1$ states, consistent with the fact that the low-temperature gap for $\nu =0$ is roughly an order of magnitude larger than that for $\left|\nu \right|=1$.