Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band in the presence of disorder by focusing on the density of states (DOS) and dc conductivity. While the central hub site does not reveal the presence of the flat band, the sublattice resolved DOS on the noncentral sites exhibits a narrow peak with height $\sim$$1/\sqrt{g}$ with $g$ the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conductivity diverges as $\ln (1/g)$ with decreasing disorder due to interband transitions around the band touching point between the propagating and the flat band. Generalizations to higher pseudospin are given.

Ferroelectric polar displacements have recently been observed in conducting electron-doped BaTiO${}_3$ ($n$-BTO). The coexistence of a ferroelectric phase and conductivity opens the door to new functionalities that may provide a unique route for novel device applications. Using first-principles methods and electrostatic modeling, we explore the effect that the switchable polarization of $n$-BTO has on the electronic properties of the SrRuO${}_3$/$n$-BTO (001) interface. Ferroelectric polarization controls the accumulation or depletion of electron charge at the interface, and the associated bending of the $n$-BTO conduction band determines the transport regime across the interface. The interface exhibits a Schottky tunnel barrier for one polarization orientation, whereas an Ohmic contact is present for the opposite polarization orientation, leading to a large change in interface resistance associated with polarization reversal. Our calculations reveal a five orders of magnitude change in the interface resistance because of polarization switching.

We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite-temperature properties of quantum systems are derived without the need of statistical mechanic ensembles, but instead using typical properties of random pure states. We show that this formalism can be useful from a computational point of view when combined with tensor network algorithms. In particular, a recently introduced Monte Carlo algorithm is considered which samples matrix product states at random for the estimation of finite-temperature observables. Here we analytically justify the effectiveness of this algorithm, and we prove that sampling one single state is in principle sufficient to obtain a very good estimation of finite-temperature expectation values. These results provide a substantial computational improvement with respect to similar algorithms for one-dimensional quantum systems based on uniformly distributed pure states. The analytical calculations are numerically supported, simulating finite-temperature interacting spin systems of size up to 100 qubits.

Quantum vortex dynamics in Bose-Einstein condensates or superfluid helium can be informatively described by the Gross-Pitaevskii (GP) equation. Various approximate analytical formulas for a single stationary vortex are recalled and their shortcomings demonstrated. Significantly more accurate two-point [2/2] and [3/3] Padé approximants for stationary vortex profiles are presented. Two straight, singly quantized, antiparallel vortices, located at a distance $d_0$ apart, form a vortex dipole, which, in the GP model, can either annihilate $or$ propagate indefinitely as a “solitary wave.” We show, through calculations performed in a periodic domain, that the details and types of behavior displayed by vortex dipoles depend strongly on the initial conditions rather than only on the separation distance $d_0$ (as has been previously claimed). It is found, indeed, that the choice of the initial two-vortex profile (i.e., the modulus of the “effective wave function”), strongly affects the vortex trajectories and the time scale of the process: annihilation proceeds more rapidly when low-energy (or “relaxed”) initial profiles are imposed. The initial “circular” phase distribution contours, customarily obtained by multiplying an effective wave function for each individual vortex, can be generalized to explicit elliptical forms specified by two parameters; then by “tuning” the elliptical shape at fixed $d_0$, a sharp transition between solitary-wave propagation and annihilation is captured. Thereby, a “phase diagram” for this “AnSol” transition is constructed in the space of ellipticity and separation and various limiting forms of the boundary are discussed.

A one-dimensional time-reversal-symmetric topological superconductor (symmetry class DIII) features a single Kramers pair of Majorana bound states at each of its ends. These holographic quasiparticles are non-Abelian anyons that obey Ising-type braiding statistics. In the special case where an additional $U\left(1\right)$ spin rotation symmetry is present, this state can be understood as two copies of a Majorana wire in symmetry class $D$, one copy for each spin block. We present a manifestly gauge invariant construction of the topological invariant for the generic case, i.e., in the absence of any additional symmetries like spin rotation symmetry. Furthermore, we show how the presence of inversion symmetry simplifies the calculation of the topological invariant. The proposed scheme is suitable for the classification of both interacting and disordered systems and allows for a straightforward numerical evaluation of the invariant since it does not rely on fixing a continuous phase relation between Bloch functions. Finally, we apply our method to compute the topological phase diagram of a Rashba wire with competing $s$-wave and $p$-wave superconducting pairing terms.

Using small angle neutron scattering, the anisotropy of the magnetic vortex lattice (VL), in the heavily hole-doped pnictide superconductor ${\text{KFe}}_2{\text{As}}_2$, was studied. Well-ordered VL scattering patterns were measured with fields applied in directions between $\mathbf{B}\parallel \mathbf{c}$ and the basal plane, rotating either towards $\left[100\right]$ or $\left[110\right]$. Slightly distorted hexagonal patterns were observed when $\mathbf{B}\parallel \mathbf{c}$. However, the scattering pattern distorted more strongly as the field was rotated away from the c axis. At low field, the arrangement of vortices is affected by the anisotropy of penetration depth in the plane perpendicular to the field. By fitting the distortion with the anisotropic London model, we obtain an estimate of $\sim$$3.4$ for the anisotropy factor $\gamma$ between the in-plane and c-axis penetration depths at the lowest temperature studied. The results further reveal VL phase transitions as a function of field direction. We discuss these transitions using the “hairy ball” theorem.

We investigated the Abrikosov vortex lattice (VL) of a pure niobium single crystal with the muon spin rotation ($\mu$SR) technique. Analysis of the $\mu$SR data in the framework of the BCS-Gor'kov theory allowed us to determine microscopic parameters and the limitations of the theory. With decreasing temperature the field variation around the vortex cores deviates substantially from the predictions of the Ginzburg-Landau theory and adopts a pronounced conical shape. This is evidence of partial diffraction of Cooper pairs on the VL predicted by Delrieu for clean superconductors.

Utilizing a modified embedded atom method potential, we performed large-scale classical molecular dynamics simulations (with up to 50 million atoms) to investigate the response of Ga single crystals to shock compression along the three major orientations of the orthorhombic A11 ground state, i.e., $\left[001\right]$, $\left[010\right]$, and $\left[100\right]$. For weak shocks with particle velocity $u_p<30$0 m/s, these defect-free single crystals respond elastically, but for stronger shocks, they undergo a structural phase transformation and then (for even stronger shocks) melt. For intermediate shock strengths ($300\text{m/s}<u_p<1.2$ km/s) a split shock wave is formed, with an elastic precursor (uniaxial compression wave) leading the slower transformation wave. The transformed region consists of a mixed phase, with stripes of the product phase embedded into the uniaxially compressed parent phase, with the ratio of product to parent phase increasing with increasing shock strength, much like in martensitic phase transformations. Upon shock release from the free surface at the end of the sample, the transformation is reversed, leaving only some defects behind, which makes it difficult to experimentally investigate the structural transformation in shock-recovered samples. We investigated the structure produced by the shock and found it to be similar to the $\beta$ phase of Ga which is obtained by supercooling from the liquid state. However, the product phase shows only half the period along $\left[100\right]$ in the calculated diffraction pattern. Further investigation showed that this is due to a different stacking sequence in this direction, namely ABCD instead of AB for the $\beta$ phase.

Inspired by a recent pressure experiment in fcc Ni, we propose a simple method to use pressure to investigate the laser-induced femtosecond magnetism. Since the pressure effect on the electronic and magnetic properties can be well controlled experimentally, this leaves little room for ambiguity when compared with theory. Here we report our theoretical pressure results in fcc Ni: Pressure first suppresses the spin moment reduction and then completely diminishes it; further increase in pressure to 40 GPa induces a demagnetization-to-magnetization transition. To reveal its microscopic origin, we slide through the $L$-$U$ line in the Brillouin zone and find two essential transitions are responsible for this change, where the pressure lowers two valence bands, resulting in an off-resonant excitation and thus a smaller spin moment reduction. In the spin-richest $L$-$W$-$W^{\prime }$ plane, two spin contours are formed; as pressure increases, the contour size retrieves and its intensity is reduced to zero eventually, fully consistent with the spin-dipole factor prediction. These striking features are detectable in time- and spin-resolved photoemission experiments.

We report neutron-scattering data and DFT calculations of the stoichiometric iron-arsenide superconductor Sr${}_2$VO${}_3$FeAs. Rietveld refinements of neutron powder patterns confirm the ideal composition without oxygen deficiencies. Experiments with polarized neutrons prove weak magnetic ordering in the V sublattice of Sr${}_2$VO${}_3$FeAs at $\approx$ 45 K with a probable propagation vector q $=$ ($\frac{1}{8},\frac{1}{8}$,0). The ordered moment of $\approx$ 0.1 ${\mu }_{\mathrm{B}}$ is too small to remove the V 3$d$ bands from the Fermi level by magnetic exchange splitting and much smaller than predicted from a recent $\mathrm{LDA}+U$ study. By using DFT calculations with a GGA+EECE functional we find the typical quasinested Fermi surface even without magnetic moment. From this we conclude that the V atoms are in a Mott state, where the electronic correlations are dominated by on-site Coulomb repulsion which shifts the V 3$d$ states away from the Fermi energy. Our results are consistent with photoemission data and explain comprehensively why Sr${}_2$VO${}_3$FeAs is a typical iron-arsenide superconductor in spite of the partially filled V 3$d$ shell.

We demonstrate the importance of the Kondo effect in artificially created $f$-electron superlattices. We show that the Kondo effect does not only change the density of states of the $f$-electron layers, but is also the cause of pronounced resonances at the Fermi energy in the density of states of the noninteracting layers in the superlattice, which are between the $f$-electron layers. Remarkably, these resonances strongly depend on the structure of the superlattice; due to interference, the density of states at the Fermi energy can be strongly enhanced or even shows no changes at all. Furthermore, we show that by inserting the Kondo lattice layer into a three-dimensional metal, the gap of the Kondo insulating state changes from a full gap to a pseudogap with quadratically vanishing spectral weight around the Fermi energy. Due to the formation of the Kondo insulating state in the $f$-electron layer, the superlattice becomes strongly anisotropic below the Kondo temperature. We prove this by calculating the in-plane and the out-of-plane conductivity of the superlattice.

We present an ab initio density functional theory study of the dominant defects in hydrogenated amorphous silicon nitrides covering different stoichiometries, the influence of hydrogen, and the influence of the annealing history. Whereas nitrogen (N) lone pair states dominate the valence band edge in stoichiometric a-Si${}_3$N${}_4$, we find that K defects, threefold coordinated silicon (Si) atoms, and Si-Si bond-related states dominate electronic defect contributions in the gap for N-deficient a-Si${}_3$N${}_{4-x}$. Hydrogen saturates the dangling Si bonds, significantly reducing the number of electronic defects related to undercoordinated Si atoms.

The interface between polar perovskite LaCrO${}_3$ and nonpolar SrTiO${}_3$(001) grown by molecular beam epitaxy is examined using a combination of electron microscopy, spectroscopy, and Rutherford backscattering spectrometry. The $A$-site cations of these $AB$O${}_3$ perovskites are found to diffuse across the interface to a greater extent than the $B$-site cations, based on high-angle annular dark-field scanning transmission electron microscopy, energy-dispersive x-ray spectroscopy, and electron-energy-loss spectroscopy (EELS). The $B$-site cation valences are shown to be partially reduced near the interface by analysis of EELS near-edge structures. The location and direction of these electronic modifications do not intuitively compensate the charge imbalance imposed by uneven cation interdiffusion, and yet both the film and interface are insulating. These results highlight the importance of considering both the physical and electronic structure of such complex interfaces in determining their characteristics.

We present a nonperturbative calculation of indirect exchange interaction between two paramagnetic impurities via two-dimensional (2D) free carriers gas separated by a tunnel barrier. The method takes into account the impurity attractive potential which can form a bound state. The calculations show that if the bound impurity state energy lies within the energy range occupied by the free 2D carriers the indirect exchange interaction is strongly enhanced due to resonant tunneling and exceeds by a few orders of magnitude what one would expect from the conventional Ruderman-Kittel-Kasuya-Yosida approach.

In recent times, trilayer graphene has attracted wide attention owing to its stacking and electric-field-dependent electronic properties. However, a direct and well-resolved experimental visualization of its band structure has not yet been reported. In this paper, we present angle-resolved photoemission spectroscopy data which show with high resolution the electronic band structure of trilayer graphene obtained on α-SiC(0001) and β-SiC(111) via hydrogen intercalation. Electronic bands obtained from tight-binding calculations are fitted to the experimental data to extract the interatomic hopping parameters for Bernal and rhombohedral stacked trilayers. Low-energy electron microscopy measurements demonstrate that the trilayer domains extend over areas of tens of square micrometers, suggesting the feasibility of exploiting this material in electronic and photonic devices. Furthermore, our results suggest that, on SiC substrates, the occurrence of a rhombohedral stacked trilayer is significantly higher than in natural bulk graphite.

Recent theoretical papers have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role in obtaining a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagome-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.

The experimental demonstration of the spin Hall effect in a high mobility two-dimensional electron system is reported. The spatial dependence is studied by Kerr rotation as a function of the external magnetic field using an applied electric field amplitude and direction as control parameters. We observe that the effect is robust in a bilayer structure with a nonzero Rashba coefficient displayed by an electrically controllable internal magnetic field, a large spin Hall conductivity in the range of the universal intrinsic value, and a mobility-enhanced spin diffusion constant. With the application of an unidirectional electric field, the role of the spin drift was also studied. The data was analyzed following both phenomenological and microscopic approaches and compared with experimental references in a single-layer configuration.

We report measurements of the spatial dependence of the electron energy distribution in carbon nanotubes, from which electron interactions are determined. Using nonequilibrium tunneling spectroscopy with multiple superconducting probes, we characterize electron transport as ballistic or diffusive, and interactions as elastic or inelastic. We find that transport in nanotubes is generally diffusive, caused by elastic scattering from a few defects. However, local inelastic scattering can be tuned “on” or “off” with a gate voltage.

Effects of the Verwey transition on the (100) surface of magnetite were studied using scanning tunneling microscopy and spin polarized low-energy electron microscopy. On cooling through the transition temperature $T_{\mathrm{V}}$, the initially flat surface undergoes a rooflike distortion with a periodicity of $\sim 0.5$ $\mu$m due to ferroelastic twinning within monoclinic domains of the low-temperature monoclinic structure. The monoclinic $c$ axis orients in the surface plane, along the ${\left[001\right]}_c$ directions. At the atomic scale, the charge-ordered ($\sqrt{2}\times \sqrt{2}$)$R{45}^{\circ }$ reconstruction of the (100) surface is unperturbed by the bulk transition, and is continuous over the twin boundaries. Time resolved low-energy electron microscopy movies reveal the structural transition to be first order at the surface, indicating that the bulk transition is not an extension of the Verwey-like ($\sqrt{2}\times \sqrt{2}$)$R{45}^{\circ }$ reconstruction. Although conceptually similar, the charge-ordered phases of the (100) surface and sub-$T_{\mathrm{V}}$ bulk of magnetite are unrelated phenomena.