Diffusion and relaxation of defects in bulk systems is a complex process that can only be accessed directly through simulations. We characterize the mechanisms of low-temperature aging in self-implanted crystalline silicon, a model system used extensively to characterize both amorphization and return to equilibrium processes, over 11 orders of magnitudes in time, from 10 ps to 1 s, using a combination of molecular dynamics and kinetic activation-relaxation technique simulations. These simulations allow us to reassess the atomistic mechanisms responsible for structural relaxations and for the overall logarithmic relaxation, a process observed in a large number of disordered systems and observed here over the whole simulation range. This allows us to identify three microscopic regimes, annihilation, aggregation, and reconstruction, in the evolution of defects and to propose atomistic justification for an analytical model of logarithmic relaxation. Furthermore, we show that growing activation barriers and configurational space exploration are kinetically limiting the system to a logarithmic relaxation. Overall, our long-time simulations do not support the amorphous cluster model but point rather to a relaxation driven by elastic interactions between defect complexes of all sizes.

Zero-energy Majorana fermion states (Majoranas) can arise at the ends of a semiconducting wire in proximity with a superconductor. A first generation of experiments has detected a zero bias conductance peak in these systems that strongly suggests these Majoranas do exist; however, a definitive demonstration of the long-ranged entanglement that is crucial for potential applications in quantum computing has yet to be carried out. This work discusses two possible measurement schemes to detect this long-ranged entanglement in a wire system with two coupled pairs of Majoranas, by varying the coupling between one pair while measuring the fermion parity of the second pair. First, in a system with two coupled pairs of Majoranas, we discuss how varying the coupling of one pair in time, while measuring temporal fermion parity correlations of the second pair, allows for an experimental probe of long-ranged Majorana entanglement. Second, we show that the power spectrum of the charge noise (fermion parity noise) of one pair contains signatures of these correlations, as well as allowing one to infer the parity relaxation rate.

We study the phase diagrams of a family of three-dimensional Walker-Wang–type lattice models, which are not topologically ordered but have deconfined anyonic excitations confined to their surfaces. We add a perturbation (analogous to that which drives the confining transition in ${\mathbb{Z}}_p$ lattice gauge theories) to the Walker-Wang Hamiltonians, driving a transition in which all or some of the variables associated with the loop-gas or string-net ground states of these models become confined. We show that in many cases the location and nature of the phase transitions involved is exactly that of a generalized ${\mathbb{Z}}_p$ lattice gauge theory, and use this to deduce the basic structure of the phase diagram. We further show that the relationship between the phases on opposite sides of the transition is fundamentally different than in conventional gauge theories: in the Walker-Wang case, the number of species of excitations that are deconfined in the bulk can increase across a transition that confines only some of the species of loops or string nets. The analog of the confining transition in the Walker-Wang models can therefore lead to bulk deconfinement and topological order.

Motivated by the remarkable experimental realizations of $f$-electron superlattices, e.g., CeIn${}_3$/LaIn${}_3$ and CeCoIn${}_5$/YbCoIn${}_5$ superlattices, we analyze the formation of heavy electrons in layered $f$-electron superlattices by means of the dynamical mean field theory. We show that the spectral function exhibits formation of heavy electrons in the entire system below a temperature scale $T_0$. However, in terms of transport, two different coherence temperatures $T_x$ and $T_z$ are identified in the in-plane and the out-of-plane resistivity, respectively. Remarkably, we find $T_z<T_x\sim T_0$ due to scatterings between different reduced Brillouin zones. The existence of these two distinct energy scales implies a crossover in the dimensionality of the heavy electrons between two and three dimensions as temperature or layer geometry is tuned. This dimensional crossover would be responsible for the characteristic behaviors in the magnetic and superconducting properties observed in the experiments.

We study the ferromagnet/semiconductor contacts formed by transition metal dichalcogenide monolayers, focusing on semiconducting MoS${}_2$ and WS${}_2$ and ferromagnetic VS${}_2$. We investigate the degree of $p$-type doping and demonstrate tuning of the Schottky barrier height by vertical compressive pressure. An analytical model is presented for the barrier heights that accurately describes the numerical findings and is expected to be of general validity for all transition metal dichalcogenide metal/semiconductor contacts. Furthermore, magnetic proximity effects induce a 100% spin polarization at the Fermi level in the semiconductor where the spin splitting increases up to 0.70 eV for increasing pressure.

We calculate the friction of fully mobile graphene flakes sliding on graphite. For incommensurately stacked flakes, we find a sudden and reversible increase in friction with load, in agreement with experimental observations. The transition from smooth sliding to stick-slip and the corresponding increase in friction is neither due to rotations to commensurate contact nor to dislocations but to a pinning caused by vertical distortions of edge atoms also when they are saturated by hydrogen. This behavior should apply to all layered materials with strong in-plane bonding.

According to the classification using projective representations of the SO(3) group, there exist two topologically distinct gapped phases in spin-1 chains. The symmetry-protected topological (SPT) phase possesses half-integer projective representations of the SO(3) group, while the trivial phase possesses integer linear representations. In the present work, we implement non-Abelian symmetries in the density matrix renormalization group (DMRG) method, allowing us to keep track of (and also control) the virtual bond representations and to readily distinguish the SPT phase from the trivial one by evaluating the multiplet entanglement spectrum. In particular, using the entropies $S^I$ ($S^H$) of integer (half-integer) representations, we can define an entanglement gap $G=S^I-S^H$, which equals 1 in the SPT phase, and $-1$ in the trivial phase. As an application of our proposal, we study the spin-1 models on various one-dimensional (1D) and quasi-1D lattices, including the bilinear-biquadratic model on a single chain, and the Heisenberg model on a two-leg ladder and a three-leg tube. Among others, we confirm the existence of a SPT phase in the spin-1 tube model and reveal that the phase transition between the SPT and the trivial phase is a continuous one. The transition point is found to be critical, with conformal central charge $c=3$ determined by fits to the block entanglement entropy.

A 3D topological insulator thin film in contact with magnetic layers exhibits exotic and intriguing magneto-optical and magnetoelectric phenomena, but little is known beyond the linear response regime. We demonstrate that two electric fields parallel to the surface of the film induce an ac perpendicular polarization, whereas a static polarization can be induced by one circularly polarized electromagnetic wave. These phenomena are determined by the second-order susceptibility, which remarkably also controls the anomalous Hall current of the surface. The anomalous Hall current is strongly modulated by an ac perpendicular electric field in resonance with the quantum transitions between the gapped Dirac surface states. If the modulation frequency is low, the anomalous Hall effect is topologically protected, and the nonlinear response vanishes.

We investigate the fate of interaction-driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest- and next-nearest-neighbor interactions. We find evidence for a charge density wave phase, a Kekulé bond order, and a sublattice charge-modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction-driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground-state degeneracy and by calculating charge-order and bond-order correlation functions.

Defect formation in the one-dimensional topological three-band model, spanned by the generators of SU(2) and containing a central flat band, is examined within both lattice and continuum theories. Classic results of Jackiw-Rebbi and Rice-Mele for the soliton charge are generalized. The charge is twice the value obtained for the two-band case with the corresponding parameters. A sudden jump in the soliton charge from zero to one as the soliton state passes through the central flat band is predicted, and confirmed by numerical calculation on a lattice model. The quantum field-theoretical calculation of Goldstone and Wilczek is generalized as well, to obtain the same soliton charge. The diamond-chain lattice is argued to be an ideal structure to host a topological three-band we examine.

We study cooperative effects in energy transfer (ET) from an ensemble of donors to an acceptor near a plasmonic nanostructure. We demonstrate that, in the cooperative regime, ET takes place from plasmonic super-radiant and subradiant states rather than from individual donors leading to a significant increase in ET efficiency. The cooperative amplification of the ET relies on the large coupling of superradiant states to external fields and on the slow decay rate of subradiant states. We show that superradiant and subradiant ET mechanisms are efficient in different energy domains and, therefore, can be utilized independently. We present numerical results demonstrating the amplification effect for a layer of donors and an acceptor on a spherical plasmonic nanoparticle.

Chemically and mechanically exfoliated MoS${}_2$ single-layer samples have substantially different properties. While mechanically exfoliated single-layers are monophase(1H polytype with Mo in trigonal prismatic coordination), the chemically exfoliated samples show coexistence of three different phases, 1H, 1T (Mo in octahedral coordination), and 1T${}^{\prime }$ (a distorted $2\times 1$ 1T superstructure). By using first-principles calculations, we investigate the energetics and the dynamical stability of the three phases. We show that the 1H phase is the most stable one, while the metallic 1T phase, strongly unstable, undergoes a phase transition towards a metastable and insulating 1T${}^{\prime }$ structure composed of separated zigzag chains. We calculate electronic structure, phonon dispersion, Raman frequencies, and intensities for the 1T${}^{\prime }$ structure. We provide a microscopical description of the $J_1$, $J_2$, and $J_3$ Raman features that were first detected more than 20 years ago but have remained unexplained up to now. Finally, we show that H adsorbates, which are naturally present at the end of the chemical exfoliation process, stabilize the 1T${}^{\prime }$ over the 1H one.

The thermodynamic properties of the electron gas in multilayer graphene depend strongly on the number of layers and the type of stacking. Here we analyze how those properties change when we vary the number of layers for rhombohedral stacked multilayer graphene and compare our results with those from a conventional two-dimensional electron gas. We show that the highly degenerate zero-energy Landau level which is partly filled with electrons and partly with holes has a strong influence on the values of the different thermodynamic quantities.

We analyze the production of defects during the dynamical crossing of a mean-field phase transition with a real order parameter. When the parameter that brings the system across the critical point changes in time according to a power-law schedule, we recover the predictions dictated by the well-known Kibble-Zurek theory. For a fixed duration of the evolution, we show that the average number of defects can be drastically reduced for a very large but finite system, by optimizing the time dependence of the driving using optimal control techniques. Furthermore, the optimized protocol is robust against small fluctuations.

We demonstrate evidence of coherent magnetic flux tunneling through superconducting nanowires patterned in a thin highly disordered NbN film. The phenomenon is revealed as a superposition of flux states in a fully metallic superconducting loop with the nanowire acting as an effective tunnel barrier for the magnetic flux, and reproducibly observed in different wires. The flux superposition achieved in the fully metallic NbN rings proves the universality of the phenomenon previously reported for ${\mathrm{InO}}_x$. We perform microwave spectroscopy and study the tunneling amplitude as a function of the wire width, compare the experimental results with theories, and estimate the parameters for existing theoretical models.

A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in implicit form, an analytic procedure is derived to obtain the transformed dispersion relation. It is shown that the dispersion relation is generally shifted in the complex $(k,\omega )$ plane, with $k$ the wave number and $\omega$ the angular frequency. The value of the shift is obtained explicitly as a function of the perturbation of material constants accounting for loss. The method is shown to predict correctly the transformation of the complex band structure $k\left(\omega \right)$. Several models of the dispersion relation near a symmetry point of the Brillouin zone are analyzed. A lower bound for the group velocity, related to the local shape of the band around symmetry points, is derived for each case.

A topological phase can often be represented by a corresponding wave function (exact eigenstate of a model Hamiltonian) that has a higher underlying symmetry than necessary. When the symmetry is explicitly broken in the Hamiltonian, the model wave function fails to account for the change due to the lack of a variational parameter. Here we exemplify the case by an integer quantum Hall system with anisotropic interaction. We show that the single-mode approximation can introduce a variational parameter for a better description of the ground state, which is consistent with the recently proposed geometric description of the quantum Hall phases.

The intersection of two ferromagnetic domain walls placed on the surface of topological insulators provides a one-way beam splitter for domain-wall Dirac fermions. Based on an analytic expression for a static two-soliton magnetic texture we perform a systematic numerical study of the propagation of Dirac wave packets along such intersections. A single-cone staggered-grid finite difference lattice scheme is employed in the numerical analysis. It is shown that the angle of intersection plays a decisive role in determining the splitting ratio of the fermion beam. For a nonrectangular intersection, the width and, to a lesser extent, the type of domain walls, e.g., Bloch or Néel, determine the properties of the splitter. As the ratio between domain-wall width and transverse localization length of the Dirac fermion is increased its propagation behavior changes from quantum-mechanical (wavelike) to classical ballistic (particlelike). An electric gate placed near the intersection offers a dynamic external control knob for adjusting the splitting ratio.

We study silicene on hexagonal boron nitride, using first-principles calculations. Since hexagonal boron nitride is semiconducting, the interaction with silicene is weaker than for metallic substrates. It therefore is possible to open a 50 meV band gap in the silicene. We further address the effect of Mn decoration by determining the onsite Hubbard interaction parameter, which turns out to differ significantly for decoration at the top and hollow sites. The induced magnetism in the system is analyzed in detail.