The origin of the large-scale stripe pattern of epitaxial silicene on the ${\mathrm{ZrB}}_2$(0001) surface observed by scanning tunneling microscopy experiments is revealed by first-principles calculations. Without stripes, the ($\sqrt{3}\times \sqrt{3}$)-reconstructed, one-atom-thick Si layer is found to exhibit a “zero-frequency” phonon instability at the $M$ point. In order to avoid a divergent response, the relevant phonon mode triggers the spontaneous formation of a new phase with a particular stripe pattern offering a way to lower both the atomic surface density and the total energy of silicene on the particular substrate. The observed mechanism is a way for the system to handle epitaxial strain and may therefore be more common in two-dimensional epitaxial materials exhibiting a small lattice mismatch with the substrate.

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this $\mathbf{K}\text{−}\mathbf{b}\text{−}\mathbf{t}$ rule, the lattice topology, represented by dislocation lines oriented in direction $\mathbf{t}$ with Burgers vector $\mathbf{b}$, combines with the electronic-band topology, characterized by the band-inversion momentum ${\mathbf{K}}_{\mathrm{inv}}$, to produce gapless propagating modes when the plane orthogonal to the dislocation line features a band inversion with a nontrivial ensuing flux $\Phi ={\mathbf{K}}_{\mathrm{inv}}·\mathbf{b}\left(\mathrm{mod}2\pi \right)$. Although it has already been discovered by Ran et al. [Nat. Phys. 5, 298 (2009)] that dislocation lines host propagating modes, the exact mechanism of their appearance in conjunction with the crystal symmetries of a topological state is provided by the $\mathbf{K}\text{−}\mathbf{b}\text{−}\mathbf{t}$ rule. Finally, we discuss possible experimentally consequential examples in which the modes are oblivious to the direction of propagation, such as the recently proposed topologically insulating state in electron-doped ${\mathrm{BaBiO}}_3$.

Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012)]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.

Motivated by the recent atomic-scale scanning tunneling microscope (STM) observation for a spatially localized in-gap state in an electron doped Mott insulator, we evaluate the local electronic state of the Hubbard model on the square lattice using the cluster perturbation theory. An in-gap state is found to exist below the upper Hubbard band around the dopant lattice site, which is consistent with the STM measurements. The emergence of this local in-gap state is accompanied with a rapid reduction of the double occupancy of electrons. A similar in-gap state is also found to exist on the triangular lattice. These results suggest that the in-gap state is an inherent feature of Mott insulators independent of the lattice structure.

Unusual transport properties deviating from the Fermi liquid are observed in ruthenates near a magnetic quantum-critical point (QCP). To understand the electronic properties of the ruthenates near and away from an antiferromagnetic (AF) QCP, I study the electronic structure and magnetic and transport properties for the $t_{2g}$-orbital Hubbard model on a square lattice in fluctuation-exchange approximation including Maki-Thompson (MT) current vertex correction (CVC). The results away from the AF QCP reproduce several experimental results of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ qualitatively and provide new mechanisms about the enhancement of spin fluctuation at ${\mathit{Q}}_{\mathrm{IC}\text{−}\mathrm{AF}}\approx (0.66\pi ,0.66\pi )$, larger mass enhancement of the $d_{xy}$ orbital than that of the $d_{xz/yz}$ orbital, and nonmonotonic temperature dependence of the Hall coefficient. Also, the results near the AF QCP explain the $T$-linear inplane resistivity in ${\mathrm{Sr}}_2{\mathrm{Ru}}_{0.075}{\mathrm{Ti}}_{0.025}{\mathrm{O}}_4$ and give an experimental test on the obtained temperature dependence of the Hall coefficient. I reveal spatial correlation including the self-energy of electrons beyond mean-field approximations is essential to determine the electronic properties of the ruthenates. I also show several ubiquitous transport properties near an AF QCP and characteristic transport properties of a multiorbital system by comparison with results of a single-orbital system near an AF QCP.

Electronic dispersion and density of states (DOS) have been calculated for the Hubbard model and the $t-J$ and $t-J^{*}$ models with three-site correlated hopping by the cluster perturbation theory. We have found a rather strong quantitative difference both in dispersion and DOS at all doping for the Hubbard and $t-J$ models at the energy scale $\omega \gtrsim t$. The three-site correlated hopping addition results in an almost negligible difference for the Hubbard and $t-J^{*}$ models. Close to the Fermi energy, at the scale $\omega \lesssim J$, the electronic structure of all three models is similar. We have found the line of zeros of the Green function for the $t-J$ model that has been previously obtained for the Hubbard model by cellular dynamical mean-field theory calculations.

Using first-principle calculations, we examine the sequence of phases in electron-doped dichalcogenides, such as recently realized in field-gated ${\mathrm{MoS}}_2$. Upon increasing the electron-doping level, we observe a succession of semiconducting, metallic, superconducting, and charge density wave regimes, i.e., in different order compared to the phase diagram of metallic dichalcogenides, such as ${\mathrm{TiSe}}_2$. Both instabilities trace back to a softening of phonons, which couple the electron populated conduction band minima. The superconducting dome, calculated using Eliashberg theory, is found to fit the experimentally observed phase diagram, obtained from resistivity measurements. The charge density wave phase at higher electron doping concentrations as predicted from instabilities in the phonon modes is further corroborated by detecting the accompanying lattice deformation in density-functional-based supercell relaxations. Upon charge density wave formation, doped ${\mathrm{MoS}}_2$ remains metallic but undergoes a Lifschitz transition, where the number of Fermi pockets is reduced.

We study the interplay between quantum Hall ordering and spontaneous sublattice symmetry breaking in multiple-Chern-number bands at fractional fillings. Primarily, we study fermions with repulsive interactions near half filling in a family of square lattice models with flat $C=2$ bands and a wide band gap. By perturbing about the particularly transparent limit of two decoupled $C=1$ bands and by exact diagonalization studies of small systems in the more general case, we show that the system generically breaks sublattice symmetry with a transition temperature $T_c>0$ and additionally exhibits a quantized Hall conductance of $e^2/h$ as $T\to 0$. We note the close analogy to quantum Hall ferromagnetism in the multicomponent problem and the connection to topological Mott insulators. We also discuss generalizations to other fillings and higher Chern numbers.

We present analytical and numerical results that demonstrate the presence of anomalous entanglement behavior on the Dirac Billiards. We investigate the statistical distribution of the characteristic entangled measures, focusing on the mean, on the variance, and on the quantum interference terms. We show a quite distinct behavior of the Dirac billiard compared with the nonrelativist (Schrödinger) ones. Particularly, we show a very plausible Bell state and a sharp amplitude of quantum interference term on entangled electrons left from the Dirac billiards. The results have remarkable relevance to the novel quantum dots build of materials like graphene or topological insulators.

We report on the fractional quantum Hall states of germanene and silicene where one expects a strong spin-orbit interaction. This interaction causes an enhancement of the electron-electron interaction strength in one of the Landau levels corresponding to the valence band of the system. This enhancement manifests itself as an increase of the fractional quantum Hall effect gaps compared to that in graphene and is due to the spin-orbit induced coupling of the Landau levels of the conduction and valence bands, which modifies the corresponding wave functions and the interaction within a single level. Due to the buckled structure, a perpendicular electric field lifts the valley degeneracy and strongly modifies the interaction effects within a single Landau level: in one valley the perpendicular electric field enhances the interaction strength in the conduction band Landau level, while in another valley, the electric field strongly suppresses the interaction effects.

We have extended an effective medium approximation theory [Fishchuk, Kadashchuk, Genoe, Ullah, Sitter, Singh, Sariciftci, and Bässler, Phys. Rev. B 81, 045202 (2010)] to investigate how polaron formation affects the Meyer-Neldel (MN) compensation behavior observed for temperature-dependent charge-carrier transport in disordered organic semiconductors at large carrier concentrations, as realized in organic field-effect transistors (OFETs). We show that the compensation behavior in organic semiconductor thin films can be consistently described for both nonpolaronic and polaronic hopping transport in the framework of the disorder formalism using either Miller-Abrahams or polaron Marcus rates, respectively, provided that the polaron binding energy is small compared to the width of the density of states (DOS) distribution in the system. We argue that alternative models based on thermodynamic reasoning, like the multiexcitation entropy (MEE) model, which assumes charge transport dominated by polarons with multiphonon processes and ignores the energy disorder, are inherently not applicable to describe adequately the charge-carrier transport in disordered organic semiconductors. We have suggested and realized a test experiment based on measurements of the compensation behavior for the temperature-dependent conductivity and mobility in OFET devices to check the applicability of these models. We point out that the MN behavior observed in thin-film OFETs has nothing to do with the genuine MN rule predicted by the MEE approach, but rather it is an apparent effect arising as a consequence of the functional dependence of the partial filling of the DOS in a disordered system with hopping transport. This fact is fully supported by experimental results. The apparent MN energy was found to depend also on the shape of the DOS distribution and polaron binding energy.

We propose a simple microscopic model to numerically investigate the stability of a two-dimensional fractional topological insulator (FTI). The simplest example of an FTI consists of two decoupled copies of a Laughlin state with opposite chiralities, or double-semion phase. We focus on bosons at half filling. We study the stability of the FTI phase upon addition of two coupling terms of different nature: an interspin interaction term, and an inversion-symmetry-breaking term that couples the copies at the single-particle level. Using exact-diagonalization and entanglement spectra, we numerically show that the FTI phase is stable against both perturbations. We compare our system to a similar bilayer fractional Chern insulator. We show evidence that the time-reversal-invariant system survives the introduction of interaction coupling on a larger scale than the time-reversal-symmetry-breaking one, stressing the importance of time-reversal symmetry in the FTI phase stability. We also discuss possible fractional phases beyond $\nu =1/2$.

The ultimate limitations on carrier mobilities in metal dichalcogenides, and the dynamics associated with carrier relaxation, are unclear. We present measurements of the frequency-dependent conductivity of multilayer dichalcogenide ${\mathrm{MoS}}_2$ by optical-pump terahertz-probe spectroscopy. We find mobilities in this material approaching 4200 ${\mathrm{cm}}^2$ ${\mathrm{V}}^{-1}$ ${\mathrm{s}}^{-1}$ at low temperatures. The temperature dependence of scattering indicates that the mobility, an order of magnitude larger than previously reported for ${\mathrm{MoS}}_2$, is intrinsically limited by acoustic phonon scattering at THz frequencies. Our measurements of carrier relaxation reveal picosecond cooling times followed by recombination lasting tens of nanoseconds and dominated by Auger scattering into defects. Our results provide a useful context in which to understand and evaluate the performance of ${\mathrm{MoS}}_2$-based electronic and optoelectronic devices.

We propose a fast method to determine the local curvature in two-dimensional (2D) systems with arbitrary shape. The curvature information, combined with elastic constants obtained for a planar system, provides an accurate estimate of the local stability in the framework of continuum elasticity theory. Relative stabilities of graphitic structures including fullerenes, nanotubes, and schwarzites, as well as phosphorene nanotubes, calculated using this approach, agree closely with ab initio density functional calculations. The continuum elasticity approach can be applied to all 2D structures and is particularly attractive in complex systems with known structure, where the quality of parameterized force fields has not been established.

We investigate the finite-size scaling behavior of the conductivity in a two-dimensional Dirac electron gas within a chiral sigma model. Based on the fact that the conductivity is a function of system size times scattering rate, we obtain a two-parameter scaling flow toward a finite fixed point. The latter is the minimal conductivity of the infinite system. Depending on boundary conditions, we also observe unstable fixed points with conductivities much larger than the experimentally observed values, which may account for results found in some numerical simulations. By including a spectral gap we extend our scaling approach to describe a metal-insulator transition.

We report on the direct observation of a large unusual antiferromagnetic exchange interaction in Fe(001) films. By measuring the magnon dispersion relation over the entire Brillouin zone of an ultrathin Fe(001) film on Rh(001), we demonstrate that the signature of this unusual antiferromagnetic exchange interaction can be observed at the high-symmetry $\overline{\mathrm{M}}$ point. The exchange parameters are quantified by comparing the measured magnon dispersion relation with the results of our first-principles calculations. We suggest a way of examining the existence of an antiferromagnetic exchange interaction in layered magnetic structures and also a way of quantifying its strength.

Crystallization of amorphous ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ (GST) has been studied using four extensive (460 atoms, up to 4 ns) density functional/molecular dynamics simulations at 600 K. This phase change material is a rare system where crystallization can be simulated without adjustable parameters over the physical time scale, and the results could provide insight into order-disorder processes in general. Crystallization is accompanied by an increase in the number of $ABAB$ squares $(A:\text{Ge},\text{Sb};B:\text{Te})$, percolation, and the occurrence of low-frequency localized vibration modes. A sample with a history of order crystallizes completely in 1.2 ns, but ordering in others was less complete, even after 4 ns. The amorphous starting structures without memory display phases $(>1\text{ns})$ with subcritical nuclei (10–50 atoms) ranging from nearly cubical blocks to stringlike configurations of $ABAB$ squares and $AB$ bonds extending across the cell. Percolation initiates the rapid phase of crystallization and is coupled to the directional $p$-type bonding in metastable GST. Cavities play a crucial role, and the final ordered structure is distorted rock salt with a face-centered cubic sublattice containing predominantly Te atoms. We comment on earlier models based on smaller and much shorter simulations.

We report the nonequilibrium behavior of disordered superconducting Al films in high Zeeman fields. We have measured the tunneling density of states of the films through the first-order Zeeman critical field transition. We find that films with sheet resistances of a few hundred ohms exhibit large avalanchelike collapses of the condensate on the superheating branch of the critical field hysteresis loop. In contrast, the transition back into the superconducting phase (i.e., along the supercooling branch) is always continuous. The fact that the condensate follows an unstable trajectory to the normal state suggests that the order parameter in the hysteretic regime is not homogeneous.