In this paper, we provide analytical counting rules for the ground states and the quasiholes of fractional Chern insulators with an arbitrary Chern number. We first construct pseudopotential Hamiltonians for fractional Chern insulators. We achieve this by mapping the lattice problem to the lowest Landau level of a multicomponent continuum quantum Hall system with specially engineered boundary conditions. We then analyze the thin-torus limit of the pseudopotential Hamiltonians, and extract counting rules (generalized Pauli principles, or Haldane statistics) for the degeneracy of its zero modes in each Bloch momentum sector.

The ground state of translationally invariant insulators comprises bands which can assume topologically distinct structures. There are few known examples where this distinction is enforced by a point-group symmetry alone. In this paper we show that 1D and 2D insulators with the simplest point-group symmetry, inversion, have a ${\mathbb{Z}}^{\ge }$ classification. In 2D, we identify a relative winding number that is solely protected by inversion symmetry. By analysis of Berry phases, we show that this invariant has similarities with the first Chern class (of time-reversal breaking insulators), but is more closely analogous to the ${\mathbb{Z}}_2$ invariant (of time-reversal invariant insulators). Implications of our work are discussed in holonomy, the geometric-phase theory of polarization, the theory of maximally localized Wannier functions, and in the entanglement spectrum.

There are a large number of atomically thin graphitic films with a structure similar to that of graphene. These films have a spread of band gaps relating to their ionicity and, also, to the substrate on which they are grown. Such films could have a range of applications in digital electronics, where graphene is difficult to use. I use the dynamical cluster approximation to show how electron-phonon coupling between film and substrate can enhance these gaps in a way that depends on the range and strength of the coupling. It is found that one of the driving factors in this effect is a charge density wave instability for electrons on a honeycomb lattice that can open a gap in monolayer graphene. The enhancement at intermediate coupling is sufficiently large that spatially varying substrates and superstrates could be used to create heterostructures in thin graphitic films with position-dependent electron-phonon coupling and gaps, leading to advanced electronic components.

We study the collective excitations and inelastic light-scattering cross section of an electron gas confined in a GaAs/AlGaAs coaxial quantum well. These systems can be engineered in a core-multishell nanowire and inherit the hexagonal symmetry of the underlying nanowire substrate. As a result, the electron gas forms both quasi-one-dimensional channels and quasi-two-dimensional channels at the quantum-well bents and facets, respectively. Calculations are performed within the random-phase approximation and time-dependent density functional theory approaches. We derive symmetry arguments which allow one to enumerate and classify charge and spin excitations and determine whether excitations may survive to Landau damping. We also derive inelastic light-scattering selection rules for different scattering geometries. Computational issues stemming from the need to use a symmetry-compliant grid are also investigated systematically.

Two self-consistent schemes involving Hedin's $GW$ approximation are studied for a set of sixteen different atoms and small molecules. We compare results from the fully self-consistent $GW$ approximation (SC$GW$) and the quasiparticle self-consistent $GW$ approximation (QS$GW$) within the same numerical framework. Core and valence electrons are treated on an equal footing in all the steps of the calculation. We use basis sets of localized functions to handle the space dependence of quantities and spectral functions to deal with their frequency dependence. We compare SC$GW$ and QS$GW$ on a qualitative level by comparing the computed densities of states (DOS). To judge their relative merit on a quantitative level, we compare their vertical ionization potentials (IPs) with those obtained from coupled-cluster calculations CCSD(T). Our results are futher compared with “one-shot” $G_0{W}_0$ calculations starting from Hartree-Fock solutions ($G_0{W}_0$-HF). Both self-consistent $GW$ approaches behave quite similarly. Averaging over all the studied molecules, both methods show only a small improvement (somewhat larger for SC$GW$) of the calculated IPs with respect to $G_0{W}_0$-HF results. Interestingly, SC$GW$ and QS$GW$ calculations tend to deviate in opposite directions with respect to CCSD(T) results. SC$GW$ systematically underestimates the IPs, while QS$GW$ tends to overestimate them. $G_0{W}_0$-HF produces results which are surprisingly close to QS$GW$ calculations both for the DOS and for the numerical values of the IPs.

We report on total-energy electronic-structure calculations in the density-functional theory performed for both monolayer and bilayer silicene on Ag(111) surfaces. The $\sqrt{3}\times \sqrt{3}$ structure observed experimentally and argued to be the monolayer silicene in the past [Chen et al., Phys. Rev. Lett. 110, 085504 (2013)] is identified as the bilayer silicene on the Ag(111) surface. The identification is based on our accurate density-functional calculations in which three approximations, the local density approximation, the generalized-gradient approximation, and the van der Waals density-functional approximation, to the exchange-correlation energy have been carefully examined. We find that the structural tristability exists for the $\sqrt{3}\times \sqrt{3}$ bilayer silicene. The calculated energy barriers among the three stable structures are in the range of 7–9 meV per Si atom, indicating possible flip-flop motions among the three. We have found that the flip-flop motion between two of the three structures produces the honeycomb structure in the STM images, whereas the motion among the three does the $1\times 1$ structure. We have found that the electron states which effectively follow the Dirac equation in the freestanding silicene couple with the substrate Ag orbitals due to the bond formation, and shift downwards deep in the valence bands. This feature is common to all the stable or metastable silicene layer on the Ag(111) substrate.

With the success of dynamical mean-field theories, solvers for quantum-impurity problems have become an important tool for the numerical study of strongly correlated systems. Continuous-time quantum Monte Carlo sampling of the expansion in powers of the hybridization between the “impurity” and the bath provides a powerful solver when interactions are strong. Here we show that the usual updates that add or remove a pair of creation-annihilation operators are rigorously not ergodic for several classes of broken symmetries that involve spatial components. We show that updates with larger numbers of simultaneous updates of pairs of creation-annihilation operators remedy this problem. As an example, we apply the four-operator updates that are necessary for ergodicity to the case of $d$-wave superconductivity in plaquette dynamical mean-field theory for the one-band Hubbard model. While the results are qualitatively similar to those previously published, they are quantitatively better than previous ones, being closer to those obtained by other approaches.

The problem of continuous quantum phase transitions in metals involves critical bosons coupled to a Fermi surface. We solve the theory in the limit of a large number, $N_B$, of bosonic flavors, where the bosons transform in the adjoint representation (a matrix representation), while the fermions are in the fundamental representation (a vector representation) of a global $SU\left(N_B\right)$ flavor symmetry group. The leading large $N_B$ solution corresponds to a non-Fermi liquid coupled to Wilson-Fisher bosons. In a certain energy range, the fermion velocity vanishes—resulting in the destruction of the Fermi surface. Subleading $1/N_B$ corrections correspond to a qualitatively different form of Landau damping of the bosonic critical fluctuations. We discuss the model in $d=3-\epsilon$ but because of the additional control afforded by large $N_B$, our results are valid down to $d=2$. In the limit $\epsilon \ll 1$, the large $N_B$ solution is consistent with the renormalization group analysis of Fitzpatrick et al. [Phys. Rev. B 88, 125116 (2013)].

$N$-type CdO is a transparent conducting oxide (TCO) which has promise in a number of areas including solar cell applications. In order to realize this potential a detailed knowledge of the electronic structure of the material is essential. In particular, standard density functional theory (DFT) methods struggle to accurately predict fundamental material properties such as the band gap. This is largely due to the underestimation of the Cd 4$d$ binding energy, which results in a strong hybridization with the valence-band (VB) states. In order to test theoretical approaches, comparisons to experiment need to be made. Here, synchrotron-radiation photoelectron spectroscopy (SR-PES) measurements are presented, and comparison with three theoretical approaches are made. In particular the position of the Cd 4$d$ state is measured with hard x-ray PES, and the orbital character of the VB is probed by photon energy dependent measurements. It is found that LDA + U using a theoretical U value of 2.34 eV is very successful in predicting the position of the Cd 4$d$ state. The VB photon energy dependence reveals the O 2$p$ photoionization cross section is underestimated at higher photon energies, and that an orbital contribution from Cd 5$p$ is underestimated by all the DFT approaches.

Scanning gate microscopy of quantum point contacts (QPC) in the integer quantum Hall regime is considered in terms of the scattering wave functions with a finite-difference implementation of the quantum transmitting boundary approach. Conductance ($G$) maps for a clean QPC as well as for a system including an antidot within the QPC constriction are evaluated. The steplike locally flat $G$ maps for clean QPCs turn into circular resonances that are reentrant in an external magnetic field when the antidot is introduced to the constriction. The current circulation around the antidot and the spacing of the resonances at the magnetic field scale react to the probe approaching the QPC. The calculated $G$ maps with a rigid but soft antidot potential reproduce the features detected recently in the electron interferometer [F. Martins et al., Sci. Rep. 3, 1416 (2013)].

We study the nonequilibrium transport properties of fully (exactly) screened Kondo quantum dots subject to a finite bias voltage or a finite temperature. First, we calculate the Fermi-liquid coefficients of the conductance for models with arbitrary spin, i.e., its leading behavior for small bias voltages or temperatures. Second, we determine the low-temperature behavior of the static susceptibility from the exactly known Bethe ansatz results for the magnetization. Third, we study the crossover from strong to weak coupling in the spin-1/2 and the spin-1 models coupled to one or two screening channels, respectively. Using a real-time renormalization group method we calculate the static and dynamical spin-spin correlation functions for the spin-1/2 model as well as the linear and differential conductance and the static susceptibility for the spin-1 model. We define various Kondo scales and discuss their relations. We assess the validity of the renormalization-group treatment by comparing with known results for the temperature dependence of the linear conductance and static susceptibility as well as the Fermi-liquid behavior at low energies.

In the study of the spin Seebeck effect (SSE) in structures with a ferromagnetic insulator (FMI) in contact with a normal metal it is important to know the distributions of the temperatures of the magnon, phonon, and electron systems. Studies of the SSE in yttrium iron garnet (YIG) have relied on the thermal properties of magnons in YIG calculated with expressions valid for low temperatures. Here we present a calculation of the magnon specific heat and thermal conductivity in YIG and show that the values at room temperature are very discrepant from numbers used in the literature. With our values we calculate the temperature profiles of the magnon and phonon systems in a FMI subject to a temperature gradient in the configurations used to study the transverse and longitudinal SSE. In both cases the results are quite different from those obtained in previous studies.

Orbital-free density functional theory (OFDFT) directly solves for the ground-state electron density. It scales linearly with respect to system size, providing a promising tool for large-scale material simulations. Removal of the orbitals requires use of approximate noninteracting kinetic energy density functionals. If replacing ionic cores with pseudopotentials, removal of the orbitals also requires these pseudopotentials to be local. These are two severe challenges to the capabilities of conventional OFDFT. While main group elements are often well described within conventional OFDFT, transition metals remain intractable due to their localized $d$ electrons. To advance the accuracy and general applicability of OFDFT, we have recently reported a general angular momentum dependent formulation as a next-generation OFDFT. In this formalism, we incorporate the angular momenta of electrons by devising a hybrid scheme based on a muffin tin geometry: inside spheres centered at the ionic cores, the electron density is expanded in a set of atom-centered basis functions combined with an onsite density matrix. The explicit treatment of the angular momenta of electrons provides an important basis for accurately describing the important ionic core region, which is not possible in conventional OFDFT. In addition to the conventional OFDFT total energy functional, we introduce a nonlocal energy term containing a set of angular momentum dependent energies to correct the errors due to the approximate kinetic energy density functional and local pseudopotentials. Our approach greatly increases the accuracy of OFDFT while largely preserving its numerical simplicity. Here, we provide details of the theoretical formulation and practical implementation, including the hybrid scheme, the derivation of the nonlocal energy term, the choice of basis functions, the direct minimization of the total energy, the procedure to determine the angular momentum dependent energies, the force formula with Pulay correction, and the solution to emerging numerical instability. To test the angular momentum dependent OFDFT formalism and its numerical implementations, we calculate a diverse set of properties of the transition metal Ti and compare with different levels of DFT approximation. The results suggest that angular momentum dependent OFDFT ultimately will extend the reliable reach of OFDFT to the rest of the periodic table.

We propose the application of nonlinear optics for studies of spatially indirect excitons in coupled quantum wells. We demonstrate that despite their vanishing oscillator strength, indirect excitons can strongly contribute to the photoinduced reflectivity and Kerr rotation. This phenomenon is governed by the interaction between direct and indirect excitons. Both dark and bright states of indirect excitons can be probed by these nonlinear optical techniques.

We study the interplay between a repulsive interaction and an almost staggered on-site potential in one dimension. Specifically, we address the Harper model for spinless fermions with nearest-neighbor repulsion, close to half filling. Using the density matrix renormalization group, we find that, in contrast to standard behavior, the system becomes more compressible as the repulsive interaction is increased. By deriving a low-energy effective model, we unveil the effect of interactions using mean-field analysis: The density of a narrow band around half filling is anticorrelated with the on-site potential, whereas the density of lower occupied bands follows the potential and strengthens it. As a result, the states around half filling are squeezed by the background density, their band becomes flatter, and the compressibility increases.

Electron spin relaxation in a spin-polarized quantum Hall state is studied. Long spin-relaxation times that are at least an order of magnitude longer than those measured in previous experiments were observed and explained within the spin-exciton relaxation formalism. The absence of any dependence of the spin-relaxation time on the electron temperature and on the spin-exciton density, and a specific dependence on the magnetic field indicate a definite relaxation mechanism—spin-exciton annihilation mediated by spin-orbit coupling and a smooth random potential.

Although light continues to be emitted from insulating crystals used as scintillators over a period of nanoseconds to microseconds after stopping of an energetic particle, much of what determines the nonlinearity of response goes on in the first picoseconds. On this time scale, free carriers and excitons are at high density near the track core and thus are subject to nonlinear quenching. The hot (free) electrons eventually cool to low enough energy that trapping on holes, dopants, or defects can commence. In the track environment, spatial distributions of trapped carriers determined on the picosecond time scale can influence the proportionality between light yield and the initial particle energy throughout the whole light pulse. Picosecond spectroscopy of optical absorption induced by a short pulse of above-gap excitation provides a useful window on what occurs during the crucial early evolution of excited populations. The laser excitation can be tuned to excite carriers that are initially very hot ($\sim$3 eV) relative to the band edges, or that are almost thermalized ($\sim$0.1 eV excess energy) at the outset. Undoped and doped samples of NaI:Tl(0%, 0.1%), CsI:Tl(0%, 0.01%, 0.04%, 0.3%), and $\mathrm{Sr}{\mathrm{I}}_2$:Eu(0%, 0.2%, 0.5%, 3%) are studied in this work.

Density functional calculations predict that the In/Si(111)-(2$\times$2) surface, a key intermediate phase leading to the complex In phase development on Si(111), consists of an intriguing one-atom-thick In overlayer. In atoms of 1 monolayer (ML) (referred to as one In atom per surface Si) there forms a quasihoneycomb network of two In units, a monomer and a triangular trimer, which well accounts for the measured microscopy images and In 4$d$ core-level shifts. This In single layer is, however, semiconducting with a band gap of 0.47 eV and thus could not represent the long-sought two-dimensional (2D) limit of metallic In overlayers. But its In coverage of 1 ML sets a definite lower bound on the coverage for such a 2D-metallic one-atom-thick In overlayer.

Using renormalization group methods, we develop a rigorous coarse-grained representation of the dissipative dynamics of quantum excitations propagating inside open macromolecular systems. We show that, at very low spatial resolution, this quantum transport theory reduces to a modified Brownian process, in which quantum delocalization effects are accounted for by means of an effective term in the Onsager-Machlup functional. Using this formulation, we derive a simple analytic solution for the time-dependent probability of observing the quantum excitation at a given point in the macromolecule. This formula can be used to predict the migration of natural or charged quantum excitations in a variety of molecular systems, including biological and organic polymers, organic crystalline transistors, or photosynthetic complexes. For illustration purposes, we apply this method to investigate inelastic electronic hole transport in a long homo-DNA chain.

We investigate the interaction of magnetic vortices and skyrmions with a spin-polarized current. In a square lattice, fixed classical spins and quantum itinerant electrons evolve according to the coupled Landau-Lifshitz and Schrödinger equations. Changes in the topology occur at microscopic time and length scales and are shown to be triggered by the nucleation of a nontrivial electron-spin structure at the vortex core.