Abstract:
We present a new implementation of the k-space interpolation scheme for electronic structure presented by E. L. Shirley, Phys. Rev. B 54, 16464 (1996). The method permits the construction of a compact k-dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of effective single-particle electronic structure calculations (based on density functional theory in this work). We provide some generalizations of the initial approach which reduce the number of required initial electronic structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone-center only for large systems. We also generalize the representation of non-local Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. Furthermore, accurate eigenfunctions - expressed in the optimal basis - provide easy access to useful matrix elements for simulating spectroscopy and we provide details for computing optical transition amplitudes. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.

Abstract:
The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wavefunction and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wavefunction of the strongly correlated solid. Exchange, correlation, and magnetic field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin-orderings are observed in the ground-state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground-state. In the quantum Hall effect regime, a strong magnetic field introduces new energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wavefunction when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wavefunctions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from $n$-doping to $p$-doping in $GaAS/AlGaAS$ heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor $\nu \sim 1/5$ to $\nu \sim 1/3$. This lends strong support to the claim that the

Abstract:
We present an {\it ab initio} approach for the computation of the magnetic susceptibility $\chi$ of insulators. The approach is applied to compute $\chi$ in diamond and in solid neon using density functional theory in the local density approximation, obtaining good agreement with experimental data. In solid neon, we predict an observable dependence of $\chi$ upon pressure.

Abstract:
Recent measurements have shown that a continuously tunable bandgap of up to 250 meV can be generated in biased bilayer graphene [Y. Zhang et al., Nature 459, 820 (2009)], opening up pathway for possible graphene-based nanoelectronic and nanophotonic devices operating at room temperature. Here, we show that the optical response of this system is dominated by bound excitons. The main feature of the optical absorbance spectrum is determined by a single symmetric peak arising from excitons, a profile that is markedly different from that of an interband transition picture. Under laboratory conditions, the binding energy of the excitons may be tuned with the external bias going from zero to several tens of meV's. These novel strong excitonic behaviors result from a peculiar, effective ``one-dimensional'' joint density of states and a continuously-tunable bandgap in biased bilayer graphene. Moreover, we show that the electronic structure (level degeneracy, optical selection rules, etc.) of the bound excitons in a biased bilayer graphene is markedly different from that of a two-dimensional hydrogen atom because of the pseudospin physics.

Abstract:
Topological defects in graphene, dislocations and grain boundaries, are still not well understood despites the considerable number of experimental observations. We introduce a general approach for constructing dislocations in graphene characterized by arbitrary Burgers vectors as well as grain boundaries, covering the whole range of possible misorientation angles. By using ab initio calculations we investigate thermodynamic and electronic properties of these topological defects, finding energetically favorable symmetric large-angle grain boundaries, strong tendency towards out-of-plane deformation in the small-angle regimes, and pronounced effects on the electronic structure. The present results show that dislocations and grain boundaries are important intrinsic defects in graphene which may be used for engineering graphene-based nanomaterials and functional devices.

Abstract:
Analysis of the electronic structure of an ordinary two-dimensional electron gas (2DEG) under an appropriate external periodic potential of hexagonal symmetry reveals that massless Dirac fermions are generated near the corners of the supercell Brillouin zone. The required potential parameters are found to be achievable under or close to laboratory conditions. Moreover, the group velocity is tunable by changing either the effective mass of the 2DEG or the lattice parameter of the external potential, and it is insensitive to the potential amplitude. The finding should provide a new class of systems other than graphene for investigating and exploiting massless Dirac fermions using 2DEGs in semiconductors.

Abstract:
A first-principles investigation of the electronic properties of boron nitride nanoribbons (BNNRs) having either armchair or zigzag shaped edges passivated by hydrogen with widths up to 10 nm is presented. Band gaps of armchair BNNRs exhibit family-dependent oscillations as the width increases and, for ribbons wider than 3 nm, converge to a constant value that is 0.02 eV smaller than the bulk band gap of a boron nitride sheet owing to the existence of very weak edge states. The band gap of zigzag BNNRs monotonically decreases and converges to a gap that is 0.7 eV smaller than the bulk gap due to the presence of strong edge states. When a transverse electric field is applied, the band gaps of armchair BNNRs decrease monotonically with the field strength. For the zigzag BNNRs, however, the band gaps and the carrier effective masses either increase or decrease depending on the direction and the strength of the field.

Abstract:
We present a new first-principles formalism for calculating forces for optically excited electronic states using the interacting Green's function approach with the GW-Bethe Salpeter Equation method. This advance allows for efficient computation of gradients of the excited-state Born-Oppenheimer energy, allowing for the study of relaxation, molecular dynamics, and photoluminescence of excited states. The approach is tested on photoexcited carbon dioxide and ammonia molecules, and the calculations accurately describe the excitation energies and photoinduced structural deformations.

Abstract:
Most materials in available macroscopic quantities are polycrystalline. Graphene, a recently discovered two-dimensional form of carbon with strong potential for replacing silicon in future electronics, is no exception. There is growing evidence of the polycrystalline nature of graphene samples obtained using various techniques. Grain boundaries, intrinsic topological defects of polycrystalline materials, are expected to dramatically alter the electronic transport in graphene. Here, we develop a theory of charge carrier transmission through grain boundaries composed of a periodic array of dislocations in graphene based on the momentum conservation principle. Depending on the grain boundary structure we find two distinct transport behaviours - either high transparency, or perfect reflection of charge carriers over remarkably large energy ranges. First-principles quantum transport calculations are used to verify and further investigate this striking behaviour. Our study sheds light on the transport properties of large-area graphene samples. Furthermore, purposeful engineering of periodic grain boundaries with tunable transport gaps would allow for controlling charge currents without the need of introducing bulk band gaps in otherwise semimetallic graphene. The proposed approach can be regarded as a means towards building practical graphene electronics.

Abstract:
We find, through first-principles calculations, that hole doping induces a ferromagnetic phase transition in monolayer GaSe. Upon increasing hole density, the average spin magnetic moment per carrier increases and reaches a plateau near 1.0 $\mu_{\rm{B}}$/carrier in a range of $3\times 10^{13}$/cm$^{2}$-$1\times 10^{14}$/cm$^{2}$ with the system in a half-metal state before the moment starts to descend abruptly. The predicted magnetism originates from an exchange splitting of electronic states at the top of the valence band where the density of states exhibits a sharp van Hove singularity in this quasi-two-dimensional system.