Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field

We present systematic study of zero modes and gaps by introducing effects of anisotropy of hopping integrals for a tight-binding model on the honeycomb lattice in a magnetic field. The condition for the existence of zero modes is analytically derived. From the condition, it is found that a tiny anisotropy for graphene is sufficient to open a gap around zero energy in a magnetic field. This gap behaves as a non-perturbative and exponential form as a function of the magnetic field. The non-analytic behavior with respect to the magnetic field can be understood as tunneling effects between energy levels around two Dirac zero modes appearing in the honeycomb lattice, and an explicit form of the gap around zero energy is obtained by the WKB method near the merging point of these Dirac zero modes. Effects of the anisotropy for the honeycomb lattices with boundaries are also studied. The condition for the existence of zero energy edge states in a magnetic field is analytically derived. On the basis of the condition, it is recognized that anisotropy of the hopping integrals induces abrupt changes of the number of zero energy edge states, which depend on the shapes of the edges sensitively.Comment: 36 pages, 20 figures; added discussion on experiments in Sec.VI, cited Refs.[35]-[40], and reworded Sec.IV

Superlattice Structures of Graphene based Nanoribbons

Based on first-principles calculations we predict that periodically repeated junctions of armchair graphene nanoribbons of different widths form superlattice structures. In these superlattice heterostructures the width and the energy gap are modulated in real space and specific states are confined in certain segments. Orientation of constituent nanoribbons, their width and length, the symmetry of the junction are the structural parameters to engineer electronic properties of these quantum structures. Not only the size modulation, but also composition modulation, such as periodically repeated, commensurate heterojunctions of BN and graphene honeycomb nanoribbons result in a multiple quantum well structure. We showed that these graphene based quantum structures can introduce novel concepts to design nanodevices.Comment: amended versio

GIS-based two-dimensional numerical simulation of rainfall-induced debris flow

International audienceThis paper aims to present a useful numerical method to simulate the propagation and deposition of debris flow across the three dimensional complex terrain. A depth-averaged two-dimensional numerical model is developed, in which the debris and water mixture is assumed to be continuous, incompressible, unsteady flow. The model is based on the continuity equations and Navier-Stokes equations. Raster grid networks of digital elevation model in GIS provide a uniform grid system to describe complex topography. As the raster grid can be used as the finite difference mesh, the continuity and momentum equations are solved numerically using the finite difference method. The numerical model is applied to simulate the rainfall-induced debris flow occurred in 20 July 2003, in Minamata City of southern Kyushu, Japan. The simulation reproduces the propagation and deposition and the results are in good agreement with the field investigation. The synthesis of numerical method and GIS makes possible the solution of debris flow over a realistic terrain, and can be used to estimate the flow range, and to define potentially hazardous areas for homes and road section

Bloch oscillations in Fermi gases

The possibility of Bloch oscillations for a degenerate and superfluid Fermi gas of atoms in an optical lattice is considered. For a one-component degenerate gas the oscillations are suppressed for high temperatures and band fillings. For a two-component gas the Landau criterion is used for specifying the regime where Bloch oscillations of the superfluid may be observed. We show how the amplitude of Bloch oscillations varies along the BCS-BEC crossover.Comment: 4 pages, 2 figures. explanations adde

Quantum scattering in one dimension

A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concept of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.Comment: 8 page

Terahertz Bloch oscillator with a modulated bias

Electrons performing Bloch oscillations in an energy band of a dc-biased superlattice in the presence of weak dissipation can potentially generate THz fields at room temperature. The realization of such Bloch oscillator is a long-standing problem due to the instability of a homogeneous electric field in conditions of negative differential conductivity. We establish the theoretical feasibility of stable THz gain in a long superlattice device in which the bias is quasistatically modulated by microwave fields. The modulation waveforms must have at least two harmonics in their spectra.Comment: 5 page

Interaction Effects Among Two-Dimensional Electrons and Holes

We report large logarithmic corrections to the conductivity of two-dimensional electrons and holes in GaSb-InAs-GaSb double heterostructures. From ∼ 40 mK to 1 K, the conductivity increased with the logarithm of the temperature but with a slope as much as 30 times larger than estimated from the theories of weak localization and carrier interaction. The discrepancy apparently results from electron-hole interactions not included in the theory

High-frequency oscillations in low-dimensional conductors and semiconductor superlattices induced by current in stack direction

A narrow energy band of the electronic spectrum in some direction in low-dimensional crystals may lead to a negative differential conductance and N-shaped I-V curve that results in an instability of the uniform stationary state. A well-known stable solution for such a system is a state with electric field domain. We have found a uniform stable solution in the region of negative differential conductance. This solution describes uniform high-frequency voltage oscillations. Frequency of the oscillation is determined by antenna properties of the system. The results are applicable also to semiconductor superlattices.Comment: 8 pages, 3 figure

Interaction Effects Among Two-Dimensional Electrons and Holes

We report large logarithmic corrections to the conductivity of two-dimensional electrons and holes in GaSb-InAs-GaSb double heterostructures. From ∼ 40 mK to 1 K, the conductivity increased with the logarithm of the temperature but with a slope as much as 30 times larger than estimated from the theories of weak localization and carrier interaction. The discrepancy apparently results from electron-hole interactions not included in the theory

Transport of strong-coupling polarons in optical lattices

We study the transport of ultracold impurity atoms immersed in a Bose-Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strong-coupling regime, we derive an extended Hubbard model describing the dynamics of the impurities in terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an Esaki-Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter.Comment: 25 pages, 6 figure