Electronic States of Graphene Nanoribbons

We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particle- and a hole-like band with evanescent wavefunctions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units is divisible by 3, and insulating otherwise. A comparison of the wavefunctions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.Comment: 5 pages, 6 figure

Canted phase in double quantum dots

We perform a Hartree-Fock calculation in order to describe the ground state of a vertical double quantum dot in the absence of magnetic fields parallel to the growth direction. Intra- and interdot exchange interactions determine the singlet or triplet character of the system as the tunneling is tuned. At finite Zeeman splittings due to in-plane magnetic fields, we observe the continuous quantum phase transition from ferromagnetic to symmetric phase through a canted antiferromagnetic state. The latter is obtained even at zero Zeeman energy for an odd electron number.Comment: 5 pages, 3 figure

Piezoelectric mechanism of orientation of stripe structures in two-dimensional electron systems

A piezoelectric mechanism of orientation of stripes in two-dimensional quantum Hall systems in GaAs heterostructures is considered. The anisotropy of the elastic moduli and the boundary of the sample are taken into account. It is found that in the average the stripes line up with the [110] axis. In double layer systems the wave vector of the stripe structure rotates from the [110] to [100] axis if the period of density modulation becomes large than the interlayer distance. From the experimental point of view it means that in double layer systems anisotropic part of resistivity changes its sign under variation of the external magnetic field.Comment: 8 page

Spin depolarization in the transport of holes across GaMnAs/GaAlAs/p-GaAs

We study the spin polarization of tunneling holes injected from ferromagnetic GaMnAs into a p-doped semiconductor through a tunneling barrier. We obtain an upper limit to the spin injection rate. We find that spin-orbit interaction interaction in the barrier and in the drain limits severely spin injection. Spin depolarization is stronger when the magnetization is parallel to the current than when is perpendicular to it.Comment: Accepted in Phys. Rev. B. 4 pages, 4 figure

Instability of the symmetric Couette-flow in a granular gas: hydrodynamic field profiles and transport

We investigate the inelastic hard disk gas sheared by two parallel bumpy walls (Couette-flow). In our molecular dynamic simulations we found a sensitivity to the asymmetries of the initial condition of the particle places and velocities and an asymmetric stationary state, where the deviation from (anti)symmetric hydrodynamic fields is stronger as the normal restitution coefficient decreases. For the better understanding of this sensitivity we carried out a linear stability analysis of the former kinetic theoretical solution [Jenkins and Richman: J. Fluid. Mech. {\bf 171} (1986)] and found it to be unstable. The effect of this asymmetry on the self-diffusion coefficient is also discussed.Comment: 9 pages RevTeX, 14 postscript figures, sent to Phys. Rev.

Transport coefficients for dense hard-disk systems

A study of the transport coefficients of a system of elastic hard disks, based on the use of Helfand-Einstein expressions is reported. The self-diffusion, the viscosity, and the heat conductivity are examined with averaging techniques especially appropriate for the use in event-driven molecular dynamics algorithms with periodic boundary conditions. The density and size dependence of the results is analyzed, and comparison with the predictions from Enskog's theory is carried out. In particular, the behavior of the transport coefficients in the vicinity of the fluid-solid transition is investigated and a striking power law divergence of the viscosity in this region is obtained, while all other examined transport coefficients show a drop in that density range.Comment: submitted to PR

Stripes in Quantum Hall Double Layer Systems

We present results of a study of double layer quantum Hall systems in which each layer has a high-index Landau level that is half-filled. Hartree-Fock calculations indicate that, above a critical layer separation, the system becomes unstable to the formation of a unidirectional coherent charge density wave (UCCDW), which is related to stripe states in single layer systems. The UCCDW state supports a quantized Hall effect when there is tunneling between layers, and is {\it always} stable against formation of an isotropic Wigner crystal for Landau indices $N \ge 1$. The state does become unstable to the formation of modulations within the stripes at large enough layer separation. The UCCDW state supports low-energy modes associated with interlayer coherence. The coherence allows the formation of charged soliton excitations, which become gapless in the limit of vanishing tunneling. We argue that this may result in a novel {\it ``critical Hall state''}, characterized by a power law $I-V$ in tunneling experiments.Comment: 10 pages, 8 figures include

Canted ground state in artificial molecules at high magnetic fields

We analyze the transitions that a magnetic field provokes in the ground state of an artificial homonuclear diatomic molecule. For that purpose, we have performed numerical diagonalizations for a double quantum dot around the regime of filling factor 2. We present phase diagrams in terms of tunneling and Zeeman couplings, and confinement strength. We identify a series of transitions from ferromagnetic to symmetric states through a set of canted states with antiferromagnetic couping between the two quantum dots

Fluctuating Navier-Stokes equations for inelastic hard spheres or disks

Starting from the fluctuating Boltzmann equation for smooth inelastic hard spheres or disks, closed equations for the fluctuating hydrodynamic fields to Navier-Stokes order are derived. This requires to derive constitutive relations for both the fluctuating fluxes and the correlations of the random forces. The former are identified as having the same form as the macroscopic average fluxes and involving the same transport coefficients. On the other hand, the random force terms exhibit two peculiarities as compared with their elastic limit for molecular systems. Firstly, they are not white, but have some finite relaxation time. Secondly, their amplitude is not determined by the macroscopic transport coefficients, but involves new coefficients