Abstract:
A review is provided of our current theoretical understanding of dynamic scaling in nonequilibrium interface growth as, for example, in MBE growth under ultrahigh vacuum deposition conditions.

Abstract:
Motivated by recent experiments on suspended graphene showing carrier mobilities as high as 200,000 cm^2/Vs, we theoretically calculate transport properties assuming Coulomb impurities as the dominant scattering mechanism. We argue that the substrate-free experiments done in the diffusive regime are consistent with our theory and verify many of our earlier predictions including (i) removal of the substrate will increase mobility since most of the charged impurities are in the substrate, (ii) the minimum conductivity is not universal, but depends on impurity concentration with cleaner samples having a higher minimum conductivity. We further argue that experiments on suspended graphene put strong constraints on the two parameters involved in our theory, namely, the charged impurity concentration n_imp and d, the typical distance of a charged impurity from the graphene sheet. The recent experiments on suspended graphene indicate a residual impurity density of 1-2 \times 10^{10} cm^{-2} which are presumably stuck to the graphene interface, compared to impurity densities of ~10^{12} cm^{-2} for graphene on SiO_2 substrate. Transport experiments can therefore be used as a spectroscopic tool to identify the properties of the remaining impurities in suspended graphene.

Abstract:
We present the results of a variational Monte Carlo calculation of the exchange-correlation energy for a spin-polarized two-dimensional electron gas in a perpendicular magnetic field. These energies are a necessary input to the recently developed current-density functional theory. Landau-level mixing is included in a variational manner, which gives the energy at finite density at finite field, in contrast to previous approaches. Results are presented for the exchange-correlation energy and excited-state gap at $\nu =$ 1/7, 1/5, 1/3, 1, and 2. We parameterize the results as a function of $r_s$ and $\nu$ in a form convenient for current-density functional calculations.

Abstract:
We comment on the theoretical interpretations applied to a recent experiment on electron lifetime in graphite. We point out that the acoustic-plasmon excitations in a layered two-dimensional electron system do not produce a linear energy dependence for the Coulomb scattering rate.

Abstract:
We calculate Coulomb scattering lifetimes of electrons in two-subband quantum wires and in double-layer quantum wells by obtaining the quasiparticle self-energy within the framework of the random-phase approximation for the dynamical dielectric function. We show that, in contrast to a single-subband quantum wire, the scattering rate in a two-subband quantum wire contains contributions from both particle-hole excitations and plasmon excitations. For double-layer quantum well structures, we examine individual contributions to the scattering rate from quasiparticle as well as acoustic and optical plasmon excitations at different electron densities and layer separations. We find that the acoustic plasmon contribution in the two-component electron system does not introduce any qualitatively new correction to the low energy inelastic lifetime, and, in particular, does not produce the linear energy dependence of carrier scattering rate as observed in the normal state of high-$T_c$ superconductors.

Abstract:
Using an exact diagonalization technique within a generalized Mott-Hubbard Hamiltonian, we predict the existence of a ground state persistent current in coherent two-dimensional semiconductor quantum dot arrays pierced by an external magnetic flux. The calculated persistent current, which arises from the nontrivial dependence of the ground state energy on the external flux, exists in isolated arrays without any periodic boundary condition. The sensitivity of the calculated persistent current to interaction and disorder is shown to reflect the intricacies of various Anderson-Mott-Hubbard quantum phase transitions in two dimensional systems.

Abstract:
We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening properties of molecular beam epitaxy. The model exhibits long-lived ``transient'' anomalous and multiaffine dynamic scaling properties similar to that found in the corresponding 1+1 - dimensional problem. Using large-scale simulations we obtain the relevant scaling exponents, and compare with continuum theories.

Abstract:
Spin-flip Eliashberg function $\alpha_S^2F$ and temperature-dependent spin relaxation time $T_1(T)$ are calculated for aluminum using realistic pseudopotentials. The spin-flip electron-phonon coupling constant $\lambda_S$ is found to be $2.5\times 10^{-5}$. The calculations agree with experiments validating the Elliott-Yafet theory and the spin-hot-spot picture of spin relaxation for polyvalent metals.

Abstract:
Prospect of building electronic devices in which electron spins store and transport information has revived interest in the spin relaxation of conduction electrons. Since spin-polarized currents cannot flow indefinitely, basic spin-electronic devices must be smaller than the distance electrons diffuse without losing its spin memory. Some recent experimental and theoretical effort has been devoted to the issue of modulating the spin relaxation. It has been shown, for example, that in certain materials doping, alloying, or changing dimensionality can reduce or enhance the spin relaxation by several orders of magnitude. This brief review presents these efforts in the perspective of the current understanding of the spin relaxation of conduction electrons in nonmagnetic semiconductors and metals.

Abstract:
A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion bias conditions. Simulations using a local coordination dependent instantaneous relaxation of the deposited atoms produce complex surface mound morphologies whose dynamical evolution is inconsistent with all the proposed continuum surface growth equations. For any finite bias, mound coarsening is found to be only an initial transient which vanishes asymptotically, with the asymptotic growth exponent being 0.5 in both 1+1 and 2+1 dimensions. Possible experimental implications of the proposed limited mobility nonequilibrium model for real interface growth under a surface diffusion bias are critically discussed.