Slow imbalance relaxation and thermoelectric transport in graphene

We compute the electronic component of the thermal conductivity (TC) and the thermoelectric power (TEP) of monolayer graphene, within the hydrodynamic regime, taking into account the slow rate of carrier population imbalance relaxation. Interband electron-hole generation and recombination processes are inefficient due to the non-decaying nature of the relativistic energy spectrum. As a result, a population imbalance of the conduction and valence bands is generically induced upon the application of a thermal gradient. We show that the thermoelectric response of a graphene monolayer depends upon the ratio of the sample length to an intrinsic length scale l_Q, set by the imbalance relaxation rate. At the same time, we incorporate the crucial influence of the metallic contacts required for the thermopower measurement (under open circuit boundary conditions), since carrier exchange with the contacts also relaxes the imbalance. These effects are especially pronounced for clean graphene, where the thermoelectric transport is limited exclusively by intercarrier collisions. For specimens shorter than l_Q, the population imbalance extends throughout the sample; the TC and TEP asymptote toward their zero imbalance relaxation limits. In the opposite limit of a graphene slab longer than l_Q, at non-zero doping the TC and TEP approach intrinsic values characteristic of the infinite imbalance relaxation limit. Samples of intermediate (long) length in the doped (undoped) case are predicted to exhibit an inhomogeneous temperature profile, whilst the TC and TEP grow linearly with the system size. In all cases except for the shortest devices, we develop a picture of bulk electron and hole number currents that flow between thermally conductive leads, where steady-state recombination and generation processes relax the accumulating imbalance.Comment: 14 pages, 4 figure

Magnetotransport in disordered delta-doped heterostructures

We discuss theoretically how electrons confined to two dimensions in a delta-doped heterostructure can arrange themselves in a droplet-like spatial distribution due to disorder and screening effects when their density is low. We apply this droplet picture to magnetotransport and derive the expected dependence on electron density of several quantities relevant to this transport, in the regimes of weak and moderate magnetic fields. We find good qualitative and quantitative agreement between our calculations and recent experiments on delta-doped heterostructures.Comment: 10 pages RevTeX, 2 figures, uses psfrag; published versio

Conduction band spin splitting and negative magnetoresistance in A3B5{\rm A}_3{\rm B}_5 heterostructures

The quantum interference corrections to the conductivity are calculated for an electron gas in asymmetric quantum wells in a magnetic field. The theory takes into account two different types of the spin splitting of the conduction band: the Dresselhaus terms, both linear and cubic in the wave vector, and the Rashba term, linear in wave vector. It is shown that the contributions of these terms into magnetoconductivity are not additive, as it was traditionally assumed. While the contributions of all terms of the conduction band splitting into the D'yakonov--Perel' spin relaxation rate are additive, in the conductivity the two linear terms cancel each other, and, when they are equal, in the absence of the cubic terms the conduction band spin splitting does not show up in the magnetoconductivity at all. The theory agrees very well with experimental results and enables one to determine experimentally parameters of the spin-orbit splitting of the conduction band.Comment: 8 pages, RevTeX, 4 Postscript figure

Phonon-induced decay of the electron spin in quantum dots

We study spin relaxation and decoherence in a GaAs quantum dot due to spin-orbit interaction. We derive an effective Hamiltonian which couples the electron spin to phonons or any other fluctuation of the dot potential. We show that the spin decoherence time $T_2$ is as large as the spin relaxation time $T_1$, under realistic conditions. For the Dresselhaus and Rashba spin-orbit couplings, we find that, in leading order, the effective magnetic field can have only fluctuations transverse to the applied magnetic field. As a result, $T_2=2T_1$ for arbitrarily large Zeeman splittings, in contrast to the naively expected case $T_2\ll T_1$. We show that the spin decay is drastically suppressed for certain magnetic field directions and values of the Rashba coupling constant. Finally, for the spin coupling to acoustic phonons, we show that $T_2=2T_1$ for all spin-orbit mechanisms in leading order in the electron-phonon interaction.Comment: 5 pages, 1 figur

D'yakonov-Perel' spin relaxation for degenerate electrons in the electron-hole liquid

We present an analytical study of the D'yakonov-Perel' spin relaxation time for degenerate electrons in a photo-excited electron-hole liquid in intrinsic semiconductors exhibiting a spin-split band structure. The D'yakonov-Perel' spin relaxation of electrons in these materials is controlled by electron-hole scattering, with small corrections from electron-electron scattering and virtually none from electron-impurity scattering. We derive simple expressions (one-dimensional and two-dimensional integrals respectively) for the effective electron-hole and electron-electron scattering rates which enter the spin relaxation time calculation. The electron-hole scattering rate is found to be comparable to the scattering rates from impurities in the electron liquid - a common model for n-type doped semiconductors. As the density of electron-hole pairs decreases (within the degenerate regime), a strong enhancement of the scattering rates and a corresponding slowing down of spin relaxation is predicted due to exchange and correlation effects in the electron-hole liquid. In the opposite limit of high density, the original D'yakonov-Perel' model fails due to decreasing scattering rates and is eventually superseded by free precession of individual quasiparticle spins.Comment: 16 pages, 5 figure

Statistics of the Charging Spectrum of a Two-Dimensional Coulomb Glass Island

The fluctuations of capacitance of a two-dimensional island are studied in the regime of low electron concentration and strong disorder, when electrons can be considered classical particles. The universal capacitance distribution is found, with the dispersion being of the order of the average. This distribution is shown to be closely related to the shape of the Coulomb gap in the one-electron density of states of the island. Behavior of the the capacitance fluctuations near the metal - insulator transition is discussed.Comment: 4 pages, LaTex, 4 Postscript figures are included Discussion of the situation with screening by metallic gate is adde