Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results

Recently a local mean field theory for both eqilibrium and transport properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77, 165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to the results of dynamic Monte Carlo simulations. In a thermal equilibrium state we compare the density of states and the occupation probabilities. We also study the transition rates between different states and find that the mean field rates underestimate a certain class of important transitions. We propose modified rates to be used in the mean field approach which take into account correlations at the minimal level in the sense that transitions are only to take place from an occupied to an empty site. We show that this modification accounts for most of the difference between the mean field and Monte Carlo rates. The linear response conductance is shown to exhibit the Efros-Shklovskii behaviour in both the mean field and Monte Carlo approaches, but the mean field method strongly underestimates the current at low temperatures. When using the modified rates better agreement is achieved

Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime

We study variable range hopping in the quantum Hall effect regime in the presence of a metallic gate parallel to the plane of a two-dimensional electron gas. Screening of the Coulomb interaction by the gate causes the partial ``filling'' of the Coulomb gap in the density of localized states. At low enough temperatures this leads to a substantial enhancement and a new temperature behavior of the hopping conductivity. As a result, the diagonal conductivity peaks become much wider. The power law dependence of the width of the peaks on the temperature changes: the corresponding exponent turns out to be twice as small as that for gateless structures. The width dependences on the current in non-ohmic regime and on the frequency for the absorption of the electromagnetic waves experience a similar modification. The experimental observation of the crossovers predicted may demonstrate the important role of the Coulomb interaction in the integer quantum Hall regime.Comment: 14 pages + 3 figures by request preprint TPI-MINN-93/58-

Universal Crossover between Efros-Shklovskii and Mott Variable-Range-Hopping Regimes

A universal scaling function, describing the crossover between the Mott and the Efros-Shklovskii hopping regimes, is derived, using the percolation picture of transport in strongly localized systems. This function is agrees very well with experimental data. Quantitative comparison with experiment allows for the possible determination of the role played by polarons in the transport.Comment: 7 pages + 1 figure, Revte

Memory effects in the electron glass

We investigate theoretically the slow nonexponential relaxation dynamics and associated memory effects of glasses far from equilibrium, which are arguably the most important characteristics of the glass phase. We focus on the electron glass which offers an advantageous starting point compared to other glassy systems both theoretically and experimentally: the model used here is discrete, and experimentally it offers new ways to address these effects by changing a simple experimental parameter —the gate voltage. The full nonlinearized self-consistent model of the dynamics of the occupation numbers in the system successfully recovers the general behavior found in experiments. Our numerical analysis is consistent with both the expected logarithmic relaxation and our understanding of how increasing disorder or interaction slows down the relaxation process, thus yielding a consistent picture of the electron glass, and shedding light on the understanding of glassy behavior in general. We also present a novel finite-size domino effect where the connection to the leads affects the relaxation process of the electron glass in mesoscopic systems. This effect speeds up the relaxation process, and may even reverse the expected effect of interaction; stronger interaction then leading to a faster relaxation