The Coulomb gap and low energy statistics for Coulomb glasses
We study the statistics of local energy minima in the configuration space of two-dimensional lattice Coulomb glasses with site disorder and the behavior of the Coulomb gap depending on the strength of random site energies. At intermediate disorder, i.e., when the typical strength of the disorder is of the same order as the nearest-neighbor Coulomb energy, the high energy tail of the distribution of the local minima is exponential. We furthermore analyze the structure of the local minima and show that most sites of the system have the same occupation numbers in all of these states. The density of states (DOS) shows a transition from the crystalline state at zero disorder (with a hard gap) to an intermediate, probably glassy state with a Coulomb gap. We analyze this Coulomb gap in some detail and show that the DOS deviates slightly from the traditional linear behavior in 2D. For finite systems these intermediate Coulomb gap states disappear for large disorder strengths and only a random localized state in which all electrons are in the minima of the random potential exists. Dedication: This paper is dedicated to Thomas Nattermann, our dearest friend, brilliant colleague, and outstanding teacher.
Statistics of deep energy states in Coulomb glasses.
We study the statistics of local energy minima in the configuration space and the energy relaxation due to activated hopping in a system of interacting electrons in a random environment. The distribution of the local minima is exponential, which is in agreement with extreme value statistics considerations. The relaxation of the system energy shows logarithmic time dependence reflecting the ultrametric structure of the system.
Long-time relaxation of interacting electrons in the regime of hopping conduction
Using numerical simulations we study the long-time relaxation of the hopping conductivity. Even though no modern computation is able to simulate the behavior of a large size system over minutes or hours so as to observe the relaxation, we have been able to show that the long-time relaxation and aging effect observed in experiments can be explained in terms of slow transitions between different pseudo ground states. This was achieved by showing that different pseudoground states may have different conductivities and that the dispersion of conductivities is in agreement with the experimental data. We considered two different two-dimensional models with electron-electron interaction: the lattice model and the random site model, corresponding to "strong" and "weak" effective disorder. For the lattice model, effectively strong disorder, we have shown that the universality of the Coulomb gap, which is responsible for the universal Efros-Shklovskii law for the conductivity, suppresses the long-time relaxation of conductivity since the universality strongly decreases the dispersion of conductivities of the pseudoground stales.