Shallow Coulomb gap and weak level-level correlations in a deeply insulating electron system with interactions - art. no. 075304

We consider a system of two-dimensional electrons strongly localized by dis order. Interactions create a gap in the average tunneling density of states nu (E) at energies E close to the Fermi level. We derive a system of self- consistent equations for the correlators of local densities of occupied and empty states. When either the interactions are screened by the gate or the temperature T is high enough, so that the Coulomb gap is shallow, the pert urbative solution of the system yields analytical expressions for the inter action-induced correction delta nu (E) and the level-level correlator. We s how that even with short-range interactions, delta nu (E) exhibits a singul ar energy dependence at T=0. We also demonstrate that at high T this energy dependence is a universal function of the the ratio E/T. Regarding the lev el correlations, we trace how the correlator falls off as a function of spa tial and energy separation between the levels. We also trace how the correl ations vanish with increasing T. Our most noticeable observation is that fo r two close energies the correlator changes sign from positive (attraction) at small distances to negative (repulsion) at large distances.