Exploration of the Coulomb Gap

The competition between disorder and Coulomb interaction leads to the depletion of the single-particle density of states in the Anderson insulators near the Fermi energy known as the Coulomb gap. The Coulomb gap is a thoroughly studied phenomena in solid state physics. It was conventionally believed that in order to observe such a gap numerically, one must enforce first-order stability criterion to generate a pseudo ground state, which corresponds to ensuring that the ground state energy is minimized with respect to the single-particle hopping. We believe that only the zeroth-order stability, which ensures all occupied single-particle levels are below the Fermi level, more or less reproduces the depletion of DOS near Fermi level. We propose a probabilistic argument regarding the algorithm used for the simulation and compare our proposed theory with the conventional Efros’ self-consistent theory. We also explore the validity of our arguments in power-law interactions outside of the Coulomb interaction.