Quantum opening of the Coulomb gap in two dimensions

TL;DR

This paper investigates how the Coulomb gap in disordered two-dimensional fermion systems opens as interaction strength increases, revealing a transition in energy level spacing distribution linked to conductivity changes.

Contribution

It provides new insights into the Coulomb gap opening and the transition in energy level spacing distribution in disordered 2D fermion systems as interaction strength varies.

Findings

Smooth opening of the Coulomb gap with increasing $r_s$

Poisson-Wigner transition at $r_s \\approx 1$

Connection to Mott to Efros-Shklovskii transition in conductivity

Abstract

For a constant density of spinless fermions in strongly disordered two dimensional clusters, the energy level spacing between the ground state and the first excitation is studied for increasing system sizes. The average indicates a smooth opening of the gap when the Coulomb energy to Fermi energy ratio $r_s$ increases from 0 to 3, while the distribution exhibits a sharp Poisson-Wigner-like transition at $r_s \approx 1$. The results are related to the transition from Mott to Efros-Shklovskii hopping conductivity recently observed at a similar ratio $r_s$.