Tunneling into the localized phase near Anderson transitions with Coulomb interaction

TL;DR

This paper investigates the behavior of the tunneling density of states in a disordered electronic system with Coulomb interactions near the Anderson transition, revealing critical phenomena, a Coulomb gap, and multifractality of excitations.

Contribution

It demonstrates the existence of a localization transition for single-particle excitations within an interacting disordered system and characterizes the scaling of the mobility edge with critical exponents.

Findings

Average TDOS exhibits critical behavior and a Coulomb gap.

Single-particle excitations undergo a localization transition at a critical energy.

Local TDOS shows strong fluctuations and multifractality.

Abstract

We study the tunneling density of states (TDOS) of a disordered electronic system with Coulomb interaction on the insulating side of the Anderson localization transition. The average TDOS shows a critical behavior at high energies, with a crossover to a soft Coulomb gap $\Delta$ at low energies. We demonstrate that the single-particle excitations experience a localization transition (which belongs to the noninteracting universality class) at an energy $E=\pm E_c$. The mobility edge $E_c$ scales with the distance $\mu_c-\mu$ from the interacting critical point according to $E_c\propto (\mu_c-\mu)^{\nu z}$, where $\nu$ and $z$ are the localization-length and the dynamical critical exponents. Local TDOS shows strong fluctuations and long-range correlations which reflect the multifractality associated with interacting and noninteracting fixed points as well the localization of low-energy excitations.