Critical behavior of density of states near Fermi energy in low-dimensional disordered metals

TL;DR

This paper investigates how electron-electron interactions affect the density of states near the Fermi energy in low-dimensional disordered metals, revealing a transition to insulating behavior at zero temperature.

Contribution

It provides a non-divergent solution for the density of states at low energies considering electron interactions, consistent with experimental observations.

Findings

Density of states vanishes at the Fermi level in 2D and 1D disordered systems at zero temperature.

Theoretical results align with tunneling experiments on GaAs/AlGaAs and carbon nanotubes.

Interaction effects lead to insulating behavior at zero temperature in low-dimensional disordered metals.

Abstract

We study the effect of electron-electron interaction on the one-particle density of states (\emph{DOS}) $\rho^{(d)}(\epsilon,T)$ of low-dimensional disordered metals near Fermi energy within the framework of the finite temperature conventional impurity diagram technique. We consider only diffusive limit and by a geometric re-summation of the most singular first order self-energy corrections via the Dyson equation we obtain a non-divergent solution for the \emph{DOS} at low energies, while for higher energies the well-known Altshuler-Aronov corrections are recovered. At the Fermi level $\rho^{(d)}(\epsilon,T=0)\to 0$, this indicates that interacting disordered two- and quasi-one-dimensional systems are in insulating state at zero temperature. The obtained results are in good agreement with recent tunneling experiments on two-dimensional GaAs/AlGaAs heterostructures and quasi-one-dimensional doped multiwall carbon nanotubes.