Metal-Insulator Transition in Two Dimensions in a Nearly Periodic Potential

TL;DR

This paper investigates a metal-insulator transition in a two-dimensional quasiparticle system influenced by a nearly periodic potential, combining periodic and weak random disorder effects, and analyzes the transition's continuous nature and conductivity changes.

Contribution

It introduces a model of a 2D quasiparticle gas with combined periodic and random potentials, analyzing the transition and calculating density of states and conductivity.

Findings

The transition is continuous with increasing potential strength.

Density of states remains non-zero at the Fermi energy in the metallic phase.

Conductivity increases from zero to approximately 2e^2/h across the transition.

Abstract

A two-dimensional gas of non-interacting quasiparticles in a nearly periodic potential is considered at zero temperature. The potential is a superposition of a periodic potential, induced by the charge density wave of a Wigner crystal, and a weak random potential due to disorder. There is a metal-insulator transition that is controlled by the strength of the periodic potential. The transition is continuous in the presence of randomness. We evaluate the density of states, which is non-zero at the Fermi energy in the metallic phase, and the dc conductivity. The latter changes with decreasing modulation of the periodic potential from 0 to $\sigma\approx2e^2/h$.