A Landau Theory for the Metal-Insulator Transition

TL;DR

This paper develops a Landau theory for the metal-insulator transition in disordered interacting electrons in dimensions greater than four, revealing mean-field critical exponents and a distinct transition behavior from lower-dimensional models.

Contribution

It provides an exact critical behavior analysis using a Landau-Ginzburg-Wilson framework for the transition in high dimensions, differing from lower-dimensional theories.

Findings

Static exponents are mean-field values

Dynamical exponent z=3

Electrical conductivity vanishes with exponent s=1

Abstract

The nonlinear $\sigma$-model for disordered interacting electrons is studied in spatial dimensions $d>4$. The critical behavior at the metal-insulator transition is determined exactly, and found to be that of a standard Landau-Ginzburg-Wilson $\phi^4$-theory with the single-particle density of states as the order parameter. All static exponents have their mean-field values, and the dynamical exponent $z=3$. $\partial n/ \partial \mu$ is critical with an exponent of $1/2$, and the electrical conductivity vanishes with an exponent $s=1$. The transition is qualitatively different from the one found in the same model in a $2+\epsilon$ expansion.