The Role of Cooperons in the Disordered Electron Problem: Logarithmic Corrections to Scaling Near the Metal-Insulator Transition

TL;DR

This paper investigates how Cooperons influence the metal-insulator transition in disordered electronic systems, revealing logarithmic corrections to scaling and proposing a new approach that challenges previous assumptions about their importance.

Contribution

It introduces a new internally consistent approach to analyze Cooperons' role, showing their significance in all universality classes without magnetic impurities or fields, and addresses the exponent puzzle.

Findings

Logarithmic corrections to scaling at the MIT due to Cooperons

Potential resolution of the conductivity exponent puzzle

Predictions on crossover effects with magnetic fields

Abstract

The effect of Cooperons on metal-insulator transitions (MIT) in disordered interacting electronic systems is studied. It is argued that previous results which concluded that Cooperons are qualitatively unimportant near the MIT might not be correct, and that the problem is much more complicated than had previously been realized. Although we do not completely solve the Cooperon problem, we propose a new approach that is at least internally consistent. Within this approach we find that in all universality classes where Cooperons are present, i.e. in the absence of magnetic impurities and magnetic fields, there are logarithmic corrections to scaling at the MIT. This result is used for a possible resolution of the so-called exponent puzzle for the conductivity near the MIT. A discussion of the relationship between theory and experiment is given. We also make a number of predictions concerning crossover effects which occur when a magnetic field is applied to a system with Cooperons.