Dimensional crossover and metal-insulator transition in quasi-two-dimensional disordered conductors

TL;DR

This paper investigates the metal-insulator transition in weakly coupled disordered planes using a Non-Linear Sigma Model, identifying the crossover length, critical interplane hopping, and effects of magnetic fields through RG and auxiliary field methods.

Contribution

It introduces a detailed analysis of the dimensional crossover and critical parameters for MIT in quasi-2D disordered conductors using two complementary theoretical approaches.

Findings

Calculated the crossover length between 2D and 3D regimes.

Determined the critical interplane hopping value for MIT.

Showed magnetic fields favor localization and mapped the phase diagram.

Abstract

We study the metal-insulator transition (MIT) in weakly coupled disordered planes on the basis of a Non-Linear Sigma Model (NL$\sigma $M). Using two different methods, a renormalization group (RG) approach and an auxiliary field method, we calculate the crossover length between a 2D regime at small length scales and a 3D regime at larger length scales. The 3D regime is described by an anisotropic 3D NL$\sigma $M with renormalized coupling constants. We obtain the critical value of the single particle interplane hopping which separates the metallic and insulating phases. We also show that a strong parallel magnetic field favors the localized phase and derive the phase diagram.