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

Abstract

We study the metal-insulator transition in weakly coupled disordered planes on the basis of a nonlinear sigma model (NL\ensuremath{\sigma}M). Using two different methods, a renormalization-group approach and an auxiliary-field method, we calculate the crossover length between a two-dimensional (2D) regime at small length scales and a 3D regime at larger length scales. The 3D regime is described by an anisotropic 3D NL\ensuremath{\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.