Magnetic field induced crossover in weakly localized regimes and scaling of the conductivity

Open Access
Publisher Website
Google Scholar
Abstract
For a complex matrix ensemble modelling a two-dimensional (2D) disordered system in a perpendicular magnetic field H⟩ the conductivity is calculated as a function of length, frequency, crossover parameter x(H⟩), and bare conductance go up to O(g -20). Above 2D the scaling forms σ ∝ Δ 1 f1((1 - x)/Δϕ1 1 ) with Δx ≡ |EF - EME(x) |/EME(x), 0 ≲ 1 - x ∝ H⟩ near the orthogonal limit and σ ∝ √Δ 0 f0(x2/Δϕo 0) with cooperon amplitude x(H⟩ ) near the phase invariant limit yield the crossover exponents ϕ 1 = 2 ν1 = 2/(D - 2) and ϕ0 = 0/D - 2 + O((D - 2)0)