Search for two-scale localization in disordered wires in a magnetic field

TL;DR

This study tests the prediction of two-scale wavefunction decay in disordered wires under magnetic fields using numerical simulations, finding no evidence of such behavior contrary to earlier theoretical predictions.

Contribution

It provides a numerical validation that challenges the previously predicted two-scale localization behavior in disordered wires with magnetic fields.

Findings

No evidence of two-scale decay in simulations

Supports single-scale localization in disordered wires

Contradicts earlier supersymmetry-based predictions

Abstract

The supersymmetry technique [A. V. Kolesnikov and K. B. Efetov, Phys. Rev. Lett. 83, 3689 (1999)] predicts a two-scale behavior of wavefunction decay in disordered wires in the crossover regime from preserved to broken time-reversal symmetry. We have tested this prediction by a transmission approach, relying on the Borland conjecture that relates the decay length of the transmittance to the decay length of the wavefunctions. Our numerical simulations show no indication of two-scale behavior.