Localization length in a random magnetic field

Abstract

The Kubo formula is used to get the dc conductance of a statistical ensemble of two-dimensional clusters of the square lattice in the presence of random magnetic fluxes. Fluxes traversing lattice plaquettes are distributed uniformly between $-\frac{1}{2}{\Phi }_0$ and $\frac{1}{2}{\Phi }_0$ with ${\Phi }_0$ the flux quantum. The localization length is obtained from the exponential decay of the averaged conductance as a function of the cluster side. Standard results are recovered when this numerical approach is applied to an Anderson model of diagonal disorder. The localization length of the complex nondiagonal model of disorder remains well below $\xi {=10\mathrm{}}^4$ in the main part of the band in spite of its exponential increase near the band edges.