Localization properties of quasi-one-dimensional conductor networks in a random magnetic field

Abstract

We investigate the localization of electrons on a ladder-shaped quasi-one-dimensional network of clean wires, with a quenched random magnetic flux across each of its square plaquettes. In the weak-disorder regime, the localization length \ensuremath{\xi} is much larger than the side of the plaquettes. Using perturbative analytic techniques, we derive scaling laws of the form \ensuremath{\xi}\ensuremath{\sim}1/${\mathit{w}}^{\mathrm{\ensuremath{\alpha}}}$, with w being the width of magnetic disorder. The critical exponent \ensuremath{\alpha} assumes different values in various energy ranges: \ensuremath{\alpha}=4 when only one channel is open, \ensuremath{\alpha}=2 when both channels are open, \ensuremath{\alpha}=1 around external and internal band edges. The corresponding scaling functions and amplitudes are accurately determined by numerical simulations. Magnetic disorder and potential disorder thus pertain to different universality classes.