The breakdown of weak-localisation theory in disordered conductors with magnetic or spin-orbit scattering

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Abstract
The wavelength dependence of quantum interference corrections to the diffusion constant is calculated in two dimensions, in the weak-localisation regime, using models belonging to the three universality classes for localisation. In each case, the corrections at second order in perturbation theory are much larger for finite wavevector than expected from previous results at zero wavevector. In two cases (systems without time-reversal invariance and systems with spin-orbit scattering), this wavevector dependence determines the way in which perturbation theory breaks down as the cut-off length for quantum interference increases. The authors speculate that these results may signal crossover from simple diffusive behaviour to a critical regime characterised by novel variation of the diffusion constant with wavevector and frequency.