Critical localisation behaviour of spin-dependent ensembles with broken time-reversal invariance

Abstract

Defines local gauge-invariant models with broken time-reversal invariance in order to describe the effects of scattering of non-interacting electrons off certain spin-dependent random potentials. The ensembles obey global rotational invariance in spin space. The author shows that the critical localisation behaviour of these models, which include random magnetic field and spin-orbit scattering, is identical with that of the phase-invariant ensemble as long as time-reversal invariance is broken. In the presence of the invariance-breaking source, e.g. a random magnetic field, the vanishing of spin-orbit scattering does not change the situation. The results are derived by a two-fold application of the 2+ epsilon expansion. A general two-loop order calculation is followed by a comparative study valid in all orders in a simplifying but criticality-conserving limit which corresponds to the non-linear sigma -model limit. The effective Hamiltonian is determined field-theoretically, and turns out to be invariant under global spin-independent unitary transformations in replica space. Moreover, the critical part is invariant under global spin-dependent unitary transformations.