Does Broken Time Reversal Symmetry Modify the Critical Behavior at the Metal-Insulator Transition in 3-Dimensional Disordered Systems?

Abstract

The critical behavior of 3-dimensional disordered systems without time reversal symmetry is investigated by analyzing the spectral fluctuations of the energy spectrum. We show that in the thermodynamic limit we have two different regimes, one for the metallic side and one for the insulating side with different level statistics. The third statistics which occurs only exactly at the critical point is independent of the presence or absence of time reversal symmetry. The critical behavior which is determined by the symmetry of the system at the critical point should therefore be independent of time reversal invariance.