Quasiparticle localization transition in dirty superconductors

In this paper, a delocalization-localization transition within a superconducting state is explored. The symmetries of the Bogoliubov deGennes Hamiltonian endow the two associated superconducting phases - the thermal metal and the thermal insulator - and the critical point between them, with properties that are in stark contrast with analogous phases in normal systems. Here, for systems preserving spin-rotational invariance and time-reversal symmetry in three dimensions, the transition is shown to be of a different universality class from its normal partner by extracting and comparing the localization length exponent. The density of states, which may be regarded as the "order parameter" for the field theory describing the superconducting system, is studied for its unusual properties about criticality.