  In this paper, a delocalization-localization transition within the
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.
