Energy Gap Induced by Impurity Scattering: New Phase Transition in Anisotropic Superconductors

It is shown that layered superconductors are subjected to a phase transition at zero temperature provided the order parameter (OP) reverses its sign on the Fermi-surface but its angular average is finite. The transition is regulated by an elastic impurity scattering rate $1/\tau$. The excitation energy spectrum, being gapless at the low level of scattering, develops a gap as soon as the scattering rate exceeds some critical value of $1/\tau_\star$.