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 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 $1/{\tau }_{*}$.