New instability model for the inhomogeneous gap states of a nonequilibrium superconductor

A new model based on the Rothwarf-Taylor-type rate equations taking the effect of relaxation phonons by decay of high-energy quasiparticles into account is proposed. This effect induces an instability toward the inhomogeneous superconducting state at a certain critical concentration significantly less than that of μ( instability. The spatial scale of an instability is also estimated to be about 100 μm. The results are in good agreement with recent experimental observations