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 ${\mu }^{*}$ 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.