Dissipationless BCS Dynamics with Large Branch Imbalance

In many situations a BCS-type superconductor will develop an imbalance between the populations of the holelike and electronlike spectral branches. This imbalance suppresses the gap. It has been noted by Gal'perin et al. [Sov. Phys. JETP 54, 1126 (1981)] that at large imbalance, when the gap is substantially suppressed, an instability develops. The analytic treatment of the system beyond the instability point is complicated by the fact that the Boltzmann approach breaks down. We study the short-time behavior following the instability, in the collisionless regime, using methods developed by Yuzbashyan et al. [J. Phys. A 38, 7831 (2005); Phys. Rev. B 72, 220503(R) (2005)].