Stability of the nonequilibrium state of a superconductor irradiated by an electromagnetic field

Irradiation of a superconductor by an electromagnetic field with a frequency ₀ larger than twice the energy gap (order parameter) decreases the order parameter . We obtain the quasiparticle distribution function n and the dependence of the order parameter on the power of the electromagnetic field P by solving numerically the kinetic equations for n and in the steady state. We take ₀/₀ = 2.1, 8, and 20, where ₀ is the equilibrium value of the order parameter at T = 0 K. In the examples considered the dependence of on the pumping power P becomes double-valued above a critical power. We allow phonons also to be out of thermal equilibrium. To discuss the stability of the steady state thus obtained, we derive kinetic equations for small deviations of the quasiparticle distribution function and the order parameter from the steady state n and by means of the nonequilibrium Green's function theory. Assuming n, exp(i kr – t), (k) is computed using n _s/, where n _sis the steadystate quasiparticle distribution function for arbitrary . It is concluded in general that the steady state on the upper branch ( > _{c 2}) is stable with respect to both spatially homogeneous and inhomogeneous fluctuations, and the lower branch ( > _{c 2}) is unstable; _{c 2}is the value where the upper and lower branches of (P) coalesce.This work is partly supported by a Grant-in-Aid for Special Project Research from the Ministry of Education, Science and Culture of Japan.