Relaxation Processes and Response Time of Superconductors to a Periodic Excitation

Abstract

The knowledge of the response time of superconductors to a periodic excitation as a result of the different relaxation processes is important because it leads to a better understanding of nonequilibrium states; it also has a practical interest in the development of superconducting electronic devices where fast switches are required [1]. Some experiments have been done in Pb to determine the response time: the result is not as short as expected [2]. We consider here a superconducting film of thickness d = 10³ Å excited by optical irradiation. With the assumption of a BCS quasiparticle (q-p) distribution at a temperature T*, the coupled phonon Boltzmann equation and q-p energy balance are solved numerically, the time-dependent gap parameter ∆ being determined by the instantaneous nonequilibrium energy distribution function f(E)

$$ {\Delta \mathord{\left/ {\vphantom {\Delta {{\Delta _0}}}} \right. \kern-\nulldelimiterspace} {{\Delta _0}}} = {\text{exp - }}\left\{ {{\text{ }}\int_{ - \infty }^{ + \infty } {{\text{d}}\varepsilon {\text{ }}{{{\text{f}}\left( {\text{E}} \right)} \mathord{\left/ {\vphantom {{{\text{f}}\left( {\text{E}} \right)} {{\text{E }}}}} \right. \kern-\nulldelimiterspace} {{\text{E }}}}} } \right\}{\text{ }}{\text{.}} $$

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