Theory of nonlinear electromagnetic rectification in a BCS superconductor

Abstract

Within the framework of the BCS pairing approximation, a theory of nonlinear electromagnetic rectification in a Cooper-paired jellium is established. It is pointed out that the electromagnetic rectification phenomenon, inevitably present as the many-body system’s reaction in a second-harmonic generation process, is of special interest in a superconductor where induced dc currents flow without resistance. Based on a density-matrix approach the nonlinear response tensor is derived and discussed. The importance of nonlocality for the rectification process in centrosymmetric media is stressed. A simple expression for the response tensor is derived in the limit in which the nonlocal pairing effects are included to lowest order. It is demonstrated that electromagnetic rectification occurs only when the nonlinear response has a diamagnetic part. By considering the electromagnetic-rectification phenomenon as a nonlinear-dynamical Meissner effect, the relation to the linear Meissner effect is emphasized. A qualitative discussion of the rectification process at a superconductor-vacuum interface is undertaken. An integrodifferential equation describing, on the basis of the semiclassical infinite-barrier model, the diamagnetic screening of the nonlinear dc magnetic field is set up and discussed.

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