Response of thin-film SQUIDs to applied fields and vortex fields: Linear SQUIDs

摘要

In this paper we analyze the properties of a dc SQUID when the Londonpenetration depth \lambda is larger than the superconducting film thickness d.We present equations that govern the static behavior for arbitrary values of\Lambda = \lambda^2/d relative to the linear dimensions of the SQUID. TheSQUID's critical current I_c depends upon the effective flux \Phi, the magneticflux through a contour surrounding the central hole plus a term proportional tothe line integral of the current density around this contour. While it is wellknown that the SQUID inductance depends upon \Lambda, we show here that thefocusing of magnetic flux from applied fields and vortex-generated fields intothe central hole of the SQUID also depends upon \Lambda. We apply thisformalism to the simplest case of a linear SQUID of width 2w, consisting of acoplanar pair of long superconducting strips of separation 2a, connected by twosmall Josephson junctions to a superconducting current-input lead at one endand by a superconducting lead at the other end. The central region of thisSQUID shares many properties with a superconducting coplanar stripline. Wecalculate magnetic-field and current-density profiles, the inductance(including both geometric and kinetic inductances), magnetic moments, and theeffective area as a function of \Lambda/w and a/w.