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

TL;DR

This paper analyzes the behavior of thin-film dc SQUIDs with large London penetration depth, deriving equations for their static properties and examining how flux focusing and inductance depend on key parameters.

Contribution

It presents a formalism for understanding the static behavior of thin-film SQUIDs with arbitrary penetration depth, including flux focusing and inductance calculations.

Findings

Flux focusing depends on bb/w ratio

Inductance varies with bb/w and a/w ratios

Profiles of magnetic field and current density are characterized

Abstract

In this paper we analyze the properties of a dc SQUID when the London penetration 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. The SQUID's critical current I_c depends upon the effective flux \Phi, the magnetic flux through a contour surrounding the central hole plus a term proportional to the line integral of the current density around this contour. While it is well known that the SQUID inductance depends upon \Lambda, we show here that the focusing of magnetic flux from applied fields and vortex-generated fields into the central hole of the SQUID also depends upon \Lambda. We apply this formalism to the simplest case of a linear SQUID of width 2w, consisting of a coplanar pair of long superconducting strips of separation 2a, connected by two small Josephson junctions to a superconducting current-input lead at one end and by a superconducting lead at the other end. The central region of this SQUID shares many properties with a superconducting coplanar stripline. We calculate magnetic-field and current-density profiles, the inductance (including both geometric and kinetic inductances), magnetic moments, and the effective area as a function of \Lambda/w and a/w.