Anomalous magnetic interference of cross-type Josephson junctions exposed to oblique magnetic fields

Abstract

Gauge-invariant phase difference and critical currents of cross-type Josephson junctions with thin and narrow superconducting strips exposed to three-dimensional magnetic fields are theoretically investigated. When a sandwich-type Josephson junction in the xy plane is exposed to parallel magnetic fields Hx and Hy, the phase difference linearly depends on the spatial coordinates, x and y, and the critical currents exhibit the standard Fraunhofer-type magnetic interference. The perpendicular field Hz, on the other hand, nonlinearly modulates the distribution of the phase difference and the critical currents as the functions of the oblique field exhibit anomalous magnetic interference. We obtain simple analytical expressions for critical currents of small cross-type junctions by neglecting the effects of magnetic screening, self-field, and trapped vortices. The resulting dc critical currents show anomalous and diverse interference patterns depending on the parallel and perpendicular magnetic fields.

Magnetic field dependence of critical currents of cross-type Josephson junctions with inhomogeneous critical current density under oblique magnetic fields

“…where q 0 is a constant independent of the magnetic field and q ( ) x y , 1 for cross-type junctions is given by 12) q p f p f…”

“…indicating that magnetic interference does not occur. 12) On the other hand, in the case of inhomogeneous J c [Figs. interference appears under perpendicular magnetic fields as well [orange line in Fig.…”

“…Furthermore, it was analytically demonstrated that anomalous magnetic interference patterns appear in crosstype junctions under oblique magnetic fields. 12) The magnetic interference of Josephson junctions is also affected by the distribution of the critical current density J c in the junction area. 4,13) Analyzes of magnetic interference of critical currents and inhomogeneity of J c have been used to investigate the edge states in topological insulators.…”