Extended Josephson Relation and Abrikosov lattice deformation

TL;DR

This paper derives an extended Josephson relation within TDGL theory that accounts for vortex lattice deformation, applied fields, and inertial effects, broadening its applicability to various experimental conditions.

Contribution

It introduces an Extended Josephson Relation that incorporates lattice deformation, time-dependent magnetic fields, and inertial effects, expanding the theoretical framework for vortex dynamics.

Findings

The relation is compatible with TDGL theory.

It applies to a wider range of experimental conditions.

Accounts for vortex lattice deformation and inertial effects.

Abstract

From the point of view of time-dependent Ginzburg Landau (TDGL) theory, a Josephson-like relation is derived for an Abrikosov vortex lattice accelerated and deformed by applied fields. Beginning with a review of the Josephson Relation derived from the two ingredients of a lattice-kinematics assumption in TDGL theory and gauge invariance, we extend the construction to accommodate a time-dependent applied magnetic field, a floating-kernel formulation of normal current, and finally lattice deformation due to the electric field and inertial effects of vortex-lattice motion. The resulting Josephson-like relation, which we call an Extended Josephson Relation, applies to a much wider set of experimental conditions than the original Josephson Relation, and is explicitly compatible with the considerations of TDGL theory.