Inertial Josephson Relation for FIR Frequencies

TL;DR

This paper extends the Josephson Relation to include inertial effects, providing a unified description of vortex dynamics and high-frequency response in superconductors across all frequencies.

Contribution

It introduces the Inertial Josephson Relation, incorporating charge carrier inertia, applicable at all frequencies and aligning with Ginzburg-Landau vortex conductivity results.

Findings

The Inertial Josephson Relation matches Ginzburg-Landau vortex conductivity.

It extends Josephson Relation to high-frequency regimes.

Provides a unified framework for vortex dynamics at all frequencies.

Abstract

Consideration of the balance of forces on superconducting condensate at low frequencies leads to the well-known Josephson Relation. Using the Ginzburg-Landau expression for the current, an expression relating the electric field to the vortex velocity via the magnetic field is obtained. This result is the Josephson Relation, supplemented by a term accounting for the inertia of charge carriers. This Inertial Josephson Relation may be used at all frequencies and may be viewed as the Josephson Relation extended to the case of sub-gap high-frequency response. When applied to vortex dynamics it yields the same conductivity as solution of the Ginzburg-Landau theory.