Electromagnetic waves in a Josephson junction in a thin film

TL;DR

This paper investigates the electrodynamics of a thin-film Josephson junction, deriving an integro-differential equation and showing that electromagnetic wave frequency scales with the square root of the wave vector in certain conditions.

Contribution

It introduces a nonlocal electrodynamics model for thin-film Josephson junctions and derives the dispersion relation for electromagnetic waves in this regime.

Findings

Electrodynamics is nonlocal when wavelength is less than Pearl penetration depth.

Derived an integro-differential equation for phase difference.

Wave frequency scales as the square root of wave vector.

Abstract

We consider a one-dimensional Josephson junction in a superconducting film with the thickness that is much less than the London penetration depth. We treat an electromagnetic wave propagating along this tunnel contact. We show that the electrodynamics of a Josephson junction in a thin film is nonlocal if the wave length is less than the Pearl penetration depth. We find the integro-differential equation determining the phase difference between the two superconductors forming the tunnel contact. We use this equation to calculate the dispersion relation for an electromagnetic wave propagating along the Josephson junction. We find that the frequency of this wave is proportional to the square root of the wave vector if the wave length is less than the Pearl penetration depth.