Field theoretic model for the Josephson effect

TL;DR

This paper proposes a field theoretic model attributing the Josephson effect to massive photon behavior in superconductors, linking the effect to photon mass, quantum equations, and junction properties.

Contribution

It introduces a novel field theoretic approach where the Josephson effect arises from massive photon propagation, differing from traditional tunneling explanations.

Findings

Josephson coupling energy equals the rest mass energy of massive photons.

Photon mass depends on the junction's electric properties.

A quantized capacitance inversely relates to the critical current.

Abstract

The Josephson effect is found to stem from the quantum behavior of massive photons existing in a superconducting medium. Accordingly, the Josephson coupling energy is found to be equal to the rest mass energy of these photons. The Josephson effect is described by propagation of massive photon field following the universal quantum equation instead of being due to quantum tunnelling. The mass of the photon is found to be dependent on the electric properties of the junction. A characteristic (critical) quantized capacitance of the junction is found to be inversely related to the critical current. The quantum (kinetic) inductance induced in the junction is found to be equal to $L_q=\mu_0\lambda_J$\,, where $\lambda_J$ is the Josephson penetration depth, and $\mu_0$ is the free space permeability.