Modified Josephson Relation

TL;DR

The paper proposes a modified Josephson relation for type II superconductors, linking the true electric field to vortex and condensate velocities, refining understanding of electric fields in superconducting vortices.

Contribution

It introduces a new relation for the true electric field in superconductors, accounting for condensate velocity, enhancing the classical Josephson relation.

Findings

The true electric field can be approximated by E=(v_s - v_L) x B at low temperatures.

The effective electric field relates to the electrochemical potential gradient.

The modified relation improves understanding of electric fields in vortex dynamics.

Abstract

For type II superconductors, Josephson has shown that vortices moving with velocity v_L create an effective electric field E'=-v_L x B. By definition the effective electric field is gradient of the electrochemical potential, what is the quantity corresponding to voltage observed with the use of Ohmic contacts. It relates to the true electric field E via the local chemical potential mu as E'=E - grad(mu)/e. We argue that at low temperatures the true electric field in the bulk can be approximated by a modified Josephson relation E=(v_s-v_L) x B, where v_S is the condensate velocity.