Hall Effect in a Superconductor Not in the Vortex State

Abstract

The Hall electric field inside a superconductor not in the vortex state is calculated using the time-dependent Ginzburg-Landau equations. The field exists only in the skin of the superconductor. Part of the electric field penetrating the material dies out in a London penetration length and part dies out in a coherence length. For an applied magnetic field of 1 G, the field is ${10}^{\ensuremath{-}7}$-${10}^{\ensuremath{-}8}$ V/m in most pure superconductors, and is proportional to the square of the applied magnetic field. The gradient of the electrochemical potential is zero, so there is no Hall voltage. The charge density producing the electric field is a dipole layer, a penetration length thick, at the surface of the material. This means that the contact potential has a part that depends quadratically on the applied magnetic field.