Self-similar magnetic structures during the vortex-glass to vortex-liquid transition of type II superconductors

Abstract

We examine the response to an external magnetic field by a multi-layer superconductor with an electrical resistance ρff(b)αbσ, where b is the dimensionless magnetic induction and σ is a parameter characterizing the ratio of the pinning activation energy to the energy of thermal fluctuations. When σ > 1 the sample is in the vortex glass phase, when 0 < σ < 1, it is in the vortex liquid phase, and a vortex glass to vortex liquid phase transition takes place at σ = 1. In the vortex glass phase, the magnetic field penetrates into the superconductor in the form of a self-similar wave. At all times it penetrates to a finite depth and its front moves at a finite velocity which depends on the parameters of the problem, such as the rate of pumping by the external magnetic field. In the vortex liquid phase the magnetic field penetrates to an infinite depth. Thus, the magnetic field penetrates to an infinite depth in the superconductor during a transition from the vortex glass phase into the vortex liquid phase.