The structure of single vortices in type II superconductors

Abstract

This paper reports the first results of a program for the investigation of the detailed electronic and magnetic structure of type II superconductors. The structure of a single flux bundle or vortex in an infinite superconducting specimen is investigated, assuming weak coupling and a spherical Fermi surface of the material. The equations governing the gap parameterΔ(r) and the vector potentialA(r) are suitably scaled and simplified using the symmetry of the system. These equations can be solved numerically only; for their solution the asymptotics ofΔ(r) andA(r) far from the center of the vortex are required. These asymptotics are derived here by properly linearising the equations; they are found to be of the typer ^−1/2 exp (−r/rin0) wherer ₀ is determined by temperature and material parameters. Implicit equations forr ₀ are derived and discussed. We find that for materials withκ-values less than 1.7 (e.g. pure niobium)r ₀ becomes complex at low temperatures; i.e. the deviation ofΔ(r) andA(r) from their values at infinity is a damped oscillation as function ofr.