Interaction between a cylindrical superconducting impurity and a vortex in a type-II superconductor

Abstract

We examined the effectiveness of an infinite cylindrical superconducting impurity of radius a in an infinite type-II superconductor as a pinning center. The impurity and the superconducting background have the penetration depth lambda(i) and lambda(s), respectively. With regard to a single-quantum vortex, the free energy of the system and the pinning potential for a vortex were calculated, based upon the London model of the vortex line. Here, the pinning potential U-pin is defined by the difference between the free energy of a vortex being at the center of the impurity and that being infinitely distant from the impurity. U-pin is negative for lambda(i) > lambda(s). On the other hand, U-pin is positive for lambda(i) < lambda(s). In the limit of a much greater than lambda(i) and lambda(s), the pinning potential is found to be U-pin = phi(0)(2)(1/lambda(i)(2) - 1/lambda(s)(2)) ln kappa/4 pi mu(0). In the limit of a much less than lambda(i) and lambda(s), the pinning potential is found to be U-pin = phi(0)(2)[(1/lambda(i)(2) - 1/lambda(ss)(2)) ln(lambda(s)/a) - (1/lambda(i)(2)) ln(lambda(i)/a)]/4 pi mu(0). There is a clear correlation between the intrinsic property of these two superconducting materials and the pinning potential.