Renormalization-group analysis of weak collective pinning in type-II superconductors

The effect of randomly distributed impurities on vortex lattices in isotrop ic type-II superconductors is studied within the framework of weak collecti ve pinning theory. Using a renormalization-group (RG) approach, we calculat e the size R-c of collectively pinned vortex bundles in the dispersive regi me, a(0)<R-c<lambda (small bundles), to two-loop accuracy. We assume impuri ty disorder to be weak and short-range correlated, and neglect thermal effe cts. Our findings quantitatively refine the lowest-order perturbation resul t due to A. I. Larkin and Yu. N. Ovchinnikov [J. Low Temp. Phys. 34, 409 (1 979)]. In particular, we determine the numerical constant in the exponentia l function and find the algebraic prefactor in R(c)proportional to B(-1/2)d elta(p)(alpha 2) exp(alpha(1)/delta(p)), where the (dimensionless) paramete r delta(p)proportional to B-3/2 is a measure of the effective disorder stre ngth, B is the magnetic induction, alpha(1) = 16/(9 root pi)approximate to 1, and alpha(2)=(7-5 ln4/3)/27 approximate to 0.2. These refinements lead t o an improved description of the activated dynamics of the vortex lattice ( creep) and provide us with a more accurate functional dependence of the cri tical current je on the magnetic field j(c)proportional to B1+3 alpha 2 exp (-constB(3/2)). [S0163-1829(99)13013-3].