Renormalization-group analysis of weak collective pinning in type-II superconductors
O. S. Wagner, V. B. Geshkenbein, A. I. Larkin, G. Blatter
DOI 10.1103/PhysRevB.59.11551 · Physical Review B
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Abstract
The effect of randomly distributed impurities on vortex lattices in isotropic type-II superconductors is studied within the framework of weak collective pinning theory. Using a renormalization-group (RG) approach, we calculate the size Rc of collectively pinned vortex bundles in the dispersive regime, a0<Rc<λ (small bundles), to two-loop accuracy. We assume impurity disorder to be weak and short-range correlated, and neglect thermal effects. Our findings quantitatively refine the lowest-order perturbation result due to A. I. Larkin and Yu. N. Ovchinnikov [J. Low Temp. Phys. 34, 409 (1979)]. In particular, we determine the numerical constant in the exponential function and find the algebraic prefactor in Rc∝B−1/2δpα2exp(α1/δp), where the (dimensionless) parameter δp∝B−3/2 is a measure of the effective disorder strength, B is the magnetic induction, α1=16/(9π)≈1, and α2=(7−5ln43)/27≈0.2. These refinements lead to an improved description of the activated dynamics of the vortex lattice (creep) and provide us with a more accurate functional dependence of the critical current jc on the magnetic field jc∝B1+3α2exp(−constB3/2).
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