Role of Impurities in Core Contribution to Vortex Friction

We present a microscopic calculation of core states contribution to vortex friction in a type II superconductor at zero temperature. In weak impurity limit, a perturbative calculation leads to a vortex friction proportional to the normal state resistivity. With the aid of random matrix theory, vortex friction due to core states is determined only by the Fermi energy and the energy gap in dirty limit, similar to the phenomenological results of Bardeen and Stephen, but disagrees with the results obtained under the relaxation time approximation. In addition, an explicit demonstration is given on the the insensitivity of transverse force to impurities.