Abstract
In the presence of a single impurity, the Ginzburg-Landau free-energy functional for a superconductor acquires extra terms. Using microscopic theory, we determine the structure of these terms and their coefficients. Our calculation is very general: we assume a k\ifmmode \hat{}\else \^{}\fi{}-dependent order parameter $\ensuremath{\Delta}(\stackrel{^}{\mathrm{k}})$, which transforms according to any one-dimensional irreducible representation of the crystalline point group. This representation may be conventional or unconventional, as appropriate to the current models of high-${T}_{c}$ superconductors. We treat an arbitrary Fermi surface. The physical significance of the theory is discussed, with emphasis on vortex pinning. We estimate the pinning energy of a single vortex.
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