Vortex state of a d-wave superconductor at low temperatures - art. no. 054504

A systematic perturbation theory is developed to describe the magnetic fiel d-induced subdominant s- and d(xy)-wave order parameters in the mixed state of a d(x2-y2)-wave superconductor, enabling us to obtain, within weak-coup ling BCS theory, analytic results for the free energy of a d-wave supercond uctor in an applied magnetic field H(c1)less than or similar toH much less thanH(c2) from T-c down to very low temperatures. Known results for a singl e isolated vortex in the Ginzburg-Landau regime are recovered, and the beha vior at low temperatures for the subdominant component is shown to be quali tatively different. In the case of the subdominant d(xy) pair component, su perfluid velocity gradients and an orbital Zeeman effect are shown to compe te in determining the vortex state, but for realistic field strengths the l atter appears to be irrelevant. On this basis, we argue that recent predict ions of a low-temperature phase transition in connection with recent therma l conductivity measurements are unlikely to be correct.