Vortex state of a d-wave superconductor at low temperatures

Mei-Rong Li; P. J. Hirschfeld; P. Wölfle

doi:10.1103/PhysRevB.63.054504

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Vortex state of a d-wave superconductor at low temperatures

Mei-Rong Li, P. J. Hirschfeld, P. Wölfle

DOI 10.1103/PhysRevB.63.054504 · Physical Review B

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Abstract

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant s- and dxy-wave order parameters in the mixed state of a dx2−y2-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field Hc1≲H≪Hc2 from Tc down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of the subdominant dxy pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.