Thermodynamics of d-wave superconductors in a magnetic field - art. no. 064513

We investigate the thermodynamic properties of a two-dimensional d-wave sup erconductor in the vortex state using a semiclassical approach, and argue t hat such an approach is valid for the analysis of the experimental data on high-temperature superconductors. We develop a formalism where the spatial average of a physical quantity is written as an integral over the probabili ty density of the Doppler shift, and evaluate this probability density for several model cases. The approach is then used to analyze the behavior of t he specific heat and the nuclear magnetic resonance (NMR) spin-lattice rela xation rate in a magnetic field. We compare our results with the experiment al measurements, and explain the origin of the discrepancy between the resu lts from different groups. We also address the observability of the recentl y predicted fourfold oscillations of the specific heat for the magnetic fie ld parallel to the copper oxide planes. We consider both the orbital and th e Zeeman effects, and conclude that at experimentally relevant temperatures Zeeman splitting does not appreciably reduce the anisotropy, although it d oes change the field dependence of the anisotropic specific heat. We predic t a scaling law for the nonexponentially decaying NMR magnetization, and di scuss different approaches to the effective relaxation rate.