Dirac quasiparticles in the mixed state

Energies and wave functions are calculated for d-wave quasiparticles in the mixed state using the formalism of Franz and Tes̆anović for the low-lying energy levels. The accuracy of the plane-wave expansion is explored by comparing approximate to exact results for a simplified one-dimensional problem, and the convergence of the plane-wave expansion to the two-dimensional case is studied. The results are used to calculate the low-energy tunneling density of states and the low-temperature specific heat, and these theoretical results are compared to semiclassical treatments and to the available data. Implications for the muon spin resonance measurements of vortex core size are also discussed.