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 …