Quasiparticle spectrum in the vortex state of d-wave superconductors

Quasiparticle spectrum associated with the nodal structure in d-wave superconductors is of great interest. We study theoretically the quasi-particle spectrum in a planar magnetic field, where the effect of the magnetic field is treated in terms of the Doppler shift. We obtain the angular dependent specific heat in the presence of a planar magnetic field and impurities, both in the superclean limit (Gamma/Delta << H/H_{c2}<< 1) and in the clean limit (H/H_{c2} << Gamma/Delta <<1). Also a similar analysis is used for the thermal conductivity tensor within the a-b plane. In particular, in contrast to the earlier works, we find a fourfold symmetry term in \kappa_{\parallel} and \kappa_{\perp} \sim -H \sin(2\theta) where kappa_{perp} are the diagonal- and the off-diagonal components of the thermal conductivity tensor and \theta is the angle between the heat current and the magnetic field.