Anisotropic thermodynamics and T/sqrt H scaling of d-wave superconductors in the vortex state

The density of states of a 2D d-wave superconductor in the vortex state with applied magnetic field $\bf H$ in the plane is shown to exhibit fourfold oscillations as a function of the angle of the field with respect to the crystal axes. We find further that the frequency dependence of the density of states and the temperature dependence of transport coefficients obey different power laws, thus leading to different magnetic scaling functions, for field in the nodal and anti-nodal direction. We discuss the consequences of this anisotropy for measurements of the specific heat.