Anisotropic thermodynamics of d-wave superconductors in the vortex state

We show that the density of states and the thermodynamic properties of a tw o-dimensional d-wave superconductor in the vortex state with applied magnet ic field H in the plane depend on the angle between H and the order-paramet er nodes. Within a semiclassical treatment of the extended quasiparticle st ates, we obtain fourfold oscillations of the specific heat, measurement of which provides a simple probe of gap symmetry. The frequency dependence of the density of states and the temperature dependence of thermodynamic prope rties obey different power laws for field in the nodal and antinodal direct ion. The fourfold pattern is changed to twofold when orthorhombicity is con sidered. [S0163-1829(99)50514-6].