The angular-dependent specific heat, Hall superfluid density, etc. in the vortex state of d-wave superconductors

Within the semi-classical approximation, we study the thermodynamic properties of the vortex state in d-wave superconductors when a magnetic field is applied parallel to the conducting plane, specially for low field and low temperature, H/H-c2 much less than 1 and T/ T-c much less than 1. We nd that the specific heat, the spin susceptibility, the super fluid density and the nuclear spin relaxation rate depend on the angle between the magnetic field and the a-axis and exhibit the scaling behavior in terms of T/rootH. We predict also a substantial Hall super fluid density (i.e. the supercurrent component perpendicular to the vector potential A(omega)). Further the Hall super fluid density decreases slowly with increasing temperature.