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 propert ies 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 t emperature, 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 th e nuclear spin relaxation rate depend on the angle between the magnetic fie ld 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.