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

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, $H/H_{\rm c2} \ll 1$ and $T/T_{\rm c} \ll 1$. We find that the specific heat, the spin susceptibility, the superfluid 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 $T/\sqrt{H}$. We predict also a substantial Hall superfluid density (i.e. the supercurrent component perpendicular to the vector potential $\bm{A}_\omega$). Further the Hall superfluid density decreases slowly with increasing temperature