Vortex state in d-wave superconductors with strong paramagnetism: Transport and specific heat anisotropy

We analyze the combined effect of orbital and Pauli depairing on the superconducting state, and apply the results to the heavy fermion CeCoIn5. We find that (a) standard extrapolation based on the slope of H-c2(T) in the vicinity of the transition temperature does not always give accurate values of the orbital upper critical field; (b) critical value of the Maki parameter, alpha, which determines onset of the first order transition, depends on the Fermi surface shape and the symmetry of the gap and is alpha*approximate to 3 for CeCoIn5; and (c) the anisotropy of the thermodynamic and transport coefficients in the low-temperature, low-field part of the phase diagram is essentially insensitive to the Zeeman field and can be used to determine the nodal directions in Pauli-limited superconductors. The latter result confirms the finding of the d(x2-y2) order parameter CeCoIn5.