Abstract
We analyse the combined effect of orbital and Pauli depairing on the superconducting state, and apply the results to the heavy fermion CeCoIn. We find that: a) standard extrapolation based on the slope of in the vicinity of the transition temperature to T=0 does not always give accurate values of the orbital upper critical field; b) critical value of the Maki parameter, , that determines onset of the first order transition depends on the Fermi surface shape and the symmetry of the gap, and is for CeCoIn; 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 order parameter CeCoIn.
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