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

TL;DR

This paper investigates the effects of orbital and Pauli depairing on the vortex state in d-wave superconductors, specifically CeCoIn$_5$, revealing how anisotropies and critical parameters influence the superconducting phase and confirming the d_{x^2-y^2} order parameter symmetry.

Contribution

It provides a detailed analysis of the combined depairing effects and their impact on critical fields and anisotropies, with specific application to CeCoIn$_5$ and its nodal structure.

Findings

Standard extrapolation methods can be inaccurate for critical field values.

The critical Maki parameter for first order transition depends on Fermi surface and gap symmetry.

Anisotropy in thermodynamic and transport properties is insensitive to Zeeman field, aiding nodal direction determination.

Abstract

We analyse the combined effect of orbital and Pauli depairing on the superconducting state, and apply the results to the heavy fermion CeCoIn$_5$. We find that: a) standard extrapolation based on the slope of $H_{c2}(T)$ 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, $\alpha$, that determines onset of the first order transition depends on the Fermi surface shape and the symmetry of the gap, and is $\alpha^*\approx 3$ for CeCoIn$_5$; 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 $d_{x^2-y^2}$ order parameter CeCoIn$_5$.