Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors

TL;DR

This paper develops a comprehensive mean-field framework for analyzing the coexistence of ferromagnetism, spin-orbit coupling, and mixed pairing in superconductors, with applications to tunneling spectra and thermodynamic properties.

Contribution

It provides exact eigenvalues, coupled gap equations, and analytical expressions for order parameters in a unified model of ferromagnetic and noncentrosymmetric superconductors.

Findings

Conductance spectra reveal gap structures and spin-orbit effects.

Conditions for coexistence of ferromagnetism and triplet superconductivity are identified.

Predicted nonuniversal heat capacity jump at the superconducting transition.

Abstract

We consider a general Hamiltonian describing coexistence of itinerant ferromagnetism, spin-orbit coupling and mixed spin-singlet/triplet superconducting pairing in the context of mean-field theory. The Hamiltonian is diagonalized and exact eigenvalues are obtained, thus allowing us to write down the coupled gap equations for the different order parameters. Our results may then be applied to any model describing coexistence of any combination of these three phenomena. As a specific application of our results, we consider tunneling between a normal metal and a noncentrosymmetric superconductor with mixed singlet and triplet gaps. The conductance spectrum reveals information about these gaps in addition to how the influence of spin-orbit coupling is manifested. We also consider the coexistence of itinerant ferromagnetism and triplet superconductivity as a model for recently discovered ferromagnetic superconductors. The coupled gap equations are solved self-consistently, and we study the conditions necessary to obtain the coexistent regime of ferromagnetism and superconductivity. Analytical expressions are presented for the order parameters, and we provide an analysis of the free energy to identify the preferred system state. Moreover, we make specific predictions concerning the heat capacity for a ferromagnetic superconductor. In particular, we report a nonuniversal relative jump in the specific heat, depending on the magnetization of the system, at the uppermost superconducting phase transition. [Shortened abstract due to arXiv submission.]