Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors

Motivated by recent findings of unconventional superconductors exhibiting multiple broken symmetries, we consider a general Hamiltonian describing coexistence of itinerant ferromagnetism, spin-orbit coupling, and mixed spin-singlet and spin-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. Explicitly, we find well-pronounced peaks and bumps in the spectrum at voltages corresponding to the sum and the difference of the magnitude of the singlet and triplet components. Our results may thus be helpful in determining the relative sizes of the singlet and triplet gaps in noncentrosymmetric superconductors. 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. It is found that the uniform coexistence of ferromagnetism and superconductivity is energetically favored compared to both the purely ferromagnetic state and the unitary superconducting state with zero magnetization. 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. We propose that this may be exploited to obtain information about the superconducting pairing symmetry realized in ferromagnetic superconductors, in addition to the magnitude of the exchange splitting between majority- and minority-spin bands.