Proximity effect of time-reversal symmetry broken noncentrosymmetric superconductors

In noncentrosymmetric superconductors the pair potential has both even-parity singlet and odd-parity triplet components. If time-reversal symmetry is broken, the superconducting phase of these components is not the same, for example in anapole superconductors. In this paper it is shown that breaking time-reversal symmetry by a phase difference between the two components significantly alters both the density of states and the conductance in $s+\mathrm{helical} p$-wave superconductors. The density of states and conductance in $s+\mathrm{chiral} p$-wave superconductors are less influenced by adding a phase difference because time-reversal symmetry is already broken in the $s+p$-wave superconductor. The Tanaka-Nazarov boundary conditions are extended to 3D superconductors, allowing us to investigate a greater variety of superconductors, such as Balian-Werthamer superconductors, in which the direction of the $d$ vector is parallel to the direction of momentum. The results are important for the determination of pair potentials in potentially time-reversal symmetry broken noncentrosymmetric superconductors.