Theory of the proximity effect at the interface of a normal metal and triplet p -wave superconductor in the clean limit

The superconducting proximity effect in normal metal (N)/triplet $p$-wave superconductor (P) junctions is studied based on the quasiclassical Green's function theory. We present theoretical results for self-consistently determined pair potentials on both the N and P sides as well as the quasiparticle local density of states near the interface. In the present study, for the P side, in order to consider promising pairing symmetries as in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$, we choose three kinds of pairings: (i) ${p}_{x}$, (ii) ${p}_{y}$, or (iii) ${p}_{x}+i{p}_{y}$ waves. Here, we assume that an attractive interelectron potential on the $N$ side can induce a subdominant $s$-wave pair potential. The spatial dependencies are sensitive to the transparency of the junctions, while the proximity-induced $s$-wave component on the N side does not enhance the magnitude of the pair potential, which breaks the time-reversal symmetry on the P side. The resulting local density of states at the interface has a zero-energy peak, and its splitting depends on the transparency and symmetry of the pair potentials of the junction.