Odd-frequency pairing in normal metal/superconductor junctions

TL;DR

This paper investigates how odd-frequency pairing states are induced in normal metal/superconductor junctions, revealing their dependence on pairing symmetry, energy, and local density of states features like MARS.

Contribution

It demonstrates the general emergence of odd-frequency pairing in N/S junctions and characterizes their symmetry and energy dependence using quasiclassical Green's functions.

Findings

Odd-frequency pairing is induced near N/S interfaces due to broken translational symmetry.

The symmetry of the odd-frequency component depends on the superconductor's pairing symmetry.

Enhanced odd-frequency pairing occurs at LDOS peaks and zero energy in different junction types.

Abstract

We study the induced odd-frequency pairing states in ballistic normal metal/superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk and a normal metal layer has an arbitrary length. Using the quasiclassical Green's function formalism, we demonstrate that, quite generally, the pair amplitude in the junction has an admixture of an odd-frequency component due to the breakdown of translational invariance near the N/S interface where the pair potential acquires spatial dependence. If a superconductor has even-parity pair potential (spin-singlet s-wave state), the odd-frequency pairing component with odd-parity is induced near the N/S interface, while in the case of odd-parity pair potential (spin-triplet $p_{x}$-wave or spin-singlet $d_{xy}$-wave) the odd-frequency component with even-parity is generated. We show that in conventional s-wave junctions, the amplitude of the odd-frequency pairing state is enhanced at energies corresponding to the peaks in the local density of states (LDOS). In $p_x$- and $d_{xy}$-wave junctions, the amplitude of the odd-frequency component on the S side of the N/S interface is enhanced at zero energy where the midgap Andreev resonant state (MARS) appears due to the sign change of the pair potential. The odd-frequency component extends into the N region and exceeds the even-frequency component at energies corresponding to the LDOS peak positions, including the MARS.