Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction

TL;DR

This paper investigates a superconductor Josephson junction with a Bogoliubov Fermi surface, revealing unique odd-frequency pairing phenomena and phase-dependent local density of states, distinct from conventional superconductors.

Contribution

It introduces a novel analysis of Bogoliubov quasiparticle pairing in Josephson junctions, highlighting odd-frequency pair potentials and their effects on physical properties.

Findings

Zero energy local density of states decreases with phase

Generation of even-frequency pair amplitude near interface

Realization of $\\pi$-junction-like current phase relation

Abstract

We study a superconductor Josephson junction with a Bogoliubov Fermi surface, employing McMillan's Green's function technique. The low-energy degrees of freedom are described by spinless fermions (bogolons), where the characteristic feature appears as an odd-frequency pair potential. The differential equation of the Green's function is reduced to the eigenvalue problem of the non-Hermitian effective Hamiltonian. The physical quantities such as the density of states and pair amplitude are then extracted from the obtained Green's function. We find that the zero energy local density of states at the interface decreases as the relative phase of the Josephson junction increases. This decrease is accompanied by the generation of an even-frequency pair amplitude near the interface. We also clarify that the $\pi$-junction-like current phase relation is realized in terms of bogolons. In contrast to conventional $s$-wave superconductor junctions, where even-frequency pairs dominate in the bulk and odd-frequency pairs are generated near the interface, our findings illuminate the distinct behaviors of junctions with Bogoliubov Fermi surfaces. We further explore spatial dependences of these physical quantities systematically using quasiclassical Green's functions.