Odd-frequency pairing and proximity effect in Kitaev chain systems including topological critical point

TL;DR

This paper explores the relationship between odd-frequency pairing and the proximity effect in Kitaev chains, especially at the topological critical point, revealing new insights into their spatial behavior and implications for topological superconductivity.

Contribution

It demonstrates that odd-frequency pair amplitudes extend into the bulk at the critical point and cause the proximity effect, providing new understanding of topological superconductivity in Kitaev chains.

Findings

Odd-frequency pairing coincides with local density of states at low frequencies.

Odd-frequency pair amplitude spreads into the bulk at the topological critical point.

Odd-frequency Cooper pairs induce the proximity effect at the critical point.

Abstract

In this paper, we investigate the relation between odd-frequency pairing and proximity effect in non-uniform Kitaev chain systems with a particular interest in the topological critical point. First, we correlate the odd-frequency pairing and Majorana fermion in a semi-infinite Kitaev chain, where we find that the spatial dependence of the odd-frequency pair amplitude coincides with that of the local density of states at low frequencies. Second, we demonstrate that, contrary to the standard view, the odd-frequency pair amplitude spreads into the bulk of a semi-infinite Kitaev chain at the topological critical point. Finally, we show that odd-frequency Cooper pairs cause the proximity effect in a normal metal/diffusive normal metal/ Kitaev chain junction even at the topological critical point. Our results hold relevance to the investigation of odd-frequency pairing and topological superconductivity in more complicated systems that involve Rashba nanowire with magnetic fields.