Emergent pair symmetries in systems with poor man's Majorana modes

TL;DR

This paper investigates the pairing symmetries in few-site Kitaev chains hosting poor man's Majorana modes, revealing tunable odd-frequency correlations and their relation to Majorana nonlocality without topological protection.

Contribution

It demonstrates that few-site Kitaev chains exhibit distinct, tunable pair correlations with specific symmetries, elucidating their connection to Majorana nonlocality.

Findings

Presence of local and nonlocal pair correlations with distinct symmetries.

Divergent odd-frequency pairing near zero frequency controlled by system parameters.

Odd-frequency pairing reflects Majorana nonlocality without topological origin.

Abstract

Few-site Kitaev chains are promising for realizing Majorana zero modes without topological protection but fully nonlocal, which are known as poor man's Majorana modes. While several signatures have already been reported both theoretically and experimentally, it still remains unknown what is the nature of superconducting correlations in the presence of poor man's Majorana modes. In this work, we study few-site Kitaev chains and demonstrate that they host pair correlations with distinct symmetries, entirely determined by the underlying quantum numbers. In particular, we find that a two-site Kitaev chain hosts local (odd-frequency) and nonlocal (odd- and even-frequency) pair correlations, both spin polarized and highly tunable by the system parameters. Interestingly, the odd-frequency pair correlations exhibit a divergent behaviour around zero frequency when the nonlocal $p$-wave pair potential and electron tunneling are of the same order, an effect that can be controlled by the onsite energies. Since a divergent odd-frequency pairing is directly connected to the intrinsic spatial nonlocality of Majorana zero modes in topological superconductors, the divergent odd-frequency pairing here reflects the intrinsic Majorana nonlocality of poor man's Majorana modes but without any relation to topology. Our findings could help understanding the emergent pair correlations in few-site Kitaev chains.