Nonlocal Cooper pairs in finite topological superconductors and their relation to Majorana nonlocality

TL;DR

This paper reveals that in finite topological superconductors, normal and anomalous Green's functions become identical up to a phase at low energies, indicating nonlocal Cooper pairs linked to Majorana modes and nonlocal transport.

Contribution

It demonstrates the emergence of nonlocal Cooper pairs and their relation to Majorana modes through Green's function analysis in finite topological superconductors.

Findings

Normal and anomalous Green's functions become identical up to a phase at low energy.

Nonlocal correlations between system ends grow exponentially with system length.

Nonlocal Cooper pairs are linked to Majorana modes and fermion parity.

Abstract

We identify two fundamental properties of the Gor'kov Green's function of finite one-dimensional topological superconductors. In the low-frequency (low-energy) regime, the normal and anomalous Green's functions, which describe single-particle and Cooper-pair correlations, respectively, become identical up to a phase factor. Moreover, they exhibit pronounced nonlocality: correlations between the two ends of the system grow exponentially with system length, whereas local correlations at either end vanish in the zero-frequency limit. These striking features signify the emergence of unconventional nonlocal Cooper pairs associated with a nonlocal fermionic mode composed of hybridized Majorana end modes. The nonlocal Cooper pairs are directly linked to fermion parity and to the nonlocal transport properties of finite topological superconductors. By focusing on pair correlations, our analysis advances the understanding of Majorana nonlocality, a key concept in topological quantum computation.