Odd frequency pairing of interacting Majorana fermions

TL;DR

This paper investigates odd-frequency pairing correlations in a model of interacting Majorana fermions coupled to a boson mode, revealing conditions for their stability and deriving related theoretical properties.

Contribution

It introduces a model demonstrating odd-frequency pairing in interacting Majorana fermions and derives the critical parameters and theoretical framework for this phenomenon.

Findings

Odd-frequency pairing occurs between Majoranas at opposite ends of a wire.

Stable when coupling exceeds a critical value g_c.

Derived gap equation, critical temperature, and Ginzburg-Landau theory.

Abstract

Majorana fermions are rising as a promising key component in quantum computation. While the prevalent approach is to use a quadratic (i.e. non-interacting) Majorana Hamiltonian, when expressed in terms of Dirac fermions, generically the Hamiltonian involves interaction terms. Here we focus on the possible pair correlations in a simple model system. We study a model of Majorana fermions coupled to a boson mode and show that the anomalous correlator between different Majorana fermions, located at opposite ends of a topological wire, exhibits odd frequency behavior. It is stabilized when the coupling strength $g$ is above a critical value $g_c$. We use both, conventional diagrammatic theory and a functional integral approach, to derive the gap equation, the critical temperature, the gap function, the critical coupling, and a Ginzburg-Landau theory allowing to discuss a possible subleading admixture of even-frequency pairing.