Odd frequency pairing of interacting Majorana fermions

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.

9 pages with supplementary, 4 figs. Minor text and ref update in v2. Three new refs added in v3 (published version)

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
• Tunneling of anyonic Majorana excitations in topological superconductors
• Strongly interacting Majorana fermions
• On stability of odd-frequency superconducting state
• Universal spin-triplet superconducting correlations of Majorana fermions
• Coherent manipulation of a Majorana qubit by a mechanical resonator

Cited by in corpus (30)

• Odd-frequency superconductivity
• Odd-frequency superconducting pairing in one-dimensional systems
• Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism
• Theory of Majorana zero modes in unconventional superconductors
• The Role of Odd-Frequency Pairing in Multiband Superconductors
• Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling
• The Majorana STM as a perfect detector of odd-frequency superconductivity
• Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes
• Inter-orbital topological superconductivity in spin-orbit coupled superconductors with inversion symmetry breaking
• Odd-frequency Superconductivity in Driven Systems
• Odd-frequency superconducting pairing in Kitaev-based junctions
• Signature of odd-frequency equal-spin triplet pairing in the Josephson current on the surface of Weyl nodal loop semimetals
• Pair symmetry conversion in driven multiband superconductors
• Suppression of odd-frequency pairing by phase-disorder in a nanowire coupled to Majorana zero modes
• Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model
• Odd-frequency Berezinskii superconductivity in Dirac semimetals
• Controllable odd-frequency Cooper pairs in multi-superconductor Josephson junctions
• Proximity-Induced Mixed Odd and Even Frequency Pairings in Monolayer NbSe${}_2$
• Emergent pair symmetries in systems with poor man's Majorana modes
• Gapless odd-frequency superconductivity induced by the Sachdev-Ye-Kitaev model
• Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping
• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Signatures of odd-frequency pairing in the Josephson junction current noise
• Spectroscopic and optical response of odd-frequency superconductors
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Ferroelectricity-induced multiorbital odd-frequency superconductivity in SrTiO${}_3$
• Quantum Pairing Time Orders
• Exactly solvable Majorana-Anderson impurity models
• Odd-frequency Pairing in Josephson Junctions Coupled by Magnetic Textures
• Eight-fold classification of superconducting orders