Electric-Field Induced Majorana Fermions in Armchair Carbon Nanotubes

TL;DR

This paper theoretically demonstrates that applying an electric field to an armchair carbon nanotube in contact with a superconductor can induce Majorana fermions by creating tunable superconducting gaps of different types, supporting potential quantum computing applications.

Contribution

It introduces a novel setup where electric fields and proximity effects in armchair CNTs enable the realization of Majorana bound states, including the influence of electron-electron interactions.

Findings

Superconducting gaps of different strengths are induced in CNT branches.

Majorana bound states are supported at each end of the CNT.

Majorana states persist even with electron-electron interactions.

Abstract

We consider theoretically an armchair Carbon nanotube (CNT) in the presence of an electric field and in contact with an s-wave superconductor. We show that the proximity effect opens up superconducting gaps in the CNT of different strengths for the exterior and interior branches of the two Dirac points. For strong proximity induced superconductivity the interior gap can be of the p-wave type, while the exterior gap can be tuned by the electric field to be of the s-wave type. Such a setup supports a single Majorana bound state at each end of the CNT. In the case of a weak proximity induced superconductivity, the gaps in both branches are of the p-wave type. However, the temperature can be chosen in such a way that the smallest gap is effectively closed. Using renormalization group techniques we show that the Majorana bound states exist even after taking into account electron-electron interactions.