Majorana quasiparticles in semiconducting carbon nanotubes

TL;DR

This paper demonstrates that semiconducting carbon nanotubes coupled with ultrathin s-wave superconductors can host Majorana quasiparticles, with localized zero-energy states confirmed as Majorana modes through numerical and analytical models.

Contribution

It shows that CNTs with ultrathin s-wave superconductors can realize topological superconductivity and Majorana quasiparticles under feasible experimental conditions.

Findings

Localized zero-energy states appear at CNT ends above a critical magnetic field.

Numerical calculations confirm the Majorana nature of these states.

Analytical models map the topological phase diagram.

Abstract

Engineering effective p-wave superconductors hosting Majorana quasiparticles (MQPs) is nowadays of particular interest, also in view of the possible utilization of MQPs in fault-tolerant topological quantum computation. In quasi one-dimensional systems, the parameter space for topological superconductivity is significantly reduced by the coupling between transverse modes. Together with the requirement of achieving the topological phase under experimentally feasible conditions, this strongly restricts in practice the choice of systems which can host MQPs. Here we demonstrate that semiconducting carbon nanotubes (CNTs) in proximity with ultrathin s-wave superconductors, e.g. exfoliated NbSe$_2$, satisfy these needs. By precise numerical tight-binding calculations in the real space we show the emergence of localized zero-energy states at the CNT ends above a critical value of the applied magnetic field. Knowing the microscopic wave functions, we unequivocally demonstrate the Majorana nature of the localized states. An accurate analytical model Hamiltonian is used to calculate the topological phase diagram.