The Formation of Majorana Zero Modes in Chiral Carbon Nanotubes under the Influence of Geometric Factors

Abstract

In this paper, we investigate the occurrence of Majorana zero modes in carbon nanotubes in contact with a conventional superconductor and placed in a longitudinal magnetic field. The influence of nanotube geometry, determined by chirality indices \((n,m)\), on the conditions for the formation of the topological superconducting phase is considered. It is shown that chirality changes the electronic structure of the nanotube, the spin–orbit interaction and the effective chemical potential, which determine the conditions of the topological phase transition. To describe the system, an effective model based on the Bogolyubov–de Gennes Hamiltonian is constructed, which allows one to obtain a criterion for the occurrence of Majorana null modes. Based on the developed model, a method for selecting the most favorable geometries of carbon nanotubes is proposed. Numerical results show that certain chiralities minimize the effective chemical potential and facilitate the transition of the system to the topological phase. The obtained results show that the geometry of the carbon nanotube is an effective parameter for controlling the topological properties of the system and can serve as a criterion for choosing the chiralities that are most promising for the experimental implementation of Majorana zero modes.