# Transverse profile and 3D spin canting of a Majorana state in carbon nanotubes

## TL;DR

This paper provides a detailed 3D spatial and spin profile of Majorana bound states in carbon nanotubes, revealing their helical structure and symmetry properties through analytical and numerical methods.

## Contribution

It introduces an analytical reconstruction of the Majorana wave function in CNTs considering spin and valley degrees of freedom, highlighting the lattice's chiral imprint.

## Key findings

- Majorana wave function has a helical, anisotropic transverse structure.
- Spin canting angle exhibits a spiral pattern around the CNT circumference.
- Three contributions to the MBS are identified from Fourier analysis.

## Abstract

The full spatial 3D profile of Majorana bound states (MBS) in a nanowire-like setup featuring a semiconducting carbon nanotube (CNT) as the central element is discussed. By accurate tight-binding calculations we show that the chiral nature of the CNT lattice is imprinted in the MBS wave function which has a helical structure, anisotropic in the transverse direction. The local spin canting angle displays a similar spiral pattern, varying around the CNT circumference. We reconstruct the intricate 3D profile of the MBS wave function analytically, using an effective low energy Hamiltonian accounting both for the electronic spin and valley degrees of freedom of the CNT. We find that the four components of the Majorana spinor are related by the three symmetries of our Bogoliubov-de Gennes (BdG) Hamiltonian, reducing the number of independent components to one. A Fourier transform analysis uncovers the presence of three contributions to the MBS, one from the $\Gamma$-point and one from each of the Fermi points, with further complexity added by the presence of two valley states in each contribution.