Theoretical elucidation of possibility of Majorana modes in a two dimensional Dirac system

TL;DR

This paper provides a theoretical analysis of conditions under which Majorana-like modes could exist in a two-dimensional Dirac system, emphasizing the roles of valley-mixing, spin-orbit coupling, and specific material properties.

Contribution

It introduces a theoretical framework showing how Majorana modes can be realized in 2D Dirac materials like graphene and silicene through engineered spin-orbit coupling and valley interactions.

Findings

Majorana modes possible near Dirac points with valley-mixing and spin degeneracy lifting.

Strong spin-orbit coupling achievable via material deformation or buckling.

Valley-spin locking in VSPM phase enables conditions for Majorana modes.

Abstract

Here we present the theoretical clarification of possibility of eight Majorana-like modes (quasi-particles which are self-conjugate) close to the experimentally inaccessible Dirac points of a two-dimensional monolayer Dirac system. The valley-mixing and the spin-degeneracy lifting are the main requirements. These are possible by wedging in the requisite ingredients in the description, viz. the atomically sharp scatterers and the strong spin-orbit coupling (SOC). The latter can possibly be achieved in graphene folding a sheet; the higher curvature of deformations correspond to stronger values of the coupling. In silicene, the buckled structure of the system generates a staggered sub-lattice potential between silicon atoms at A sites and B sites for an applied electric field perpendicular to its plane. The stronger SOC in silicene has its origin also in the buckled structure of the system. Tuning of electric field, allows for rich behavior varying from a topological insulator to a normal insulator with a valley spin-polarized metal (VSPM) at a critical value in between. The VSPM stage is characterized by the valley-spin locking, i.e. the opposite spin polarization at different valleys. We shall see that in this phase, if the inter-valley scattering process and the real spin-flip process in moderation are allowed to take place, we have the right condition for capturing Majoranas in the proximity of a s-wave superconductor.