Majorana modes in graphene strips: polarization, wavefunctions, disorder, and Andreev states

TL;DR

This paper provides a detailed theoretical analysis of Majorana zero modes in graphene nanoribbons, exploring their topological properties, wavefunctions, and robustness against disorder to guide future quantum device design.

Contribution

It offers a comprehensive study of topological phases in graphene strips with various geometries, identifying conditions for stable Majorana modes and distinguishing them from trivial states.

Findings

Armchair graphene strips with short zigzag edges are most robust.

Majorana polarization and wavefunction analysis effectively identify topological phases.

Disorder impacts the stability of Majorana modes, with certain geometries being more resilient.

Abstract

Topologically protected Majorana zero modes (MZMs) have attracted intense interest due to their potential application in fault-tolerant quantum computation (TQC). Graphene nanoribbons, with tunable edge terminations and compatibility with planar device architectures, offer a promising alternative to semiconductor nanowires. Here we present a comprehensive theoretical study of finite graphene strips with armchair, zigzag, and nearly square geometries, proximitized by an s-wave superconductor and subject to Rashba spin-orbit coupling, Zeeman fields, and disorder. Using exact diagonalization of the Bogoliubov-de Gennes tight-binding Hamiltonian, we analyze Majorana polarization, low-energy spectra, and real-space wavefunctions to identify the non-trivial topological phases supporting MZMs and distinguish them from from partially separated Andreev bound states (psABS) or the quasi-Majoranas. We systematically chart the robustness of these modes across geometries and disorder regimes, finding that armchair strips with short zigzag edges provide the most stable platform. Our results unify polarization diagnostics with spatial wavefunction analysis and disorder effects, yielding concrete design guidelines for graphene-based topological superconductors.