Corner Majorana states in semi-Dirac materials

TL;DR

This paper proposes a theoretical method to realize Majorana bound states in semi-Dirac materials by inducing topological superconductivity at their edges, enabling potential quantum computing applications.

Contribution

It introduces a framework for generating Majorana modes in semi-Dirac systems through edge state manipulation and proximity effects, without complex nanostructures.

Findings

Edge states can host non-chiral modes propagating along specific edges.

Applying Rashba spin-orbit coupling and Zeeman field induces effective p-wave pairing.

Corner modes emerge as zero-energy Majorana states in finite geometries.

Abstract

Proximity-induced superconductivity in low-dimensional systems offers a powerful pathway to engineer topological superconducting phases in, otherwise, non-superconducting systems. These exotic phases are of fundamental and technological interest due to the presence of robust zero-energy modes, the Majorana bound states. In this work, we propose a theoretical framework to realize Majorana bound states from the edge states of a two-dimensional semi-Dirac system. This anisotropic system, under specific conditions, can host non-chiral edge states that propagate only along particular edges, effectively forming separated one-dimensional channels. We show that the interplay between Rashba spin-orbit coupling and a Zeeman field on this setup provides the right conditions to get an effective p-wave pairing between the edge states by proximity with a s-wave superconductor. In finite geometries, each edge can independently undergo a topological phase transition into a one-dimensional topological superconductor and give rise to four zero-energy modes localized at the strip corners. At low energies, the edge states subspace admits a description in terms of coupled Kitaev chains, providing a clear picture of the origin, robustness, and tunability of the corner Majorana modes. Our results establish semi-Dirac materials as a natural platform for realizing Majorana modes in two dimensions without relying on engineered nanostructures, vortices, or crystalline higher-order topology.