Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with $d$-wave superconductors

TL;DR

This paper investigates the behavior of Majorana fermions in a 2D electron gas with spin-orbit coupling and a d-wave superconductor, revealing their localization, oscillation, and robustness, with implications for quantum technologies.

Contribution

It introduces a microscopic lattice model with d-wave pairing, derives its topological invariant, and demonstrates the robustness of Majorana fermions against disorder.

Findings

Majorana fermions exhibit similar localization and oscillation properties as in s-wave superconductors.

The lattice model includes nearest and next-to-nearest neighbor pairing.

Chiral Majorana fermions are robust against static disorder.

Abstract

We study the localization and oscillation properties of the Majorana fermions that arise in a two-dimensional electron gas (2DEG) with spin-orbit coupling (SOC) and a Zeeman field coupled with a d-wave superconductor. Despite the angular dependence of the d-wave pairing, localization and oscillation properties are found to be similar to the ones seen in conventional s-wave superconductors. In addition, we study a microscopic lattice version of the previous system that can be characterized by a topological invariant. We derive its real space representation that involves nearest and next-to-nearest-neighbors pairing. Finally, we show that the emerging chiral Majorana fermions are indeed robust against static disorder. This analysis has potential applications to quantum simulations and experiments in high-$T_c$ superconductors.