Topological in-gap chiral edge states in superconducting Haldane model with spin-orbit coupling

TL;DR

This paper investigates topological superconductivity in the Haldane model with spin-orbit coupling, revealing in-gap chiral edge states that are confirmed through band inversion and real-space lattice analysis.

Contribution

It demonstrates that spin-orbit coupling enables edge modes to lie within the superconducting gap, leading to gapless states, a novel finding in the Haldane model context.

Findings

Edge states can exist within the superconducting gap due to spin-orbit coupling.

The topological and chiral nature of edge states is confirmed via band inversion and real-space analysis.

Presence of gapless states for certain parameter ranges.

Abstract

Topological superconductivity is currently one of the prime interests, given the properties of its exotic nature of chiral edge states. A broken time-reversal symmetry (TRS) is an essential ingredient in the recipe of a chiral edge state. The Haldane model is one of the many factors that can break TRS in a system. Thus, we explore the possibility of topological superconductivity in the Haldane model under the influence of a conventional superconductor. The edge states originating from such recipes mostly remain outside the superconducting gap. Contrary to this, in the presence of spin-orbit coupling, the edge modes lie within the superconducting gap, and can lead to a gapless state for some range of parameters. Moreover, we use band inversion and projection on the real-space lattice to confirm the topological and chiral nature of the obtained edge states.