Chiral Majorana Edge Modes and Vortex Majorana Zero Modes in Superconducting Antiferromagnetic Topological Insulator

TL;DR

This paper explores how superconducting pairings affect antiferromagnetic topological insulators, revealing the distribution of Majorana modes and the impact of exchange fields on vortex phases, advancing understanding of topological superconductivity.

Contribution

It demonstrates the distribution of chiral Majorana modes in multilayer AFTI and shows how exchange fields enhance topological vortex phases.

Findings

Majorana edge modes can localize near surface layers or occupy all layers depending on parameters.

The local Chern number distribution influences the spatial localization of Majorana modes.

Exchange fields expand the topological vortex phase space and improve stability.

Abstract

The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetry $\mathcal{T}_c$. In this paper we investigate the effects of the $s$-wave superconducting pairings on the multilayers of AFTI, which breaks $\mathcal{T}_c$ symmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern number $C=\pm 2$. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.