Topological Edge States of a Majorana BBH Model

Alfonso Maiellaro,Roberta Citro

doi:10.3390/condmat6020015

Abstract

We investigate a Majorana Benalcazar–Bernevig–Hughes (BBH) model showing the emergence of topological corner states. The model, consisting of a two-dimensional Su–Schrieffer–Heeger (SSH) system of Majorana fermions with π flux, exhibits a non-trivial topological phase in the absence of Berry curvature, while the Berry connection leads to a non-trivial topology. Indeed, the system belongs to the class of second-order topological superconductors (HOTSC2), exhibiting corner Majorana states protected by C4 symmetry and reflection symmetries. By calculating the 2D Zak phase, we derive the topological phase diagram of the system and demonstrate the bulk-edge correspondence. Finally, we analyze the finite size scaling behavior of the topological properties. Our results can serve to design new 2D materials with non-zero Zak phase and robust edge states.

Highlights

The notion of higher order topological phases first appeared for insulating systems (HOTIs) [1,2,3,4]
Non-trivial topological corner states associated with 2D Zak phases are shown in panel (b) of Figure 3, where we fix the parameters to those corresponding to the red circle of panel
We have proposed and analyzed the topological phases of a Majorana BBH model, consisting of a Majorana 2D SSH model with a synthetic magnetic flux of π

Summary

Introduction

The notion of higher order topological phases first appeared for insulating systems (HOTIs) [1,2,3,4]. A second-order topological insulator is a d dimensional system with gapped d − 1 dimensional boundaries and d − 2 localized modes (corner states in two-dimensional systems). This new topological phase can be protected by a variety of crystalline symmetries, such as reflection symmetries and C4 symmetry [1]. Topological insulators are phases of matter characterized by topological edge states that propagate in a unidirectional manner that is robust to imperfections and disorder. They propose a concept that exploits topological effects in a unique way: Condens. −iw associated with continuous red lines and −iv associated to dashed red lines

Topological Phase

Topological Properties of Finite Size Systems

Conclusions