Topological Phases of an Interacting Majorana Benalcazar–Bernevig–Hughes Model

Alfonso Maiellaro,Roberta Citro,Fabrizio Illuminati

doi:10.3390/condmat7010026

Abstract

We study the effects of Coulomb repulsive interactions on a Majorana Benalcazar–Bernevig–Huges (MBBH) model. The MBBH model belongs to the class of second-order topological superconductors (HOTSC2), featuring robust Majorana corner modes. We consider an interacting strip of four chains of length L and perform a density matrix renormalization group (DMRG) numerical simulation based on a tensor-network approach. Study of the non-local fermionic correlations and the degenerate entanglement spectrum indicates that the topological phases are robust in the presence of interactions, even in the strongly interacting regime.

Highlights

In recent years, higher-order topological superconductors (HOTSCs) have attracted significant interest and have been investigated in depth as novel platforms to realize topological superconductivity [1–5]
In Ref. [13], we introduced a model of second-order topological superconductor (HOTSC2 ) based on Majorana fermions (Mfs) operators
In order to go beyond the mean field treatment, we add repulsive Coulomb interactions to the Majorana Benalcazar–Bernevig– Huges (MBBH) model with the aim of gaining insight on how the interactions affect the stability of the topological phases, which is still an open problem despite intense investigations [23,35–37]

Summary

Introduction

Higher-order topological superconductors (HOTSCs) have attracted significant interest and have been investigated in depth as novel platforms to realize topological superconductivity [1–5]. Aside from their theoretical interest, such systems are potentially relevant for applications; in particular, devices based on two-dimensional. The topology of the system is intrinsically two-dimensional, the quasi one-dimensional case provides signatures of the robustness of the topological regime against repulsive interactions These robust fermionic modes are expected to split into corner Majorana modes for a fully two-dimensional square lattice system with length L equal to the width N. Appendix A contains details on the matrix product operator (MPO) tensors built for our model

Majorana BBH Model

Strip of Four Interacting Chains

Analytical Results

Numerical Results

Conclusions