Phase Diagram and Edge States of Surface States of Topological Superconductors

Weihao Zhao

doi:10.4236/wjcmp.2021.113005

Abstract

Majorana fermions in two-dimensional systems satisfy non-Abelian statistics. They are possible to exist in topological superconductors as quasi particles, which is of great significance for topological quantum computing. In this paper, we study a new promising system of superconducting topological surface state topological insulator thin films. We also study the phase diagrams of the model by plotting the Majorana edge states and the density of states in different regions of the phase diagram. Due to the mirror symmetry of the topological surface states, the Hamiltonian can be block diagonalized into two spin-triplet p-wave superconductors, which are also confirmed by the phase diagrams. The chiral Majorana edge modes may provide a new route for realizing topological quantum computation.

Highlights

In 1937, Ettore Majorana [1] proposed the existence of a type of fermion, known as Majorana fermion, which is its own antiparticle [2] [3]
Due to the mirror symmetry of the topological surface states, the Hamiltonian can be block diagonalized into two spin-triplet p-wave superconductors, which are confirmed by the phase diagrams
We study the phase diagram, edge state and density distribution diagram of the topological surface state superconducting in detail

Summary

Introduction

In 1937, Ettore Majorana [1] proposed the existence of a type of fermion, known as Majorana fermion, which is its own antiparticle [2] [3]. Because of the non-abelian weaving of Majorana fermions, topological quantum computation can be realized based on them. The quantum anomalous Hall insulator can transform into a two-dimensional chiral topological superconducting phase driven by the s-wave superconducting proximity effect. Topological surface state superconductivity is proposed by Fu-Kane [5], which is realized by inducing superconductivity in topological surface states of strong topological insulators by s-wave superconductivity proximity effect.

Model Hamiltonian

Topological Phase Diagram

Density Distribution of States in Real Space of Wave Function

Conclusion