Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models

TL;DR

This paper introduces a method to construct low energy effective models for superconducting pairings in generalized Bernevig-Hughes-Zhang systems, clarifying the topological nature of surface Andreev bound states and revealing conditions for multiple SABS pairs.

Contribution

It presents a unified approach to understand pairing and topological surface states in a two-orbital model, identifying conditions for multiple SABS pairs and their connection to topological states.

Findings

Identified conditions for two pairs of SABSs.

Showed SABSs connect with topological surface states.

Provided a simple characterization of SABS anisotropy.

Abstract

A method for constructing the low energy effective models for pairings in the generalized Bernevig-Hughes-Zhang model for materials like Bi$_{2}$Se$_{3}$ is proposed. Pairings in this two-orbital model are identified with those familiar in one-orbital models, enabling a unified understanding. The theory provides an easy way to understand the topological nature of the superconducting state that is not directly related to the topological order in the normal state but due to subtle coupling among the degrees of freedom. Furthermore this approach shows a simple way to characterize the anisotropic nature of surface Andreev bound states (SABSs). In particular, we have identified the conditions to have a surprising new result of having two pairs of SABSs. It also leads to a conclusion that SABSs always connect with the topological surface states if the latter are well defined at the chemical potential.