A rigorous proof of non-existence of edge state in the semi-infinite armchair edged graphene

TL;DR

This paper rigorously proves that edge states do not exist in semi-infinite armchair edged graphene using transfer matrix methods, clarifying the conditions under which edge states can or cannot occur.

Contribution

It provides an analytical and rigorous proof of the non-existence of edge states in semi-infinite armchair edged graphene, clarifying previous ambiguities.

Findings

Edge states do not exist in the model for semi-infinite armchair edged graphene.

Zero-energy and non-zero-energy edge states are absent in this configuration.

The transfer matrix method effectively demonstrates the non-existence of edge states.

Abstract

With the help of transfer matrix method, the conditions for the existence of the edge states in the semi-infinite armchair edged graphene is given. We discuss zero-energy and non-zero-energy edge states separately, and show the nonexistence of the edge states in the model analytically and rigorously.