Effect of edge decoration on the energy spectrum of semi-infinite lattices

TL;DR

This paper analytically investigates how edge decoration influences the energy spectrum and edge states in semi-infinite lattices, including 1D chains with Peierls transition and zigzag-edged graphene, revealing conditions for edge state existence and manipulation.

Contribution

It provides a comprehensive analytical framework using transfer matrix method to determine conditions for edge states in decorated semi-infinite lattices, including novel edge state control.

Findings

Zero-energy edge states occur with Peierls transition regardless of decoration.

Non-zero-energy edge states can be induced and tuned via edge decoration.

Edge decoration conditions determine the existence of novel edge states in ZEG.

Abstract

Analytical studies of the effect of edge decoration on the energy spectrum of semi-infinite one-dimensional (1D) lattice chain with Peierls phase transition and zigzag edged graphene (ZEG) are presented by means of transfer matrix method, in the frame of which the sufficient and necessary conditions for the existence of the edge states are determined. For 1D lattice chain, the zero-energy edge state exists when Peierls phase transition happens regardless whether the decoration exists or not, while the non-zero-energy edge states can be induced and manipulated through adjusting the edge decoration. On the other hand, the semi-infinite ZEG model with nearest-neighbor interaction can be mapped into the 1D lattice chain case. The non-zero-energy edge states can be induced by the decoration as well, and we can obtain the condition of the decoration on the edge for the existence of the novel edge states.