Edge states in a honeycomb lattice: effects of anisotropic hopping and mixed edges

TL;DR

This paper investigates how mixed edge types and anisotropic electron hopping in graphene affect edge states and local density of states, highlighting implications for interpreting scanning tunneling microscopy data.

Contribution

It introduces the combined effects of mixed edges and anisotropic hopping on edge states in graphene, which were not thoroughly explored before.

Findings

Mixed edges smear the LDOS enhancement at E=0 in zigzag graphene.

Anisotropic hopping enhances LDOS at E=0 in armchair graphene.

Careful interpretation of STM data is necessary due to these effects.

Abstract

We study the edge states in graphene in the presence of a magnetic field perpendicular to the plane of the lattice. Most of the works done so far discuss the edge states in either zigzag or armchair edge graphene considering an isotropic electron hopping. In practice, graphene can have mixture of armchair and zigzag edges and the electron hopping can be anisotropic, which is the subject of this article. We predict that the mixed edges smear the enhanced local density of states (LDOS) at E=0 of the zigzag edge and, on the other hand, the anisotropic hopping gives rise to the enhanced LDOS at E=0 in the armchair edge. The behavior of the LDOS can be studied using scanning tunneling microscopy (STM) experiments. We suggest that care must be taken while interpreting the STM data. It is because the clear distinction between the zigzag edge (enhanced LDOS at E=0) and armchair edge (suppressed LDOS at E=0) can be lost if the hopping is not isotropic and if the edges are mixed.