Edge states at the boundary of graphene-like and Lieb lattices

TL;DR

This paper investigates boundary edge states in graphene-like and Lieb lattices under magnetic fields, revealing their connection to Berry phases and resulting in distinctive features in the density of states.

Contribution

It demonstrates the existence of boundary edge states in graphene-like and Lieb lattices and links their properties to Berry phases, highlighting their impact on the density of states.

Findings

Edge states are present at the boundary of both lattice types.

These edge states are related to trivial and nontrivial Berry phases.

Characteristic features appear in the density of states due to these edge states.

Abstract

Properties of the boundary of two conductors in a quantizing magnetic field are studied: with conventional Dirac charge carriers and so-called pseudospin-1 fermions, which are realized in graphene-like and Lieb lattices respectively. It is shown that edge states arise that relate the properties of conductors to the trivial and nontrivial Berry phase. These edge states lead to the appearance of a characteristic series of root features in the density of states.