Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons

TL;DR

This paper investigates the topological phases of electronic edge states in periodically driven zigzag graphene nanoribbons, revealing new types of band touching points and their associated topologically protected edge states.

Contribution

It introduces a comprehensive topological phase diagram for driven graphene nanoribbons and identifies two novel types of band touching points with topological significance.

Findings

Identification of two types of touching band points with Dirac-like features

Confirmation of topologically protected edge states via Berry phase and winding number

Construction of a topological phase diagram based on driving parameters

Abstract

The topological properties of electronic edge states in time-periodically driven spatially-periodic corrugated zigzag graphene nanoribbons are studied. An effective one-dimensional Hamiltonian is used to describe the electronic properties of graphene and the time-dependence is studied within the Floquet formalism. Then the quasienergy spectrum of the evolution operator is obtained using analytical and numeric calculations, both in excellent agreement. Depending on the external parameters of the time-driving, two different kinds (type I and type II) of touching band points are found, which have a Dirac-like nature at both zero and $\pm\pi$ quasienergy. These touching band points are able to host topologically protected edge states for a finite size system. The topological nature of such edge states was confirmed by an explicit evaluation of the Berry phase in the neighborhood of type I touching band points and by obtaining the winding number of the effective Hamiltonian for type II touching band points. Additionally, the topological phase diagram in terms of the driving parameters of the system was built.