Topological edge states on time-periodically strained armchair graphene nanoribbons

TL;DR

This paper investigates the emergence of topological edge states in time-periodically strained armchair graphene nanoribbons, revealing both gapless and gapped phases with unique edge states through numerical and analytical methods.

Contribution

It introduces a novel analysis of topological edge states in periodically driven strained graphene nanoribbons using Floquet formalism and analytical spectrum calculations.

Findings

Edge states appear in both gapped and gapless phases.

Zero quasienergy edge states exist despite zero Chern number.

Topological modes emerge at band edge crossings as a function of driving period.

Abstract

We report the emergence of electronic edge states in time-periodically driven strained armchair terminated graphene nanoribbons. This is done by considering a short-pulse spatial-periodic strain field. Then, the tight-binding Hamiltonian of the system is mapped into a one dimensional ladder. The time periodicity is considered within the Floquet formalism. Thus the quasienergy spectrum is found numerically by diagonalizing the evolution operator. For some particular cases, the quasienergy spectrum is found analytically. We find that the system is able to support gapless and gapped phases. Very different edge states emerge for both the gapless and the gapful phases. In the case of the gapped phase, edge states emerge at the gap centered at zero quasienergy, although the Chern number is zero due to the chiral symmetry of the system. For the gapless phase, besides edge states at zero quasienergy, cosine like edge states which merge and coexist with the bulk band are observed. To confirm the topological nature of these edge states, we analytically obtained the effective Hamiltonian and its spectrum for a particular case, finding that the edge states are topologically weak. Finally, we found analytically the evolution of band edges and its crossings as a function of the driven period. Topological modes arise at such crossings.