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We study the emergence of electronic non-trivial topological flat bands intime-periodically driven strained graphene within a tight binding approachbased on the Floquet formalism. In particular, we focus on uniaxial spatiallyperiodic strain since it can be mapped onto an effective one-dimensionalsystem. Also, two kinds of time-periodic driving are considered: a short pulse(delta kicking) and a sinusoidal variation (harmonic driving). We prove thatfor special strain wavelengths, the system is described by a two level DiracHamiltonian. Even though the study case is gapless, we find that topologicallynon-trivial flat bands emerge not only at zero-quasienergy but also at $\pm\pi$quasienergy, the latter being a direct consequence of the periodicity of theFloquet space. Both kind of flat bands are thus understood as dispersionlessbands joining two inequivalent touching band points with opposite Berry phase.This is confirmed by explicit evaluation of the Berry phase in the touchingband points' neighborhood. Using that information, the topological phasediagram of the system is built. Additionally, the experimental feasibility ofthe model is discussed and two methods for the experimental realization of ourmodel are proposed.

Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons