Emergence of dynamical energy gap in an oscillating graphene membrane*

One intriguing aspect of graphene is the effect of strain on its electronic properties, which manifests as a pseudo-magnetic field producing peculiar local charge distributions and Landau level-like flat bands. It is challenging however, to generate global energy gaps for semiconductor applications- the strain needed is either too large or requires precise engineering. Irradiation with polarized light has been proposed as a mechanism for gap generation, but the high frequency and intensity needed may induce sample damage. Oscillating mechanical deformations appear like an alternative that is particularly well suited for suspended samples. Besides, spatial strain variation allows more flexibility in gap engineering. We study the effect of a Gaussian-shaped deformation in graphene with a time-periodic amplitude. Using an effective Floquet Hamiltonian, we predict the appearance of anisotropic dynamical gaps with Green’s function methods and degenerate perturbation theory. The profile of the gap closely follows the modulations in the local density of states caused by strain. We find that the optimal regime for gap generation occurs when a deformation extends over the whole sample, with a magnitude determined by its geometrical parameters.