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We investigate geometric phase of fermion states under relative vibrations oftwo sublattices in graphene by solving time-dependent Sch\"{o}dinger equationusing Floquet scheme. In a period of vibration the fermions acquire differentgeometric phases depending on their momenta. There are two regions in themomentum space: the adiabatic region where the geometric phase can beapproximated by the Berry phase and the chaotic region where the geometricphase drastically fluctuates in changing parameters. The energy of fermions dueto vibrations shows spikes in the chaotic region. The results suggest apossible dephasing mechanism which may cause classical-like transportproperties in graphene.

Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty of Fermions in Graphene