  To construct Lagrangian based on plate theory and tight-binding model,
deflection-field coupling to Dirac fermions in graphene can be investigated. As
have been known, deflection-induced strain may cause an effect on the motion of
the electron, like a pseudo gauge field. In the present work, we will
investigate the effect of the Dirac field on the motion of the deflection-field
in graphene derived from Lagrangian density. Due to the interaction of the
deflection- and Dirac-fields, the current-induced surface-tension up to about
N/m in graphene membrane is predicted. This result may lead to controllable
resonant frequency by currents in graphene. The high resonant frequency is
found to be perfectly linearly controlled by both charge and valley currents.
Our work reveals the potential of graphene for application of
nano-electro-mechanical device and the physics of interaction of electron and
deflection-filed in graphene system is investigated.
