Smoothly varying lattice strain in graphene affects the Dirac carriers through a synthetic gauge field. When the lattice strain is time dependent, as in connection with phononic excitations, the gauge field becomes time dependent and the synthetic vector potential is also associated with an electric field. We show that this synthetic electric field has observable consequences. Joule heating associated with the currents driven by the synthetic electric field dominates the intrinsic damping, caused by the electron-phonon interaction, of many acoustic phonon modes of graphene and metallic carbon nanotubes when including the effects of disorder and Coulomb interactions. Several important consequences follow from the observation that by time-reversal symmetry, the synthetic electric field associated with the vector potential has opposite signs for the two valleys. First, this implies that the synthetic electric field drives charge-neutral valley currents and is therefore unaffected by screening. This frequently makes the effects of the synthetic vector potential more relevant than a competing effect of the scalar deformation potential which has a much larger bare coupling constant. Second, valley currents decay by electron-electron scattering (valley Coulomb drag) which causes interesting temperature dependence of the damping rates. While our theory pertains first and foremost to metallic systems such as doped graphene and metallic carbon nanotubes, the underlying mechanisms should also be relevant for semiconducting carbon nanotubes when they are doped.
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