  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.
