  We calculate the phonons in a graphene nanoconstriction(GNC) in the presence
of a high current density. The Joule-heating, current-induced forces, and
coupling to electrode phonons is evaluated using first principles
nonequilibrium DFT-NEGF calculations. Close to a resonance in the electronic
structure we observe a strongly nonlinear heating with bias and breakdown of
the harmonic approximation. This behavior results from negatively damped
phonons driven by the current. The effect may limit the stability and capacity
of graphene nanoconstrictions to carry high currents.
