Non-linear resistivity and heat dissipation in monolayer graphene
  We have experimentally studied the nonlinear nature of electrical conduction in monolayer graphene devices on silica substrates. This nonlinearity manifests itself as a nonmonotonic dependence of the differential resistance on applied DC voltage bias across the sample. At temperatures below ~70K, the differential resistance exhibits a peak near zero bias that can be attributed to self-heating of the charge carriers. We show that the shape of this peak arises from a combination of different energy dissipation mechanisms of the carriers. The energy dissipation at higher carrier temperatures depends critically on the length of the sample. For samples longer than 10um the heat loss is shown to be determined by optical phonons at the silica-graphene interface. 
A. S. Price, S. M. Hornett, A. V. Shytov, E. Hendry, D. W. Horsell
cond-mat.mes-hall cond-mat.mtrl-sci