Charge Transport in graphene including thermal effetcs

In this paper we present a hydrodynamical model for the description of the charge 7 transport in graphene, including heating eects on the crystal lattice, and conversely the in uence of 8 crystal heating on charge transport. The state variables used for the physical system are moments 9 of the electron, hole, and phonon occupation numbers, and their evolution equations are derived 10 by integration from the respective Boltzmann equations. The closure of the system is obtained by 11 means of the maximum entropy principle and all the main scattering mechanisms between charges 12 and phonons and among phonons themselves are taken into account. Numerical simulations are 13 presented in the case of a graphene monolayer, evaluating the in uence of the optical and acoustical 14 phonons dynamics on the current-voltage characteristics and the raise rate of the lattice temperature.