Some Electric, Thermal, and Thermoelectric Properties of Suspended Monolayer Graphene

In this paper we investigate some electric, thermal, and thermoelectric properties of suspended monolayer graphene. By means of a numerical experiment, which was made employing a previously developed macroscopic model for charge and energy transport in graphene, we analyze how fast a suspended graphene sheet heats up when it is subject to a constant homogeneous electric field and how it reaches the equilibrium state once the electric field is turned off. We consider electrons and all phonon branches and show that the influence of the out-of-plane acoustical phonons on the final equilibrium temperature is notable due to their great surface heat capacity. The influence of the electrons on the equilibrium temperature depends on their density; in fact the higher it is, the more energy they gain from the electric field. The behavior of the system can be theoretically justified on the basis of two important physical properties: the conservation of the total energy and the increase of the total entropy of the electron-phonon system; of the latter we give an almost explicit expression. After that, we study the electronic thermal and electric conductivity and the thermopower by finding formulas which express them as functions of the electron and phonon temperatures and the electron density by using a suitable recasting of the macroscopic model in the framework of linear irreversible thermodynamics.