Thermoelectric and thermospin transport in a ballistic junction of graphene

We consider theoretically a wide graphene ribbon, that on both ends is attached to electronic reservoirs which generally have different temperatures. The graphene ribbon is assumed to be deposited on a substrate, that leads to a spin-orbit coupling of Rashba type. We calculate the thermally induced charge current in the ballistic transport regime as well as the thermoelectric voltage (Seebeck effect). Apart from this, we also consider thermally induced spin current and spin polarization of the graphene ribbon. The spin currents are shown to have generally two components; one parallel to the temperature gradient and the other one perpendicular to this gradient. The latter corresponds to the spin current due to the spin Nernst effect. Additionally, we also consider the heat current between the reservoirs due to transfer of electrons.