Seebeck effects in two-dimensional spin transistors

We consider a spin-orbit-coupled two-dimensional electron system under the influence of a thermal gradient externally applied to two attached reservoirs. We discuss the generated voltage bias (charge Seebeck effect), spin bias (spin Seebeck effect) and magnetization-dependent thermopower (magneto-Seebeck effect) in the ballistic regime of transport at linear response. We find that the charge thermopower is an oscillating function of both the spin-orbit strength and the quantum well width. We also observe that it is always negative for normal leads. We carefully compare the exact results for the linear response coefficients and a Sommerfeld approximation. When the contacts are ferromagnetic, we calculate the spin-resolved Seebeck coefficient for parallel and antiparallel magnetization configuration. Remarkably, the thermopower can change its sign by tuning the Fermi energy. This effect disappears when the Rashba coupling is absent. Additionally, we determine the magneto-Seebeck ratio, which shows dramatic changes in the presence of a the Rashba potential.