Exchange and electric fields enhanced spin thermoelectric performance of germanene nano-ribbon

The spin thermoelectric performance in a germanene nano-ribbon is studied by using the nonequilibrium Green’s function method. We demonstrate theoretically that the temperature bias Δ T can generate spin thermopower when an exchange field breaks the edge states of germanene leads. However, the spin thermoelectric efficiency is quite low with its maximum {{Z}_s}T≃ 0.01 . When applying strong electric field in the central region, a relatively large spin-dependent band gap can be opened, and hence the spin figure of merit is predicted to be more than 100 times larger than the case without external field. The remarkably enhancement of ZsT (larger than one) comes from the suppression of the thermal conductance and the improvement of the spin Seebeck effect. These striking properties make ferromagnetic leads germanene nano-ribbon a promising pure spin thermoelectric nanogenerator.