Spin Nernst effect and Nernst effect in two-dimensional electron systems

We study the Nernst effect and the spin Nernst effect and show that a longitudinal thermal gradient induces a transverse voltage and a spin current. A mesoscopic four-terminal cross-bar device having the Rashba spin-orbit interaction (SOI) under a perpendicular magnetic field is considered. For zero SOI, the Nernst coefficient peaks when the Fermi level crosses the Landau levels. In the presence of the SOI, the Nernst peaks split and the spin Nernst effect appears and exhibits a series of oscillatory structures. The larger the SOI or the weaker the magnetic field is, the more pronounced the spin Nernst effect is. The results also show that the Nernst and spin Nernst coefficients are sensitive to the detailed characteristics of the sample and the contacts. In addition, the Nernst effect is found to survive in strong disorder better than the spin Nernst effect.