Tunneling spin Nernst effect for a single quantum dot

We describe theoretically the spin Nernst effect for electrons tunneling to a quantum dot from a quantum wire with the heat flowing along it. Such a tunneling spin Nernst effect is shown to take place due to the spin-dependent electron tunneling produced by the spin-orbit coupling. The Coulomb interaction of electrons in the quantum dot is taken into account using nonequilibrium Green's functions and is shown to increase significantly the accumulated spin in a single quantum dot. The largest possible degree of spin polarization is discussed.