Anomalous spin Nernst effect in Weyl semimetals

Abstract

The spin Nernst effect describes a transverse spin current induced by the longitudinal thermal gradient in a system with the spin–orbit coupling. Here we study the spin Nernst effect in a mesoscopic four-terminal cross-bar Weyl semimetal device under a perpendicular magnetic field. Because the spin current is a tensor, it has three elements with the spin direction pointing to the x, y and z directions when the spin current flows along the transverse lead. By using the tight-binding Hamiltonian combined with the nonequilibrium Green’s function method, the three elements of the spin current in the transverse leads and the spin Nernst coefficients are obtained. The results show that the spin Nernst effect in the Weyl semimetal has an essential difference to the traditional Nernst effect: we found that the z direction spin current is zero without the magnetic field while it appears under the magnetic field, and the x and y direction spin currents in the two transverse leads flow out or in together, in contrast to the traditional spin Nernst effect, in which the spin current is induced by the spin–orbit coupling and flows out from one lead and flows in on the other. We call it the anomalous spin Nernst effect. In addition, we show that the Weyl semimetals have inversion-type symmetry, mirror-reversal-type symmetry and electron–hole-type symmetry, which lead to the spin Nernst coefficients being either odd or even functions of the Fermi energy, the magnetic field and the transverse terminals. Moreover, the spin Nernst effect in the Weyl semimetals are strongly anisotropic and its coefficients are strongly dependent on both the direction of thermal gradient and the direction of the transverse lead connection. Three non-equivalent connection modes (x-z, z-x and x-y modes) are studied in detail, and the spin Nernst coefficients for three different modes exhibit very different behaviors. These strongly anisotropic behaviors of the spin Nernst effect can be used as the characterization of magnetic Weyl semimetals.