Magnetoinduced spin Nernst effect in topological nodal-line semimetals

The spin Nernst effect (SNE) of a topological nodal-line semimetals (TNLSMs) nanowire in a four-terminal cross-bar device is studied. Based on the nonequilibrium Green's function method combining with the tight-binding Hamiltonian, the spin Nernst coefficients Ns3z, Ns3x and Ns3y of the two thermal transport models (kz-y case and kx-y case) under a perpendicular magnetic field are obtained. The traditional SNE describes the transverse voltage and spin current caused by the longitudinal thermal gradient. The transverse spin current is generated by the spin–orbit interaction rather than the perpendicular magnetic field. Here we find that the spin Nernst coefficients are equal to zero at the zero-magnetic field, but have finite values for non-zero magnetic fields in TNLSMs. The spin Nernst coefficient is closely related to the strength of the magnetic field and temperature. With the increase of the magnetic field strength, the peak height of the spin Nernst coefficient increases. These results indicate that the SNE is induced by the perpendicular magnetic field in the present TNLSMs system, which can be considered as an anomalous spin Nernst phenomenon. In addition, we find that Ns3z displays a series of peaks when the transmission coefficient TLR jumps from one integer plateau to another, and the spin Nernst coefficient Ns3i (i=x,y,z) is an odd function of the Fermi energy EF with Ns3z/x/y(−EF)=−Ns3z/x/y(EF) in connection mode kz-y. For the kx-y connection mode, due to the presence of the mass term m opening the energy gap, a sudden jump of the transmission coefficient TLR in the vicinity of the energy gap edge causes a very larger peak for the spin Nernst coefficient Ns3z/x/y, and the symmetrical properties of the spin Nernst coefficient Ns3z/x/y are completely broken in the strong magnetic field. These results indicate that the spin Nernst coefficient in TNLSMs strongly depends on the thermal gradient direction and the transverse lead connection direction. The spin Nernst coefficient in TNLSMs has strongly spatial anisotropy, which can be used as the characterization of the experimental detection of TNLSMs.