Nernst effect in anisotropic four-terminal topological nodal-line semimetals

The Nernst effect is the transverse mode of thermoelectric transport, in which a longitudinal thermal gradient induces a transverse current in the conductor while under a perpendicular magnetic field. Here the Nernst effect in a mesoscopic topological nodal-line semimetals (TNLSMs) system of four-terminal cross-bar with the spin-orbit coupling under a perpendicular magnetic field is studied. The Nernst coefficient N-c in two non-equivalen connection modes (k(z)-y mode and k(x)-y mode) is calculated based on the tight-binding Hamiltonian combined with the nonequilibrium Green's function method. When the magnetic field is absent with phi= 0.0, the Nernst coefficient N-c = 0 is exactly regardless of the temperature. When the magnetic field is not zero, the Nernst coefficient exhibits a series of densely oscillating peaks. The height of peak strongly depends on the magnetic field, and the Nernst coefficient is an even function of the Fermi energy EF satisfying the symmetrical property N-c(-EF) = N-c(EF). The Nernst coefficient is also closely related to the temperature T. When the temperature is very low (or T. 0), the Nernst coefficient depends linearly on temperature. In the presence of a strong magnetic field, the Nernst coefficient shows peaks when the Fermi energy crosses the Landau levels. Under the weak magnetic field, the influence of spin-orbit coupling in TNLSMs materials on Nernst effect is very obvious. In the presence of the mass term, the PT-symmetry of the system is destroyed, the nodal ring of TNLSMs is broken and an energy gap will be opened. The Nernst coefficient N-c has a large value in the energy gap, which is very promising for the application of the transverse thermoelectric transport.