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 coefficientNcin two non-equivalen connection modes (kz-ymode andkx-ymode) is calculated based on the tight-binding Hamiltonian combined with the nonequilibrium Green's function method. When the magnetic field is absent withφ = 0.0, the Nernst coefficientNc=0is 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 energyEFsatisfying the symmetrical propertyNc(-EF)=Nc(EF). The Nernst coefficient is also closely related to the temperatureT. When the temperature is very low (orT→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, thePT-symmetry of the system is destroyed, the nodal ring of TNLSMs is broken and an energy gap will be opened. The Nernst coefficientNchas a large value in the energy gap, which is very promising for the application of the transverse thermoelectric transport.

Linear and nonlinear thermoelectric transport in a quantum spin Hall insulators coupled with a nanomagnet.

Thermoelectric effects in quantum systems have been focused in recent years. Thermoelectric energy conversion study of systems with edge states, such as quantum Hall insulators and quantum spin Hall insulators, is one of the most important frontier topics in material science and condensed-matter physics. Based on the previous paper (Gresta in Phys Rev Lett 123:186801, 2019), we further investigated the linear and nonlinear thermoelectric transport properties of helical edge states of the quantum spin Hall insulators coupled with double nanomagnet, calculated the Seebeck coefficients [Formula: see text] and the thermoelectrical figure of merit ZT, discussed the influence of the length of the nanomagnet and the relative tilt angle of component of the magnetization perpendicular on the thermoelectric coefficients ([Formula: see text] and ZT), and summarized some meaningful conclusions in the linear response regime. In the nonlinear regime, we calculated the equivalent figure of merit [Formula: see text] and the power-generation efficiency [Formula: see text] in different length of the nanomagnet, obtain the temperature difference of achieving optimal thermoelectricity. The results of this paper further confirm that the setup can indeed be used as a device for achieving high performance thermoelectric.

Thermoelectric transport in two-terminal topological nodal-line semimetals nanowires.

Recently discovered topological nodal-line semimetals (TNLSMs) have received considerable research interest due to their rich physical properties and potential applications. TNLSMs have the particular band structure to lead to many novel properties. Here we theoretically study the thermoelectric transport of a two-terminal pristine TNLSM nanowires and TNLSMsp-n-pjunctions. The Seebeck coefficientsScand the thermoelectrical figure of meritZTare calculated based on the Landauer-Büttiker formula combined with the nonequilibrium Green's function method. In pristine TNLSM nanowires, we discuss the effect of the magnetic fieldsφ, the disorderD, the on-site energyµz, and the mass termmon the thermoelectric coefficient and find that the transport gap can lead to a largeScandZT. When transmission coefficient jumps from one integer plateau to another,ScandZTshow a series of peaks. The peaks ofScandZTare determined by the jump of the transmission coefficient plateau and are not associated with the plateau itself. For TNLSMsp-n-pjunctions,ScandZTstrongly depend on the parameterξof potential well. We can get a largeZTby adjusting the parameterξand magnetic fieldφ. In TNLSMsp-n-pjunctions,ZThas the large value and is easily regulated. This setup has promising application prospects as a thermoelectric device.

Anomalous spin Nernst effect in Weyl semimetals.

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.