Spin Nernst effect in the absence of a magnetic field Xuele Liu 1 and X.C. Xie 1 , 2 $^{1}$Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078 $^{2}$Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China We study the spin Nernst effect of a mesoscopic four-terminal cross-bar device with the Rashba spin-orbit interaction (SOI) in the absence of a magnetic field. The interplay between the spin Nernst effect and the seebeck coefficient is investigated for a wide range of the Rashba SOI. When no peaks appeared in the seebeck coefficient, an oscillatory spin Nernst effect still occurs. In addition, the disorder effect on the spin Nernst effect is also studied. We find that the spin Nernst effect can be enhanced up to three-fold by disorder. Besides, due to the interface effect, the counter-propagating of the charge current to the direction of the temperature gradient is possible for a nonuniform system. PACS numbers: 72.15.Jf,72.25.-b, 73.23.-b, 73.43.-f Keywords: A. Rashba spin-orbit interaction; C. Disorder; D. Spin Nernst Effect; D. seebeck coefficient With the development of the micro-fabrication technol- ogy and the low-temperature measurement technology, a great amount of efforts have been paid for the research of the thermoelectric properties in the last two decades $^{2,3}$. Comparing to the conductance, the thermoelectric co- efficients of electronic systems are more sensitive to the details of the density of states $^{4–6}$, which is very important for the design of the electronic devices. The thermopower (seebeck coefficient) of the quantum dot was measured in the last few years $^{2}$. Recently, the Nernst effect, a Hall- like thermal effect, has been theoretically studied 7 and had been detected, for example, in bismuth 8 in which, with the existence of a perpendicular magnetic field, a transverse current is induced by the longitudinal ther- mal gradient. In the spintronics area, the spin thermal coefficients are also of focus recently $^{4–6}$. In a recent paper, by con- sidering a system with a spin-orbit interaction (SOI), the Nernst effect and a novel thermal effect, the spin Nernst effect, have been fully studied in a two-dimensional elec- tron gas $^{9}$. It is found that, because of a perpendicular magnetic field B , the Nernst signal exhibits a series of peaks. When the SOI exists, the peaks split and the spin Nernst effect appears. With a small B or a large SOI, the spin Nernst effect becomes more pronounced. It also shows that the spin Nernst effect is easier to be affected by disorder than the Nernst effect. There is no doubt that a perpendicular magnetic field B is essential for the existence of the Nernst effect. How- ever, in the spin Hall effect, the transverse spin current is due to a SOI rather than a perpendicular magnetic field. Similarly, for the spin Nernst effect, B may not be needed either. One may suspect that the spin Nernst effect is in fact the combination of the existence of thermopower and a SOI. Thus, the focus of the current work is to study the spin Nernst effect in the absence of a perpendicular magnetic field, and its interplay with the thermopower. In this paper, the property of spin Nernst effect is de- veloped in a two-dimensional electron gas system with a Rashba SOI but without a perpendicular magnetic field B . For this set-up, the Nernst effect disappears thus we In the tight-binding representation, the Hamiltonian By using a tight-binding model and the Landauer- Buttiker (LB) formula, the spin Nernst coefficient N$_{s}$ ( N$_{s}$ ≡ J$_{s}$/ Δ T ) and the seebeck coefficient S ( S ≡ − Δ V/ Δ T ) are calculated. The Rashba SOI used in our calculations covers a wide range with some beyond the accessibility of today’s sample. The seebeck coefficient S shows a few peaks consequently when the fermi energy E$_{F}$ goes through the energy band. Due to the interface of our setting (zero Rashba SOI at lead 2,4), we find a negative S . It is confirmed that spin Nernst effect can not be simply thought as the combination of the seebeck coefficient and the Spin hall effect $^{9}$. A big spin Nernst coefficient N$_{s}$ can be found with a zero seebeck coeffi- cient S . However, when the peaks of seebeck coefficient occur with a non-zero Rashba SOI, the spin Nernst ef- fect exhibits big amplitude or sometimes also peaks. The Fermi energy E$_{F}$ also affects N$_{s}$ . When the Fermi energy E$_{F}$ is close to the bottom of the energy band ( − 4 t ), the oscillatory amplitude of N$_{s}$ becomes more pronounced. The effect of disorder on N$_{s}$ is also investigated. When E$_{F}$ = − 3 . 8 t , we can see a large increase of N$_{s}$ with in- creasing of the strength of disorder. Its value at the peak is about three-fold of that without disorder. In addition, we find that the strength of disorder when N$_{s}$ vanishes, indicating that the system goes into an insulating regime, is independent of the Fermi energy. focus on the spin Nernst effect – a transverse spin cur- rent induced by a longitudinal thermal gradient Δ T . A traditional way to analyze such a Hall-like system is to add vertical probes to detect the transverse properties. Thus we set a four-terminal cross-bar sample, as shown in Fig.1 $^{9}$. A longitudinal thermal gradient Δ T is added between the leads 1 and 3. This thermal gradient induces a transverse spin current J$_{s}$ in the closed boundary condi- tion with a SOI, which can be measured at leads 2 and 4. The seebeck coefficient of such a system can be directly measured at leads 1 and 3. arXiv:1001.0999v1 [cond-mat.mes-hall] 6 Jan 2010