Department of Physics, Northwest University, Xi'an 710069, People's Republic of China.
J Phys Condens Matter. 2012 Sep 26;24(38):385302. doi: 10.1088/0953-8984/24/38/385302. Epub 2012 Sep 3.
The spin thermoelectric properties of a zigzag edged ferromagnetic (FM) graphene nanoribbon are studied theoretically by using the non-equilibrium Green's function method combined with the Landauer-Büttiker formula. By applying a temperature gradient along the ribbon, under closed boundary conditions, there is a spin voltage ΔV(s) inside the terminal as the response to the temperature difference ΔT between two terminals. Meanwhile, the heat current ΔQ is accompanied from the 'hot' terminal to the 'cold' terminal. The spin thermopower S = ΔV(s)/ΔT and thermoconductance κ = ΔQ/ΔT are obtained. When there is no magnetic field, S versus E(R) curves show peaks and valleys as a result of band selective transmission and Klein tunneling with E(R) being the on-site energy of the right terminal. The results are in agreement with the semi-classical Mott relation. When |E(R)| < M (M is the FM exchange split energy), κ is infinitesimal because tunneling is prohibited by the band selective rule. While |E(R)| > M, the quantized value of κ = π2k2(B)T/3h appears. In the quantum Hall regime, because Klein tunneling is suppressed, S peaks are eliminated and the quantized value of κ is much clearer. We also investigate how the thermoelectric properties are affected by temperature, FM exchange split energy and Anderson disorder. The results indicate that S and κ are sensitive to disorder. S is suppressed for even small disorder strengths. For small disorder strengths, κ is enhanced and for moderate disorder strengths, κ shows quantized values.
锯齿形边缘铁磁（FM）石墨烯纳米带的自旋热电器件性能通过使用非平衡格林函数方法结合朗道-比尔特定律进行了理论研究。通过在 ribbon 上施加沿 ribbon 的温度梯度，并在闭合边界条件下，在终端内部会有一个自旋电压ΔV(s)，作为对两个终端之间的温差ΔT 的响应。同时，伴随着从“热”端到“冷”端的热流ΔQ。得到自旋热电势 S = ΔV(s)/ΔT 和热导率 κ = ΔQ/ΔT。当没有磁场时，S 与 E(R) 曲线的关系会由于能带选择性传输和 Klein 隧道而出现峰谷，其中 E(R) 是右侧终端的局域能量。结果与半经典 Mott 关系一致。当 |E(R)| < M 时（M 是 FM 交换分裂能量），由于能带选择性规则禁止隧道，κ 是无穷小的。而当 |E(R)| > M 时，κ 的量子化值 κ = π2k2(B)T/3h 出现。在量子霍尔区，由于 Klein 隧道被抑制，S 峰被消除，κ 的量子化值更加明显。我们还研究了热电器件性能如何受到温度、FM 交换分裂能量和安德森无序的影响。结果表明，S 和 κ 对无序很敏感。即使无序强度很小，S 也会受到抑制。对于较小的无序强度，κ 会增强，而对于中等的无序强度，κ 会呈现量子化值。
