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arXiv 1707.04051cond-mat.mes-hall
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自旋-动量锁定材料的传输线模型

Transmission Line Model for Materials with Spin-Momentum Locking

Shehrin Sayed, Seokmin Hong, Supriyo Datta

摘要:

我们提供了一个传输线表示通道表现出自旋动量锁定(SML),可用于时间相关和稳态输运分析的各种材料与自旋轨道耦合,如拓扑绝缘体,重金属,氧化物界面,和窄带隙半导体。该模型是基于一个依赖于时间的四分量扩散方程,从玻尔兹曼传输方程假设线性响应和弹性散射的通道。我们根据自旋指数(上($U$),下($D$))和群速度的$x$分量($+,-$)的符号将通道中的所有电子状态分为四组($U^+$,$D^+$,$U^-$和$D^-$),并为四组中的每一组分配平均电化学势以获得四分量扩散方程。对于正常的金属通道,该模型是众所周知的传输线模型的电荷和时间依赖版本的Valet-Fert方程的自旋。我们首先表明,在稳态极限下,我们的模型导致简单的表达式与现有的实验数据在不同的材料在SML通道的电荷-自旋相互转换。然后,我们使用完全的时间依赖模型来研究自旋-电荷分离的存在下,SML,在过去一直有争议的主题。我们的模型表明,电荷和自旋信号以两种不同的速度传播,从而导致众所周知的自旋-电荷分离,即使在SML存在下,这种分离也会持续存在。然而,我们的模型预测,较低的速度信号是纯粹的自旋,而较高的速度信号在很大程度上是电荷与一个额外的自旋分量,这是以前没有注意到的。最后,我们注意到,我们的模型可以在标准的电路模拟器,如SPICE中使用,以获得复杂几何形状的数值结果。

英文摘要:

We provide a transmission line representation for channels exhibiting spin-momentum locking (SML) which can be used for both time-dependent and steady-state transport analysis on a wide variety of materials with spin-orbit coupling such as topological insulators, heavy metals, oxide interfaces, and narrow bandgap semiconductors. This model is based on a time-dependent four-component diffusion equation obtained from the Boltzmann transport equation assuming linear response and elastic scattering in the channel. We classify all electronic states in the channel into four groups ($U^+$, $D^+$, $U^-$, and $D^-$) depending on the spin index (up ($U$), down ($D$)) and the sign of the $x$-component of the group velocity ($+,-$) and assign an average electrochemical potential to each of the four groups to obtain the four-component diffusion equation. For normal metal channels, the model decouples into the well-known transmission line model for charge and a time-dependent version of Valet-Fert equation for spin. We first show that in the steady-state limit our model leads to simple expressions for charge-spin interconversion in SML channels in good agreement with existing experimental data on diverse materials. We then use the full time-dependent model to study spin-charge separation in the presence of SML, a subject that has been controversial in the past. Our model shows that the charge and spin signals travel with two distinct velocities resulting in well-known spin-charge separation which is expected to persist even in the presence of SML. However, our model predicts that the lower velocity signal is purely spin while the higher velocity signal is largely charge with an additional spin component which has not been noted before. Finally, we note that our model can be used within standard circuit simulators like SPICE to obtain numerical results for complex geometries.

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