Rashba自旋轨道耦合

目录

一、RashbaSOC资料

从狄拉克方程推导出自旋轨道耦合项可以见曾书量子力学卷二。

书：

Advanced Quantum Condensed Matter Physics (cambridge.org) 的第4章及第12章的第4节，写得很好，非常推荐。

Spin—Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems | SpringerLink

综述：

Spintronic 2D Materials-Fundamentals and Applications 第二章：Rashba spin–orbit coupling in two-dimensional systems - ScienceDirect （写得很好，推荐）

Spin–Orbit Coupling in 2D Semiconductors: A Theoretical Perspective：https://pubs.acs.org/doi/abs/10.1021/acs.jpclett.1c03662 （推荐)

Rashba 自旋轨道耦合的新视角：New perspectives for Rashba spin–orbit coupling | Nature Materials

摘要：1984 年，Bychkov 和 Rashba 引入了一种简单的自旋轨道耦合形式来解释二维半导体中电子自旋共振的特性。在过去的 30 年里，Rashba 自旋轨道耦合激发了大量远超半导体的预测、发现和创新概念。过去十年特别有创意，实现了通过在空间中移动电子来操纵自旋方向、使用自旋作为方向盘控制电子轨迹以及发现新的拓扑材料类别。这一进展重新激发了物理学家和材料科学家对反演不对称结构发展的兴趣，从层状石墨烯类材料到冷原子。本评论讨论了 Rashba 物理学在凝聚态中的相关最新和正在进行的实现。

Bihlmayer, et al. Rashba-like physics in condensed matter. Nat Rev Phys (2022).：https://www.nature.com/articles/s42254-022-00490-y

Rashba及Dresselhaus自旋轨道耦合(SOC)的推导及一些理解 - 主页 (yxli8023.github.io)(非常推荐)

二、两种自旋轨道耦合表达式(\(\hat{H}_{\mathrm{soc} }=\xi \hat{\mathbf{L}} \cdot \hat{\boldsymbol{\sigma}}\)与\(\frac{e \hbar}{4 m^{2} c^{2}} \hat{\boldsymbol{\sigma}} \cdot(\mathbf{E} \times \hat{\mathbf{p}})\))之间的关系：

image

此图来自Rashba spin–orbit coupling in two-dimensional systems - ScienceDirect

证明：

\[\begin{equation} \begin{aligned} \vec{E} &=-\nabla_{r} \phi \frac{\vec{r}}{r} \\ H_{\text {soc }} &=\frac{e \hbar}{4 m^{2} c^{2}} \hat{\vec{\sigma}} \cdot(\vec{E} \times \vec{p}) \\ &=-\frac{e \hbar}{4 m^{2} c^{2}} \frac{\nabla_{r} \phi}{r} \hat{\vec{\sigma}} \cdot(\hat{\hat{r}} \times \hat{\vec{p}}) \\ &=\hat{\xi} \vec{L} \cdot \vec{\sigma} \end{aligned} \end{equation} \]

其中：
\begin{equation} \begin{aligned}
\xi=-e \hbar\left\langle\partial_{r} \Phi / r\right\rangle / 4 m^{2} c^{2}
\end{aligned} \end{equation}
得证。
此表达式确实是在取e>0(对电子，其电量q=-e)这个约定下的正确表达式，与金老师高量讲义中SOC哈密顿量表达式一致：

\[\begin{aligned} H_{\text {SOC }} &=-\frac{e}{2 m c^{2}}\left(\frac{1}{r} \frac{\partial \phi}{\partial r}\right) \vec{S} \cdot \vec{L} \\ &=-\frac{e \hbar}{4 m c^{2}}\left(\frac{1}{r} \frac{\partial \phi}{\partial r}\right) \vec{L} \cdot \vec{\sigma} \end{aligned} \]

特别注意，在上面图片中(2.4)、金老师高量讲义、我的本科量子力学笔记本、xiaodi2010年综述中，都是取的e>0(对电子，其电量q=-e)这个约定！！！

特别注意，根据金老师高量讲义或曾谨言的量子力学卷二知，上面图片中应该都是高斯单位制下的表达式，(2.4)中的第一项中应该是\(\frac{1}{2 m}(\hat{\mathbf{p}}+e \mathbf{A}/c)^{2}\)，第三项塞曼项应该是\(\frac{e \hbar}{2 mc} \hat{\boldsymbol{\sigma}} \cdot \mathbf{B}\) （塞曼项的作用见xiaodi2010综述（3.15）下面一段话及其中的参考文献。提到了：塞曼项使得系统是铁磁的，而且破缺了时间反演对称性）

不过曾书中好像并没有上面图片中的(2.4)这样一个公式？

三、国际单位制下的自旋轨道耦合公式：

在曾书量子力学卷二(这本书是高斯单位制)407页中提到高斯单位制中的自旋轨道耦合公式：
image

在朱林繁原子物理书(这本书使用的是国际单位制)中国际单位制下的自旋轨道耦合公式：
image
将(3.3.4)与上面曾书(10.4.33)对比知：

国际单位制下的自旋轨道耦合公式就是高斯单位制中的自旋轨道耦合公式再多除以一个\(4\pi\varepsilon_0\)！

1.在 https://www.chegg.com/homework-help/questions-and-answers/4-hydrogen-atom-spin-orbit-coupling-given-1-1dvc-hls-ls-2m2c2-r-dr-si-units-need-division--q59317556 中也提到：国际单位制中还应除以\(4\pi\varepsilon_0\)：
image
2.高斯和国际单位制可以见我的博客 https://www.cnblogs.com/quantum-condensed-matter-physics/p/14743515.html

四、RashbaSOC:

image

此图来自Rashba spin–orbit coupling in two-dimensional systems - ScienceDirect

不过以上\(\nabla \Phi \approx-E z\)公式错误，以及(2.8)中\(\alpha_{\mathrm{R}}\)的表达式中少了一个e，正确公式应为：

\[\begin{equation} \begin{aligned} \nabla \Phi \approx-E \vec{e}_z \end{aligned} \end{equation} \]

\[\begin{equation} \begin{aligned} \alpha_{\mathrm{R}} \approx e\hbar^{2} \partial_{z} \Phi / 4 m^{2} c^{2}\end{aligned} \end{equation} \]

特别注意，(2.8)中的\(\mathbf{z}\) 应该理解为 \(\vec{e}_{z}\)！！！

证明：
设电场：

\[\begin{align} \vec{E} & \approx-\nabla_{z} \phi \vec{e}_{z} & = E \vec{e}_{z} \\ \Rightarrow E & = -\nabla_{z} \phi \end{align}\]

\[\begin{equation} \begin{aligned} H_{\text {soc }} &=\frac{e \hbar}{4 m^{2} c^{2}} \hat{\sigma} \cdot(\vec{E} \times \vec{p}) \\ &=\frac{E e \hbar}{4 m^{2} c^{2}} \hat{\vec{\sigma}} \cdot\left(\vec{e}_{z} \times \vec{p}\right) \\ &=\frac{\partial_{z} \phi e \hbar}{4 m^{2} c^{2}} \hat{\sigma} \cdot\left(\vec{p} \times \vec{e}_{z}\right) \\ &=\frac{\alpha_{R}}{\hbar} \hat{\sigma} \cdot\left(\vec{p} \times \vec{e}_{z}\right) \end{aligned} \end{equation} \]

得证。

五、自旋轨道耦合的其他表达式

还可以注意到：混合积的轮换对称性：

故： $$ \begin{equation} \begin{array}{l} \vec{\sigma} \cdot(\vec{E} \times \vec{p})=\vec{E} \cdot(\vec{p} \times \vec{\sigma})=\vec{p} \cdot(\vec{\sigma} \times \vec{E}) \\ \vec{\sigma} \cdot\left(\vec{p} \times \vec{e}_{z}\right)=\vec{p} \cdot\left(\vec{e}_{z} \times \vec{\sigma}\right)=\vec{e}_{z} \cdot(\vec{\sigma} \times \vec{p}) \end{array} \end{equation} $$ 故(2.4)(2.8)还有其他表达式。

对二维材料：

\[\begin{equation} \begin{aligned} \hat{\vec{p}} &=\left(\hat{p}_{x}, \hat{p}_{y}\right) \\ \Rightarrow H_{R} &=\frac{\alpha_{R}}{\hbar} \hat{\vec{\sigma}} \cdot\left(\hat{\vec{p}} \times \vec{e}_{z}\right)=\frac{\alpha_{R}}{\hbar} \vec{e}_{z} \cdot(\vec{\sigma} \times \hat{\vec{p}}) \\ &=\frac{\alpha_{R}}{\hbar}\left(\sigma_{x} \hat{p}_{y}-\sigma_{y} \hat{p}_{x}\right) \\ &=\frac{\alpha_{R}}{\hbar}\left(\begin{array}{cc} 0 & \hat{p}_{y}+i \hat{p}_{x} \\ \hat{p}_{y}-i \hat{p}_{x} & 0 \end{array}\right) \end{aligned} \end{equation} \]

六、Chen-2021-Spin-Orbit Coupling in 2D Semiconductor的要点

[Chen-2021-Spin-Orbit Coupling in 2D Semiconduc.pdf](https://assets.b3logfile.com/siyuan/1619246215189/assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf)

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SOC exists in noncentrosymmetric structures and mainly consists of two types: the Rashba effect induced by the structure inversion asymmetry (SIA) 3,4 and the Dresselhaus effectinduced by the bulk inversion asymmetry (BIA). 2">>

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e 2D nonpolar semiconductors lack the intrinsic Rashba effect, such as phosphorene and transition-metal dichalcogenides (TMDs).">>

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内禀和外禀：

2D polar semiconductors with the intrinsic Rashba effect

而外电场、界面效应产生的Rashba效应称为外禀Rashba效应。

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In crystals, the intrinsic electric field is the gradient of the crystal potential (E = −∇V). That is, in spatial inversion symmetry-breaking structures, the spin degeneracy disappears across the dispersion diagrams within the Brillouin zone, except for some special high-symmetry points.">>

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自旋结构

spin texture is determined by the expectation value ofthe spin operator,">>

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Rashba效应

Rashba effect has two importantfeatures: energy band splitting and spin splitting">>

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This Rashba Hamiltonian can apply to most 2D semiconductors.">>6-16

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特别注意，RashbaSOC劈裂以后，能带上称为+、-分支，而不是自旋向上向下

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623113958-1pgutn4 "where the symbol + (−) denotes the inner (outer) branch, and energy difference ER and momentum offset kR can be measuredin the DFT band structures as shown in Figure 2d.">>

特别注意，Rashba效应可以通过DFT来算！

估算RashbaSOC系数：image.png

内禀和外禀都能算吗？wte2的有人算过吗

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自旋结构：

image.png，就是电子自旋平均值。

image.png

红色和蓝色表示\(\langle\sigma_y\rangle\)是正还是负。

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一系列二维Rashba半导体

二维Rashba半导体必须破缺空间反演对称性！<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623115221-e2vzp87 "The main characteristics of Rashbamaterials are broken inversion symmetry and strong SOC.">>

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623115421-z1mv84c "a series of 2D Rashba semiconductorstheoretically, including AB binary buckled monolayers, 6−8Janus monolayers (especially for MXY Janus monolayers),9−152D perovskites, 16,40−42 and so on.">>

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Rashba states should locate in the valence band maximum (VBM) or conductionband minimum (CBM) for practical applications. In">>

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比较大的Rashba系数是：超过1 eV.A：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623115950-29lnxn1 "giant Rashba constants largerthan 1.0 eV·Å.">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623120423-sgptek6 "showthe intrinsic Rashba effect due to the built-in electric fieldperpendicular to the monolayer plane.9−13">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623121357-9gfekvz "Janus TMDs monolayers, the WSeTemonolayer has the largest Rashba constant (α = 0.479 eV·Å)">> janus 单层的Rashba系数不算很大吧

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铁电Rashba半导体

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122153-blizwi2 "external electric field can switch between two ferroelectric states and reverse the spin texture of the Rashba bands. 59−">>61

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122246-sevboww "possess ferroelectric polarization.">>有铁电极化的Rashba半导体：

image.png

WS2的Rashba效应更强！

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Rashba效应可以用铁电场来控制：铁电极化切换能导致本征电场有很大改变，这意味着Rashba效应能被铁电场操控：

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122907-5zgrymi ". Ferroelectrics with switchable polarization can induce alarge change in the intrinsic electric field, which means theRashba effect can be manipulated by the ferroelectric field.">>

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Rashba效应的控制

其实Rashba效应还是由内禀的晶体势导致的：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623123752-lhpdwkk ". Because SOC removesthe spin degeneracy due to the intrinsic electric field E that is thegradient of the crystalline potential,">> 内禀电场是晶体势的梯度！

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外电场的影响

外电场改变总电场强度，从而影响Rashba效应。

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624121524-hpp45ua "the external electric field caninfluence the total electric field, thus changing the strength of the Rashba effect.">>

特征：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624141543-munacbq "response of the Rashba effect to an external electric field, which is denoted by|Δα/ΔE|.">>

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  • 一方面：在缺乏本征Rashba效应的材料中诱导Rashba效应

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624121709-f2uaetl "external electric field can induce theRashba effect in structures that lack the intrinsic Rashba effect.For example, nonpolar TMDs monolayers MX 2 (M = W, Mo; X= S, Se, Te) lack the Rashba effect in the absence of the externalelectric field, and their α values are linearly proportional to theexternal electric field.12">>（最大电场到0.8V/埃时，单层wte2的Rashba系数才0.34，不算很大，所以我还是不研究此方面了吧，不过这里说非极性TMD单层，我看了这篇12文章，是2H的wte2，没什么意思，不如Td的wte2）

阴离子在这种外电场诱导的Rashba效应的强度上起了重要作用：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624122007-wj7a6om "anions play an important role in thestrength of the Rashba effect under the external electric field">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624122442-9kx3x6h ", the planar square PbX (X =S, Se, Te) monolayer lacks the Rashba effect without an externalelectric field, as mentioned above">> ：原因：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624135037-4ybyfdo "In contrast, the planar square PbS monolayerlacks the Rashba effect because of the inversion symmetry">> 他们具有反演对称性

image.png的buckled square相的材料的Rashba系数不大，才0.6。

但这种image.png材料的Rashba系数居然达到2点几，但它有内禀Rashba效应。我查了一下，没人算其铁电性，不过我觉得可能有？参考文献中说它有内建电场，其实就是有极性。

image.png

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从以上方面来看：image.png（最后一个提到的是三元化合物，也不好），在缺乏本征Rashba效应的材料中诱导Rashba效应其实很无聊，没有意思！我不研究！

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  • 另一方面，在具有本征Rashba效应的材料中，外电场能操控Rashba效应

查20贝里曲率存储器那篇实验wte2的极化随外电场变化怎么变化

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JanusTMD其实很好：极化随外电场下的变化都已经有DFT计算了，所以我可以直接使用，算非线性光学响应应该也挺方便：

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624144828-be37cu0 "on. For WSSe, MoSSe, WSeTe, and MoSeTe,Rashba constants are increased linearly with the positive external electric field and suppressed linearly with the negative external electric field. 10">>

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624194437-ld8acch ", WSeTe has the largest change of 0.031 eV·Å for α (which is around the Γ point in the Γ-Kdirection) by comparison without the external electric field andwith a large external electric field (0.5 V/Å).">>

不过：janus 单层的Rashba系数不算很大吧，而且电场调控的效果还不是很大，还不如压力调控(以及电荷掺杂调控：电荷掺杂调节SOC的机制可以用以下模型和方法来解释：Themechanism is explained by the elect...[1]）：Phys. Rev. B 97, 235404 (2018) - Intrinsic and anisotropic Rashba spin splitting in Janus transition-metal dichalcogenide monolayers (aps.org)

image.pngimage.png

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624192744-562ms3d "But MX 2 bilayers have the Rashba effect, although their Rashba constants are less than 0.1 eV·Å.">>(但这篇的参考文献69指的是2H结构的wte2，这不用相信，因为实验上合成的是Td结构的wte2。

压力

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624195751-9ktfgon "PBi has the most giantRashba effect among three PX (X = As, Sb, Bi) monolayers, withα = 1.56 eV·Å. 46 Its α increases to 4.41 eV·Å when a 10% biaxialstrain is applied, and the corresponding |Δα/Δε| is 28.5 eV·Å.">>

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624195635-v1vlkm7 "The strong Rashba effect and sensitive strain tunability make thePBi monolayer a promising candidate for spintronics.">>

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电荷掺杂

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623124015-54ua1a0 "The intrinsic electric fieldis proportional to the charge density; thus, it can be controlled by charge doping. I">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624193817-321eyee ". As for distorted 1T-phase TMDs MX2(M= Mo, W; X= S, Se, Te), charge doping has a greater impacton SOC compared with the electric field and can nonlinearlytune the SOC strength.66">>

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电荷掺杂对应的\(\alpha\)值可以用DFT来计算。

电荷掺杂调节SOC的机制可以用以下模型和方法来解释：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624194022-zl18so6 "Themechanism is explained by the electric-triple-layer model andthe Bader charge analysi">>

image.png（来自20年Tunable Rashba spin splitting in Janus transitionmetal dichalcogenide monolayers via charge doping)

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电荷掺杂实际上在实验上是怎么实现的？

多层材料拥有不同于原始材料的本征电场

I<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624121402-rcp8zet "nterlayer interactions and proximity effect of substrates can manipulate the Rashba effect, because multilayers and heterostructures possess intrinsic electric fields different from that of original materials.">>

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内禀和外禀：

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623112030-ytcmzke "2D polar semiconductors with the intrinsic Rashba effect">>

而外电场、界面效应产生的Rashba效应称为外禀Rashba效应。

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623112830-ldi1f5h "In crystals, the intrinsic electric fieldis the gradient of the crystal potential (E = −∇V). That is, inspatial inversion symmetry-breaking structures, the spindegeneracy disappears across the dispersion diagrams withinthe Brillouin zone, except for some special high-symmetrypoints.">>

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自旋结构

s<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623113210-nhpgj2w "pin texture is determined by the expectation value ofthe spin operator,">>

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Rashba效应

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623113745-8punbti "Rashba effect has two importantfeatures: energy band splitting and spin splitting">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623113851-ik70mpg "This Rashba Hamiltonian can apply to most 2D semiconductors.">>6-16

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特别注意，RashbaSOC劈裂以后，能带上称为+、-分支，而不是自旋向上向下

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623113958-1pgutn4 "where the symbol + (−) denotes the inner (outer) branch, and energy difference ER and momentum offset kR can be measuredin the DFT band structures as shown in Figure 2d.">>

特别注意，Rashba效应可以通过DFT来算！

估算RashbaSOC系数：image.png

内禀和外禀都能算吗？wte2的有人算过吗

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自旋结构：

image.png，就是电子自旋平均值。

image.png

红色和蓝色表示\(\langle\sigma_y\rangle\)是正还是负。

‍

一系列二维Rashba半导体

二维Rashba半导体必须破缺空间反演对称性！<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623115221-e2vzp87 "The main characteristics of Rashbamaterials are broken inversion symmetry and strong SOC.">>

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623115421-z1mv84c "a series of 2D Rashba semiconductorstheoretically, including AB binary buckled monolayers, 6−8Janus monolayers (especially for MXY Janus monolayers),9−152D perovskites, 16,40−42 and so on.">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623115404-rwui7uo "Rashba states should locate in the valence band maximum (VBM) or conductionband minimum (CBM) for practical applications. In">>

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比较大的Rashba系数是：超过1 eV.A：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623115950-29lnxn1 "giant Rashba constants largerthan 1.0 eV·Å.">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623120423-sgptek6 "showthe intrinsic Rashba effect due to the built-in electric fieldperpendicular to the monolayer plane.9−13">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623121357-9gfekvz "Janus TMDs monolayers, the WSeTemonolayer has the largest Rashba constant (α = 0.479 eV·Å)">> janus 单层的Rashba系数不算很大吧

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铁电Rashba半导体

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122153-blizwi2 "external electric field can switch between two ferroelectric states and reverse the spin texture of the Rashba bands. 59−">>61

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122246-sevboww "possess ferroelectric polarization.">>有铁电极化的Rashba半导体：

image.png

WS2的Rashba效应更强！

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Rashba效应可以用铁电场来控制：铁电极化切换能导致本征电场有很大改变，这意味着Rashba效应能被铁电场操控：

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122907-5zgrymi ". Ferroelectrics with switchable polarization can induce alarge change in the intrinsic electric field, which means theRashba effect can be manipulated by the ferroelectric field.">>

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Rashba效应的控制

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其实Rashba效应还是由内禀的晶体势导致的：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623123752-lhpdwkk ". Because SOC removesthe spin degeneracy due to the intrinsic electric field E that is thegradient of the crystalline potential,">> 内禀电场是晶体势的梯度！

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外电场的影响

外电场改变总电场强度，从而影响Rashba效应。

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624121524-hpp45ua "the external electric field caninfluence the total electric field, thus changing the strength of the Rashba effect.">>

特征：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624141543-munacbq "response of the Rashba effect to an external electric field, which is denoted by|Δα/ΔE|.">>

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  • 一方面：在缺乏本征Rashba效应的材料中诱导Rashba效应

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624121709-f2uaetl "external electric field can induce theRashba effect in structures that lack the intrinsic Rashba effect.For example, nonpolar TMDs monolayers MX 2 (M = W, Mo; X= S, Se, Te) lack the Rashba effect in the absence of the externalelectric field, and their α values are linearly proportional to theexternal electric field.12">>（最大电场到0.8V/埃时，单层wte2的Rashba系数才0.34，不算很大，所以我还是不研究此方面了吧，不过这里说非极性TMD单层，我看了这篇12文章，是2H的wte2，没什么意思，不如Td的wte2）

阴离子在这种外电场诱导的Rashba效应的强度上起了重要作用：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624122007-wj7a6om "anions play an important role in thestrength of the Rashba effect under the external electric field">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624122442-9kx3x6h ", the planar square PbX (X =S, Se, Te) monolayer lacks the Rashba effect without an externalelectric field, as mentioned above">> ：原因：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624135037-4ybyfdo "In contrast, the planar square PbS monolayerlacks the Rashba effect because of the inversion symmetry">> 他们具有反演对称性

image.png的buckled square相的材料的Rashba系数不大，才0.6。

但这种image.png材料的Rashba系数居然达到2点几，但它有内禀Rashba效应。我查了一下，没人算其铁电性，不过我觉得可能有？参考文献中说它有内建电场，其实就是有极性。

image.png

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从以上方面来看：image.png（最后一个提到的是三元化合物，也不好），在缺乏本征Rashba效应的材料中诱导Rashba效应其实很无聊，没有意思！我不研究！

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  • 另一方面，在具有本征Rashba效应的材料中，外电场能操控Rashba效应

查20贝里曲率存储器那篇实验wte2的极化随外电场变化怎么变化

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JanusTMD其实很好：极化随外电场下的变化都已经有DFT计算了，所以我可以直接使用，算非线性光学响应应该也挺方便：

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624144828-be37cu0 "on. For WSSe, MoSSe, WSeTe, and MoSeTe,Rashba constants are increased linearly with the positive external electric field and suppressed linearly with the negative external electric field. 10">>

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624194437-ld8acch ", WSeTe has the largest change of 0.031 eV·Å for α (which is around the Γ point in the Γ-Kdirection) by comparison without the external electric field andwith a large external electric field (0.5 V/Å).">>

不过：janus 单层的Rashba系数不算很大吧，而且电场调控的效果还不是很大，还不如压力调控(以及电荷掺杂调控：电荷掺杂调节SOC的机制可以用以下模型和方法来解释：Themechanism is explained by the elect...[1:1]）：Phys. Rev. B 97, 235404 (2018) - Intrinsic and anisotropic Rashba spin splitting in Janus transition-metal dichalcogenide monolayers (aps.org)

image.pngimage.png

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624192744-562ms3d "But MX 2 bilayers have the Rashba effect, although their Rashba constants are less than 0.1 eV·Å.">>(但这篇的参考文献69指的是2H结构的wte2，这不用相信，因为实验上合成的是Td结构的wte2。

压力

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624195751-9ktfgon "PBi has the most giantRashba effect among three PX (X = As, Sb, Bi) monolayers, withα = 1.56 eV·Å. 46 Its α increases to 4.41 eV·Å when a 10% biaxialstrain is applied, and the corresponding |Δα/Δε| is 28.5 eV·Å.">>

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624195635-v1vlkm7 "The strong Rashba effect and sensitive strain tunability make thePBi monolayer a promising candidate for spintronics.">>

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电荷掺杂

<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623124015-54ua1a0 "The intrinsic electric fieldis proportional to the charge density; thus, it can be controlled by charge doping. I">>

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<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624193817-321eyee ". As for distorted 1T-phase TMDs MX2(M= Mo, W; X= S, Se, Te), charge doping has a greater impacton SOC compared with the electric field and can nonlinearlytune the SOC strength.66">>

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电荷掺杂对应的\(\alpha\)值可以用DFT来计算。

电荷掺杂调节SOC的机制可以用以下模型和方法来解释：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624194022-zl18so6 "Themechanism is explained by the electric-triple-layer model andthe Bader charge analysi">>

image.png（来自20年Tunable Rashba spin splitting in Janus transitionmetal dichalcogenide monolayers via charge doping)

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电荷掺杂实际上在实验上是怎么实现的？

多层材料拥有不同于原始材料的本征电场

I<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624121402-rcp8zet "nterlayer interactions and proximity effect of substrates can manipulate the Rashba effect, because multilayers and heterostructures possess intrinsic electric fields different from that of original materials.">>

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  1. 电荷掺杂调节SOC的机制可以用以下模型和方法来解释：<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220624194022-zl18so6 "Themechanism is explained by the electric-triple-layer model andthe Bader charge analysi">> ↩︎ ↩︎

posted @ 2022-04-26 12:00  初心如磐使命在肩！  阅读(4001)  评论(7)  编辑  收藏  举报