- 一、RashbaSOC資料
- 二、兩種自旋軌道耦合表達式(\(\hat{H}_{\mathrm{soc} }=\xi \hat{\mathbf{L}} \cdot \hat{\boldsymbol{\sigma}}\)與\(\frac{e \hbar}{4 m^{2} c^{2}} \hat{\boldsymbol{\sigma}} \cdot(\mathbf{E} \times \hat{\mathbf{p}})\))之間的關系：
- 三、國際單位制下的自旋軌道耦合公式：
- 四、RashbaSOC:
- 五、自旋軌道耦合的其他表達式
- 六、Chen-2021-Spin-Orbit Coupling in 2D Semiconductor的要點
一、RashbaSOC資料
從狄拉克方程推導出自旋軌道耦合項可以見曾書量子力學卷二。
書：
Advanced Quantum Condensed Matter Physics (cambridge.org) 的第4章及第12章的第4節，寫得很好，非常推薦。
Spin—Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems | SpringerLink
綜述：
Spintronic 2D Materials-Fundamentals and Applications 第二章：Rashba spin–orbit coupling in two-dimensional systems - ScienceDirect （寫得很好，推薦）
Spin–Orbit Coupling in 2D Semiconductors: A Theoretical Perspective：https://pubs.acs.org/doi/abs/10.1021/acs.jpclett.1c03662 （推薦)
Rashba 自旋軌道耦合的新視角：New perspectives for Rashba spin–orbit coupling | Nature Materials
摘要：1984 年，Bychkov 和 Rashba 引入了一種簡單的自旋軌道耦合形式來解釋二維半導體中電子自旋共振的特性。在過去的 30 年里，Rashba 自旋軌道耦合激發了大量遠超半導體的預測、發現和創新概念。過去十年特別有創意，實現了通過在空間中移動電子來操縱自旋方向、使用自旋作為方向盤控制電子軌跡以及發現新的拓撲材料類別。這一進展重新激發了物理學家和材料科學家對反演不對稱結構發展的興趣，從層狀石墨烯類材料到冷原子。本評論討論了 Rashba 物理學在凝聚態中的相關最新和正在進行的實現。
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自旋軌道耦合(SOC)的推導及一些理解 - 主頁 (yxli8023.github.io)(非常推薦)
二、兩種自旋軌道耦合表達式(\(\hat{H}_{\mathrm{soc} }=\xi \hat{\mathbf{L}} \cdot \hat{\boldsymbol{\sigma}}\)與\(\frac{e \hbar}{4 m^{2} c^{2}} \hat{\boldsymbol{\sigma}} \cdot(\mathbf{E} \times \hat{\mathbf{p}})\))之間的關系：
證明：
\[\begin{equation} \begin{aligned} \vec{E} &=-\nabla_{r} \phi \frac{\vec{r}}{r} \\ H_{\text {soc }} &=\frac{e \hbar}{4 m^{2} c^{2}} \hat{\vec{\sigma}} \cdot(\vec{E} \times \vec{p}) \\ &=-\frac{e \hbar}{4 m^{2} c^{2}} \frac{\nabla_{r} \phi}{r} \hat{\vec{\sigma}} \cdot(\hat{\hat{r}} \times \hat{\vec{p}}) \\ &=\hat{\xi} \vec{L} \cdot \vec{\sigma} \end{aligned} \end{equation} \]
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}
得證。
此表達式確實是在取e>0(對電子，其電量q=-e)這個約定下的正確表達式，與金老師高量講義中SOC哈密頓量表達式一致：\[\begin{aligned} H_{\text {SOC }} &=-\frac{e}{2 m c^{2}}\left(\frac{1}{r} \frac{\partial \phi}{\partial r}\right) \vec{S} \cdot \vec{L} \\ &=-\frac{e \hbar}{4 m c^{2}}\left(\frac{1}{r} \frac{\partial \phi}{\partial r}\right) \vec{L} \cdot \vec{\sigma} \end{aligned} \]
特別注意，在上面圖片中(2.4)、金老師高量講義、我的本科量子力學筆記本、xiaodi2010年綜述中，都是取的e>0(對電子，其電量q=-e)這個約定！！！
特別注意，根據金老師高量講義或曾謹言的量子力學卷二知，上面圖片中應該都是高斯單位制下的表達式，(2.4)中的第一項中應該是\(\frac{1}{2 m}(\hat{\mathbf{p}}+e \mathbf{A}/c)^{2}\)，第三項塞曼項應該是\(\frac{e \hbar}{2 mc} \hat{\boldsymbol{\sigma}} \cdot \mathbf{B}\) （塞曼項的作用見xiaodi2010綜述（3.15）下面一段話及其中的參考文獻。提到了：塞曼項使得系統是鐵磁的，而且破缺了時間反演對稱性）
不過曾書中好像並沒有上面圖片中的(2.4)這樣一個公式？
三、國際單位制下的自旋軌道耦合公式：
在曾書量子力學卷二(這本書是高斯單位制)407頁中提到高斯單位制中的自旋軌道耦合公式：
在朱林繁原子物理書(這本書使用的是國際單位制)中國際單位制下的自旋軌道耦合公式：
將(3.3.4)與上面曾書(10.4.33)對比知：
國際單位制下的自旋軌道耦合公式就是高斯單位制中的自旋軌道耦合公式再多除以一個\(4\pi\varepsilon_0\)！
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：國際單位制中還應除以\(4\pi\varepsilon_0\)：
2.高斯和國際單位制可以見我的博客 https://www.cnblogs.com/quantum-condensed-matter-physics/p/14743515.html
四、RashbaSOC:
不過以上\(\nabla \Phi \approx-E z\)公式錯誤，以及(2.8)中\(\alpha_{\mathrm{R}}\)的表達式中少了一個e，正確公式應為：
特別注意，(2.8)中的\(\mathbf{z}\) 應該理解為 \(\vec{e}_{z}\)！！！
證明：
設電場：\[\begin{align} \vec{E} & \approx-\nabla_{z} \phi \vec{e}_{z} & = E \vec{e}_{z} \\ \Rightarrow E & = -\nabla_{z} \phi \end{align}\]\[\begin{equation} \begin{aligned} H_{\text {soc }} &=\frac{e \hbar}{4 m^{2} c^{2}} \hat{\sigma} \cdot(\vec{E} \times \vec{p}) \\ &=\frac{E e \hbar}{4 m^{2} c^{2}} \hat{\vec{\sigma}} \cdot\left(\vec{e}_{z} \times \vec{p}\right) \\ &=\frac{\partial_{z} \phi e \hbar}{4 m^{2} c^{2}} \hat{\sigma} \cdot\left(\vec{p} \times \vec{e}_{z}\right) \\ &=\frac{\alpha_{R}}{\hbar} \hat{\sigma} \cdot\left(\vec{p} \times \vec{e}_{z}\right) \end{aligned} \end{equation} \]
得證。
五、自旋軌道耦合的其他表達式
還可以注意到：混合積的輪換對稱性：
對二維材料：
六、Chen-2021-Spin-Orbit Coupling in 2D Semiconductor的要點
[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)
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">>
e 2D nonpolar semiconductors lack the intrinsic Rashba effect, such as phosphorene and transition-metal dichalcogenides (TMDs).">>
內稟和外稟：
2D polar semiconductors with the intrinsic Rashba effect
而外電場、界面效應產生的Rashba效應稱為外稟Rashba效應。
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.">>
自旋結構
spin texture is determined by the expectation value ofthe spin operator,">>
Rashba效應
Rashba effect has two importantfeatures: energy band splitting and spin splitting">>
This Rashba Hamiltonian can apply to most 2D semiconductors.">>6-16
特別注意，RashbaSOC劈裂以后，能帶上稱為+、-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.">>
特別注意，Rashba效應可以通過DFT來算！
估算RashbaSOC系數：
內稟和外稟都能算嗎？wte2的有人算過嗎
自旋結構：
，就是電子自旋平均值。
紅色和藍色表示\(\langle\sigma_y\rangle\)是正還是負。
一系列二維Rashba半導體
二維Rashba半導體必須破缺空間反演對稱性！<<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.">>
Rashba states should locate in the valence band maximum (VBM) or conductionband minimum (CBM) for practical applications. In">>
比較大的Rashba系數是：超過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.">>
<<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">>
<<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 單層的Rashba系數不算很大吧
鐵電Rashba半導體
<<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
<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122246-sevboww "possess ferroelectric polarization.">>有鐵電極化的Rashba半導體：
WS2的Rashba效應更強！
Rashba效應可以用鐵電場來控制：鐵電極化切換能導致本征電場有很大改變，這意味着Rashba效應能被鐵電場操控：
<<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.">>
Rashba效應的控制
其實Rashba效應還是由內稟的晶體勢導致的：<<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,">> 內稟電場是晶體勢的梯度！
外電場的影響
外電場改變總電場強度，從而影響Rashba效應。
<<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|.">>
- 一方面：在缺乏本征Rashba效應的材料中誘導Rashba效應
<<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">>（最大電場到0.8V/埃時，單層wte2的Rashba系數才0.34，不算很大，所以我還是不研究此方面了吧，不過這里說非極性TMD單層，我看了這篇12文章，是2H的wte2，沒什么意思，不如Td的wte2）
陰離子在這種外電場誘導的Rashba效應的強度上起了重要作用：<<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">>
<<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">> 他們具有反演對稱性
的buckled square相的材料的Rashba系數不大，才0.6。
但這種
材料的Rashba系數居然達到2點幾，但它有內稟Rashba效應。我查了一下，沒人算其鐵電性，不過我覺得可能有？參考文獻中說它有內建電場，其實就是有極性。
從以上方面來看：
（最后一個提到的是三元化合物，也不好），在缺乏本征Rashba效應的材料中誘導Rashba效應其實很無聊，沒有意思！我不研究！
- 另一方面，在具有本征Rashba效應的材料中，外電場能操控Rashba效應
查20貝里曲率存儲器那篇實驗wte2的極化隨外電場變化怎么變化
JanusTMD其實很好：極化隨外電場下的變化都已經有DFT計算了，所以我可以直接使用，算非線性光學響應應該也挺方便：
<<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).">>
不過：janus 單層的Rashba系數不算很大吧，而且電場調控的效果還不是很大，還不如壓力調控(以及電荷摻雜調控：電荷摻雜調節SOC的機制可以用以下模型和方法來解釋：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)
<<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.">>(但這篇的參考文獻69指的是2H結構的wte2，這不用相信，因為實驗上合成的是Td結構的wte2。
壓力
<<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.">>
電荷摻雜
<<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">>
<<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">>
電荷摻雜對應的\(\alpha\)值可以用DFT來計算。
電荷摻雜調節SOC的機制可以用以下模型和方法來解釋：<<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">>
（來自20年Tunable Rashba spin splitting in Janus transitionmetal dichalcogenide monolayers via charge doping)
電荷摻雜實際上在實驗上是怎么實現的？
多層材料擁有不同於原始材料的本征電場
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.">>
內稟和外稟：
<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623112030-ytcmzke "2D polar semiconductors with the intrinsic Rashba effect">>
而外電場、界面效應產生的Rashba效應稱為外稟Rashba效應。
<<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.">>
自旋結構
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,">>
Rashba效應
<<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">>
<<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
特別注意，RashbaSOC劈裂以后，能帶上稱為+、-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.">>
特別注意，Rashba效應可以通過DFT來算！
估算RashbaSOC系數：
內稟和外稟都能算嗎？wte2的有人算過嗎
自旋結構：
，就是電子自旋平均值。
紅色和藍色表示\(\langle\sigma_y\rangle\)是正還是負。
一系列二維Rashba半導體
二維Rashba半導體必須破缺空間反演對稱性！<<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.">>
<<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">>
比較大的Rashba系數是：超過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.">>
<<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">>
<<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 單層的Rashba系數不算很大吧
鐵電Rashba半導體
<<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
<<assets/Chen-2021-Spin-Orbit Coupling in 2D Semiconduc-20220623111413-6gm14ob.pdf/20220623122246-sevboww "possess ferroelectric polarization.">>有鐵電極化的Rashba半導體：
WS2的Rashba效應更強！
Rashba效應可以用鐵電場來控制：鐵電極化切換能導致本征電場有很大改變，這意味着Rashba效應能被鐵電場操控：
<<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.">>
Rashba效應的控制
其實Rashba效應還是由內稟的晶體勢導致的：<<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,">> 內稟電場是晶體勢的梯度！
外電場的影響
外電場改變總電場強度，從而影響Rashba效應。
<<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|.">>
- 一方面：在缺乏本征Rashba效應的材料中誘導Rashba效應
<<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">>（最大電場到0.8V/埃時，單層wte2的Rashba系數才0.34，不算很大，所以我還是不研究此方面了吧，不過這里說非極性TMD單層，我看了這篇12文章，是2H的wte2，沒什么意思，不如Td的wte2）
陰離子在這種外電場誘導的Rashba效應的強度上起了重要作用：<<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">>
<<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">> 他們具有反演對稱性
但這種
從以上方面來看：（最后一個提到的是三元化合物，也不好），在缺乏本征Rashba效應的材料中誘導Rashba效應其實很無聊，沒有意思！我不研究！
- 另一方面，在具有本征Rashba效應的材料中，外電場能操控Rashba效應
查20貝里曲率存儲器那篇實驗wte2的極化隨外電場變化怎么變化
JanusTMD其實很好：極化隨外電場下的變化都已經有DFT計算了，所以我可以直接使用，算非線性光學響應應該也挺方便：
<<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).">>
不過：janus 單層的Rashba系數不算很大吧，而且電場調控的效果還不是很大，還不如壓力調控(以及電荷摻雜調控：電荷摻雜調節SOC的機制可以用以下模型和方法來解釋：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)
<<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.">>(但這篇的參考文獻69指的是2H結構的wte2，這不用相信，因為實驗上合成的是Td結構的wte2。
壓力
<<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.">>
電荷摻雜
<<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">>
<<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">>
電荷摻雜對應的\(\alpha\)值可以用DFT來計算。
電荷摻雜調節SOC的機制可以用以下模型和方法來解釋：<<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">>
（來自20年Tunable Rashba spin splitting in Janus transitionmetal dichalcogenide monolayers via charge doping)
電荷摻雜實際上在實驗上是怎么實現的？
多層材料擁有不同於原始材料的本征電場
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.">>