半经验赝势方法用于二维材料

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姓名

柯莫(RAJ KUMAR PAUDEL) 查詢紙本館藏

畢業系所

物理學系

論文名稱

半经验赝势方法用于二维材料
(Semiempirical Pseudopotential Method for Two Dimensional Materials)

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摘要(中)

我們開發了一種半經驗贗勢（SEPM）之計算方法，可大幅簡化石墨烯、armchair石墨烯奈米帶（aGNR）和單層過渡金屬二硫屬化物（TMDC）之能帶結構的計算。我們的SEPM方法使用二維平面波與沿垂直方向的 B-spline函數作為基函數。此 SEPM 方法結合了局部項和非局部項，這些項被參數化可得到與使用密度泛函理論 (DFT) 計算中獲得的相關量幾乎一致的結果。重點是，儘管我們的方法簡單且僅使用少量參數，但我們能夠忠實地重現從 DFT 獲得的二維材料的完整能帶結構，偏差幾乎可以忽略。

為了進一步證明我們的 SEPM 方法的多功能性，我們將其應用於計算armchair石墨烯奈米帶的能帶結構。通過對奈米帶邊緣處的局部贗勢引入一個簡單的校正項來解釋邊緣效應，我們獲得了與 DFT 計算結果非常接近的能帶結構。這使我們能夠以最少的計算資源來模擬由石墨烯奈米帶構建的真實奈米器件的光學和傳輸特性。我們的方法提供了一種實用且有效的替代方案，可以替代僅依賴於計算要求較高的 DFT 計算，使研究人員能夠以更容易理解的方式研究基於奈米帶系統的電子及光學特性。

除了armchair石墨烯奈米帶之外，我們還將 SEPM 方法的適用性擴展到單層過渡金屬二硫屬化物 (TMDC)。通過參數化 SEPM 方法來擬合DFT 計算中可獲得的相關量，我們能夠準確地得到TMDC 的能帶結構。這為研究 TMDC 的光電特性並探索其在奈米器件中的潛在應用提供了機會。我們的 SEPM 方法為二維材料領域的研究人員提供了一個有價值的工具，提供了一種有效的計算方法來研究其能帶結構和光電特性。

我們的 SEPM 方法的優點在於其簡單性、計算效率以及能準確得到石墨烯、armchair石墨烯奈米帶和單層 TMDC 之能帶結構的能力。只需少量參數，我們的方法就可以對這些材料的電子特性進行可靠的模擬。與僅依賴 DFT 計算相比，我們的方法顯著的減少了計算負擔，為探索奈米材料的電子行為提供了實用且有效的工具。這為進一步研究這些材料的光學和傳輸特性及其在奈米器件中的潛在應用鋪平了道路。

摘要(英)

We have developed a semi-empirical pseudopotential (SEPM) method for efficiently calculating the electronic structures of graphene, armchair graphene nanoribbons (aGNRs), and monolayer transition metal dichalcogenides (TMDCs). Our approach combines the use of two-dimensional plane waves with B-spline functions along the perpendicular direction as basis functions. The SEPM method incorporates both local and non-local terms, which are parameterized to accurately reproduce relevant quantities obtained from density-functional theory (DFT) calculations. Remarkably, despite the simplicity of our method and the use of only a small number of parameters, we are able to faithfully reproduce the complete band structure of graphene obtained from DFT with negligible deviation.

To further demonstrate the versatility of our SEPM method, we apply it to compute the band structures of armchair graphene nanoribbons. By introducing a simple correction term to the local pseudopotentials at the nanoribbon edges, which accounts for the edge effects, we obtain band structures that closely match the results obtained from DFT calculations. This capability allows us to simulate the optical and transport properties of realistic nanodevices constructed from graphene nanoribbons with minimal computational effort. Our method offers a practical and efficient alternative to solely relying on computationally demanding DFT calculations, enabling researchers to investigate the electronic and optical properties of nanoribbon-based systems in a more accessible manner.

In addition to armchair graphene nanoribbons, we extend the applicability of our SEPM method to monolayer transition metal dichalcogenides (TMDCs). By parameterizing the SEPM to fit the relevant quantities obtained from DFT calculations, we are able to accurately reproduce the band structures of TMDCs. This opens up opportunities to investigate the optoelectronic properties of TMDCs and explore their potential applications in nanodevices. Our SEPM method provides a valuable tool for researchers working in the field of two-dimensional materials, offering a computationally efficient approach to study their band structures and optoelectronic properties.

The advantages of our SEPM method lie in its simplicity, computational efficiency, and ability to accurately capture the band structures of graphene, armchair graphene nanoribbons, and monolayer TMDCs. With only a small number of parameters, our method allows for reliable simulations of these materials′ electronic properties. By significantly reducing the computational burden compared to solely relying on DFT calculations, our approach provides a practical and efficient tool for exploring the electronic behavior of nanomaterials. This paves the way for further investigations into the optical and transport properties of these materials and their potential applications in nanodevices.

關鍵字(中)

★ 密度泛函理論
★ 半經驗贗勢
★ 石墨烯
★ 過渡金屬二硫屬化物
★ 能帶結構
★ 扶手椅石墨烯納米帶

關鍵字(英)

★ Density Functional Theory
★ Semiempirical pseudooptential
★ Graphene
★ TMDC
★ Bandstructure
★ armchair graphene nanoribbons

論文目次

Contents
Abstract v
1 Introduction and Theory Overview 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Two dimensional Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Planar basis method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Outline of the dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Theoretical overview 14
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 The Many body Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Pseudopotential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Semiemperical pseudopotential . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 B-spline basis Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Electronic states of Graphene using SEPM 31
3.1 Fitting of the Local Pseudopotential for Graphene . . . . . . . . . . . . . 31
3.2 Fitting of the Non-Local Pseudopotential for Graphene . . . . . . . . . . 39
3.3 Fourier representation of Kohn-Sham equation in planar basis . . . . . . 40
3.4 Band structure of graphene . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Electronic states of armchair graphene nanoribbons (aGNRs) using SEPM 49
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Band structure of armchair graphene nanoribbon . . . . . . . . . . . . . . 51
viii
5 Electronic structure of monolayer transition metal dichalcogenides (TMDCs)
using SEPM 65
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Fitting strategy for the Local Pseudopotential for monolayer TMDC . . . 66
5.3 Fitting of the Non-Local Pseudopotential for WSe2 . . . . . . . . . . . . . 74
5.4 Kinetic and Overlap Matrix Element within Planar Basis . . . . . . . . . 78
5.5 Local Pseudopotential Matrix Element . . . . . . . . . . . . . . . . . . . . 78
6 Conclusions 80
Bibliography 83

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指導教授

張亞中(Yia-Chung Chang)

審核日期

2023-10-31

推文