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Title: | 空間與時間反演對稱材料之非線性光學性質:理論與第一原理計算 Nonlinear Optical Properties of PT-symmetric Materials: A GGA+U Study |
Authors: | 劉冠甫 Guan-Fu Liu |
Advisor: | 郭光宇 Guan-Yu Guo |
Keyword: | 第一原理計算,二階諧波產生,光學非互易性,非線性光學,PT對稱材料, First-principles calculation,Second-harmonic generation,Optical nonreciprocity,Nonlinear optics,PT-symmetric materials, |
Publication Year : | 2023 |
Degree: | 碩士 |
Abstract: | 關於固體中的二次諧波產生,有許多不同的公式。由於相關的代數相當繁雜, 要確定不同公式彼此是否等價相當困難。有些作者假設系統帶有特定的對稱性以簡化公式。這讓二次諧波產生的理論研究困難重重。本研究以長度規範場微擾理論從頭推導,以得到適用於磁性材料的二次諧波產生計算。本形式適用於半導體與絕緣體。
磁偶極矩二次諧波產生是一個相當新穎的現象。一般電偶極矩二次諧波產生的效應相對大許多,但在特定的材料磁偶極矩的貢獻不可忽略。Cr2O3中的電-磁偶極矩干涉就是一個例子。本研究讓以第一原理計算材料的二階諧波產生。 在電偶極矩近似下,中心對稱材料中的二次光學效應一般為零。PT對稱半導材料的中心對稱只被磁序破壞。這讓特定的磁生效應的偵測容易分辨。舉例來說,圓偏振位移電流與線偏振注入電流是PT對稱材料中的僅有兩個不為零的二階光電效應。 For second-harmonic generation in solids, many different expressions can be found in the literature. However, due to the complexity of the algebra involved, their equivalence are difficult to confirm. There is also the problem of hidden assumptions. Many authors chose to simplify the formulas for systems with time reversal symmetry without explicitly stating so. When one wishes to study the second-harmonic generation in magnetic materials, it is not always clear which formulas are applicable. In this study, we started from scratch in the length gauge perturbation theory (originally developed by Aversa et al.) to derive formulas for second-harmonic generation suitable for numerical calculations of magnetic materials. This formalism is applicable to semiconductors and insulators. The elusive magnetic dipole second-harmonic generation has also been investigated theoretically and numerically. This effect, while usually dominated by the electric dipole counterpart, is important in certain materials where their magnitudes are comparable. One such example is the inteference of EDSHG and MDSHG in Cr2O3, which gives rise to optical nonreciprocity. The tools developed in this study allows us to calculate EDSHG and MDSHG efficiently with a first-principles code (via the wannier90 package). It is well known that any second-order optical effect (in the electric dipole approximation) vanishes when the system is centrosymmetric. The class of PT-symmetric semiconductors has the following special property: its inversion symmetry is only broken by the magnetic order. This symmetry property allow us to isolate certain nonlinear responses from the rest of the possible effects. For example, the novel circular shift current and linear injection current (also known as the quantum metric current) are the only second-order photocurrent responses in PT-symmetric materials. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/87232 |
DOI: | 10.6342/NTU202300559 |
Fulltext Rights: | 未授權 |
Appears in Collections: | 物理學系 |
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ntu-111-1.pdf Restricted Access | 3.41 MB | Adobe PDF |
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