以第一原理計算研究尖端材料之光學與超導性質

Abstract

這篇論文以第一原理計算為基礎，深入探討多種尖端材料中的光學性質與超 導特性，並著重於量子幾何在其中所扮演的關鍵角色。首先，我們研究了在拓樸 磁性籠目材料鐵錫合金 (FeSn) 和鈷閃鋅礦化合物 (Co3Sn2S2) 中的線性光學反應， 揭示了光學異向性、可調變的拓樸結構與低能量電子能帶等現象。

在鐵錫合金 (FeSn) 的研究中，透過詳細的第一原理分析，我們透過選擇不同 原子間的共振了解到來自於籠目平面與錫緩衝層之間的激發對於其異常的強垂直 導電性的重要性。這本與該材料作為結構上理想的籠目金屬所預期的行為相反。 而在鈷閃鋅礦化合物 (Co3Sn2S2) 中，我們揭示了節線共振對於其強反常霍爾效 應的貢獻，並進一步顯示透過改變磁化方向可以生成或湮滅節線與外爾點 (Weyl points)。在此同時，低能量的能帶結構改變伴隨著光學導電譜的紅移，反映出量 子度量 (quantum metric)的增強。

在此基礎上，我們拓展研究至二階非線性光學效應，特別是第二諧波響應。 本研究引入了數學上的四分體形式 (vielbein formalism)，建立了量子力學中仿射 連接 (affine connection) 的數學形式以及其物理詮釋。我們提出了具有物理意義的“量子變形張量"，並將扭率 (torsion) 與應變效應(strain)類比於量子態在希爾伯 特空間的演化，進而與非線性光學中電子激發態的位移機制建立直接關聯。此理 論以第一原理計算節線半金屬鈣-銀-磷化合物 (CaAgP) 的第二諧波響應當作實例 得到驗證，展現量子幾何如何引致顯著的非線性光學反應。

最後，我們探討了在含有過渡金屬元素的鈧六碲二-過渡金屬化合物 [Sc6MTe2(M = Fe, Co, Ni)] 的聲子媒介超導性質。我們的計算揭示了強烈的高諧 聲子效應與低頻率的搖擺聲子 (rattling phonons)，不僅大幅增強了電子-聲子耦合， 也提高了超導相變溫度。透過自洽聲子理論與聲子頻譜的分析，我們釐清了這些 複雜材料中超導現象的起源，並強調高諧聲子在第一原理預測超導的重要性。此外，透過引入電負度概念，我們亦展示了如何利用磁性元素與非超導元素的結合 來設計新型超導體。

This thesis presents a comprehensive first-principles investigation of the optical properties and superconductivity in various advanced materials, emphasizing the role of quantum geometry. We first explore the linear optical responses of topological magnetic kagome materials FeSn and Co3Sn2S2, highlighting phenomena such as optical anisotropy, tunable topology, and low-energy electronic bands.

Detailed ab initio analysis on site-selected resonances on FeSn reveals the importance of the excitation between the kagome plane and Sn buffer plane, explaining the origin of the stronger out-of-plane conductivity that is counterintuitive to the usual belief for a structurally ideal kagome metal FeSn is. For Co3Sn2S2, we reveal the nodal-line resonance toward the strong anamolous Hall effect and a generation or annihilation of nodal lines and Weyl points by tuning the magnetic direction. Upon modifying the low-energy band structures, we observe a redshift of the optical conductivity, indicating an enhancement of the quantum metric for Co3Sn2S2.

Building on this foundation, we extend our analysis to second-order nonlinear optical effects, particularly second harmonic generation. By introducing a vielbein-based formal- ism, we uncover a deep geometrical interpretation of the affine connections in quantum mechanics. The physically interpretable form of the quantum deformation tensor is proposed. The torsion and strain effects are analogous in quantum states, which is directly related to the shift mechanism in nonlinear optics. This approach is validated through a case study of the second harmonic generation of nodal-line semimetal CaAgP, where we demonstrate how nontrivial quantum geometry gives rise to pronounced nonlinear responses.

In the final part of the thesis, we investigate phonon-mediated superconductivity in d-element-rich compounds Sc6MTe2 (M = Fe, Co, Ni). Our calculations reveal strong anharmonic effects and low-frequency rattling phonons that significantly enhance the electron-phonon coupling and superconducting transition temperature. Through the self-consistent phonon method and analysis of Eliashberg spectral functions, we elucidate the origin of superconductivity in these complex systems and highlight the importance of incorporating anharmonicity in predictive ab initio frameworks. Also, by incorporating electronegativity, we can design superconductors by combining nonsuperconducting elements with magnetic elements.