| 摘要: | 本論文中，使用第一原理計算研究電聲子超導體的電子和振動性質。首先，對於鎵不同固態相的超導性進行研究。基於物件式隨機結構預測方法，我們得到了固態鎵的八個最低能量結構。物件式隨機結構方法不僅準確地預測出現有文獻中提到的最小基態結構α-Ga和其他亞穩態結構，同時也預測了新的未知結晶結構Imma-Ga。隨後，我們對於這些固態鎵的結構進行電子和電聲子耦合計算，以解釋鎵超導相其臨界溫度的大幅差異。計算結果顯示不同固態相的超導溫度可分為兩類：Tc > 5K與Tc $\leq$ 1K。主要的超導溫度區別來自於其結構特徵。例如，實驗上已發現的β和γ相的超導溫度較高，其組成結構不包含鎵二聚體。然而，低超導溫度的相結構包含了共價鍵結的鎵二聚體，其費米能階的能態密度顯著減少，從而減弱了電子-聲子耦合強度，導致超導溫度顯著降低。
其次，我們研究二維材料，即單層厚的二氧化鈷以及它的固態晶體和雙層對應物的超導性。計算結果預測單層二氧化鈷具有金屬鐵磁基態。非自旋極化的計算顯示，這種2D材料在25-28 K時具有電聲子介導的超導性。單層CoO$_2$中的強電子-聲子耦合主要貢獻來自於聲學聲子，這使得CoO$_2$成為目前發表的二維材料中，最高溫超導體之一。CoO$_2$薄片可以通過剝離方法來合成，因為層中間的結合能相對較小，因此能在一般實驗條件下保持其穩定性。
我們接著使用第一原理計算對鋁(100)、(110)和(111)表面的表面能、功函數、電子-聲子耦合常數和超導轉變溫度的振盪量子尺度效應(QSE)進行研究。結果顯示這些物理特性具有顯著的振盪量子尺度效應, 與隨著材料厚度變化的受限電子能量是相關聯的。Al(111)薄膜的表面能和功函數可以由沿著[111]方向的一個費米波矢量決定的周期性阻尼正弦函數擬和的很好，其可表述為薄膜厚度的函數，而對於Al(110)薄膜，必需使用在[110]方向上的三個費米波矢量的組合來做擬和。因此，藉由固體能帶結構來定量描述這些量子尺度效應是必要的。
本論文除了電聲子超導體的相關研究外，最後一章討論在能源轉換材料領域的工作，包括熱電材料和金屬有機鈣鈦礦太陽能電池。我們首先研究溫度改變對於硒化錫(SnSe)能帶結構的影響，其中與溫度相關的晶格常數由實驗量測決定。計算結果顯示，硒化錫Cmcm相的能帶結構產生了間接到直接能隙的改變，對於瞭解這個新一代優異的熱電材料提供了新的視角。本章最後，我們使用第一原理計算對於金屬有機鈣鈦礦MAPbBr3晶體進行研究，藉由改變有機陽離子分子偶極方向而計算得到與實驗量測(STM)相符的表面結構。此部分研究顯示了理論計算可以幫助瞭解此種新興材料對於光照誘導改變其表面結構背後的潛在機制。;In this thesis, the electronic and vibrational properties of selected phonon-mediated superconductors are investigated using the first-principles calculations. First, the superconductivity of various bulk phases of Gallium are studied. Based on structural predictions using \textit{ab-initio} random structure searching with the \textit{object} (RSSWO) concept, we have obtained eight lowest energy structures of Ga. RSSWO not only captures accurately the global minima ground state $\alpha$-Ga and other metastable structures reported in the literature but also reveals the unknown crystalline \textit{Imma}-Ga. Subsequently, the electronic structures and electron-phonon coupling calculations of these structures were carried out to explain the large variation in superconducting transition temperatures of Ga phases. We found that The T$_c$s were separated into two categories for different phases: T$_c$ > 5K, and T$_c$ $\leq$ 1K. Such major distinction is found owing to the structural feature. Some of the higher-T$_c$ structures Ga, which are experimentally identified as $\beta$ and $\gamma$ phase, do not contain Ga dimers. However, the low T$_c$ phases, which contains Ga dimers with the partial covalent bonding, significantly decreases the density of state at Fermi level. This weakens the electron-phonon coupling strength, leading to a considerably lower T$_c$.
Second, we explore the superconductivity in a two-dimensional lattice, the single layer thick CoO$_2$ as well as its bulk and bilayer counterpart. We show that the monolayer CoO$_2$ sheets have a metallic ferromagnetic ground state. The non-spinpolarized calculation shows that this 2D material possesses a phonon-mediated superconductivity at 25-28 K. The strong electron-phonon coupling in monolayer CoO$_2$ is mainly driven by the acoustic phonons making CoO$_2$ one of the highest-temperature superconductor in existing 2D materials. In addition, CoO$_2$ sheets can be synthesized by exfoliating bulk because of the relatively small binding energy in the interlayer while maintaining their stability under normal experimental conditions.
We then present first-principles calculations for Al(100), Al(110), and Al(111) to study the oscillatory quantum size effects (QSE) exhibited in the surface energy, work function, electron-phonon coupling constant, and superconductivity transition temperature $T_c$. These physical characteristics are found to have significant oscillatory QSE that are associated with the thickness dependence of the energies of confined electrons. A damped sinusoidal function with the periodicity determined by one Fermi Wave vector along the [111] direction can well fit the surface energy and work function of Al(111) films as a function of film thickness while it is required for the case of Al(110) films a combination of three Fermi wave vectors over the direction [110]. To describe these QSE quantitatively, a full consideration of the crystal band structure is necessary.
While the main part of the thesis relates to phonon-mediated superconductors, the final chapter discusses of the work carried out in the field of energy conversion material, including thermoelectric and metal-organic perovskite solar cells. We study the temperature dependence of band structure in SnSe whose lattice constant is determined from experiments. The indirect-direct band gap transition was found as a function of temperature in the \textit{Cmcm} phase of SnSe, which gives new perspective into the understanding of this record-breaking thermoelectric material. Finally, the agreement between STM simulation and experimental work on the metal-organic perovskite solar cell MAPbBr$_3$ crystal is then presented in the last part of chapter 6. The theoretical calculations may shed some light on the underlying mechanism of illumination-induced organic cation molecule dipole orientation in this emergent material. |
