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  • 學位論文

新穎材料的電子結構

Electronic Structure of Novel Materials

指導教授 : 鄭弘泰

摘要


我們使用密度泛函理論(density functional theory)第一原理方法(first-principles)去研究幾種材料的電子結構(electronic structure). 例如多鐵(multiferroic)材料TbMn2O5, 鐵基超導(iron-base superconductor) Sr2VO3FeAs, 新發現的錸基(rhenium-based)六角晶格超導 HgxReO3, 以及量子自旋霍爾(quantum spin hall)材料, 矽烯(Silicene). 先前理論計算計算TbMn2O5的電子鐵電極化強度(electric polarization), 發現廣義梯度近似法(generalized-gradient approximation : GGA)給出的值比實驗高了一百倍. 這是因為GGA計算所給出的鍵結能量比實驗來的高. 當考慮晶格點庫倫斥能(on-site Hubbard U : GGA+U), 我們成功修正了GGA的鍵結能量. 這時所得的電子鐵電極化強度和實驗非常吻合. 另外我們也有分析鐵電極化強度和電荷-軌域有序(charge-orbital ordering)的關係. 鐵基超導是個很大的家族, 其中Sr2VO3FeAs是最複雜的結構. 之前的文獻指出, 一般鐵基超導需要做化學參雜(chemical doping)才會變成超導體, 但Sr2VO3FeAs不需要做任何參雜就會表現出超導性質, 這種有別於一般鐵機超導的現象, 是Sr2VO3FeAs最引人注目的特性. 根據GGA計算結果, 我們發現VO3層會提供電子到FeAs層. 這種自洽添加(self-doping)電子的行為等效於其他類鐵機超導的化學參雜. 另外我們也發現VO層具有半金屬(half-metal)的態密度(density of states), 這暗示說Sr2VO3FeAs的一般態有幾會可以應用於製作自旋電子學(Spintronics)元件.HgxReO3的超導相變溫度(phase transition temperature)是目前六角晶格超導中最高的. 它是由三維的ReO6和延著z方向的一維 Hg鏈所構成. 藉由電子結構計算, 我們發現在ReO6面上具有極性的二維自由電子氣(two dimensional electron gas). 這結果告訴我們要得到二維電子氣並不一定需要二維材料, 因為HgxReO3是一個三維加一維材料, 但依然存在二維自由電子氣.最後我們來檢查這幾年最熱門的材料, 矽烯. 它和石墨烯(graphene)類似, 都是蜂巢狀結構(honeycomb structure), 差別在於把石墨烯的碳原子全部替換成矽原子. 矽烯相對於石墨烯具有較強的自旋軌域交互作用(spin-orbital coupling), 理論預測矽烯可能是量子自旋霍爾材料, 因此這幾年有非常多理論和實驗方面的文獻在討論這個材料. 我們發現, 外加一個垂直於矽烯平面的電場能使得倒空間中狄拉克錐(Dirac cone)的自旋產生分裂. 電場越大分裂的程度越大. 當電場達到某個臨界值, 導帶(conduction band)和價帶(valence band)的能帶重和, 自旋軌域交互作用所產生的能隙(energy gap)關閉了. 因為此時自旋分裂很大, 因此費米能(Fermi’s energy)附近的能帶都是100%的自旋極化. 這種可調的自旋極化效應有非常高的潛力能應用於自旋電子學.

並列摘要


By using first-principles calculations based on density functional theory (DFT), we study the electronic structures of several novel materials such as the multiferroic material TbMn2O5, the iron-base superconductor Sr2VO3FeAs, the newly found rhenium-based hexagonal bronze superconductor HgxReO3, as well as the quantum spin Hall material Silicene. For the multiferroic material TbMn2O5, previous calculations based on the generalized-gradient approximation (GGA) gives an electric polarization value two orders of magnitude larger than the experimental data. Taking the on-site Hubbard U (GGA+U) into consideration, we successfully correct the over-binding problem in GGA and gives a much smaller polarization close to the experimental value. The close relations with the charge orbital ordering are also analyzed in detail. On the other hand, among the whole families of the iron-base superconductors, Sr2VO3FeAs has the most complex structure with a unique character that it is a superconductor by itself without any chemical doping. It is of high interests to investigate why the mother compound is already a superconductor whereas all the other Fe-based superconductors require suitable doping. Our GGA calculations demonstrate that the V ions of the VO layers in between the FeAs layers play the role of an electron donor to the FeAs layers, forming the self-doping mechanism. We also found that the VO layers exhibit half-metallic behaviour adjacent to the superconducting FeAs layers. As for HgxReO3, the crystal structure shows a 3D ReO6 network with 1D Hg chains along the c-axis. It was found superconducting in 2011. By studying the electronic structures, we found a spin polarized 2D electron gas (SP-2DEG) on the ReO plan. It is therefore very interesting that we found a SP-2DEG in a 3D+1D structure. This also gives an important indication that a 2DEG can exist in a system without any 2D structure. Finally the silicene, which is a Si version of graphene, has been a very attractive material in the passed few years. A large number of theoretical and experimental groups are studying this material. By applying an out-of-plane electric field, we found the spin degeneracy of the Dirac cone can be lifted. As long as the electric field strength increases, the Dirac cone splits itself into spin up and spin down bands with opposite directions in the occupied and unoccupied states. Consequently the small spin-orbit gap at the Fermi level is closed by fully spin polarized bands, resulting in a 100% spin polarized half-metallic behaviour. The tunable character in both spin-polarization and gap by the electric field would make silicene a very high potential material in spintronics.

參考文獻


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