- 學位論文
不完美石墨烯系統的電子和自旋傳輸行為
The electron and spin transport in imperfect graphene system
摘要
本文建立石墨烯(graphene)系統中可能的線缺陷結構，並且利用非平衡格林函 數方法(Non-equilibrium Green function)去獲得石墨烯奈米緞帶(graphene nano ribbon)包含每一種不同的線缺陷結構的能帶結構(band structure)、傳輸行為、電子與自旋密度分布。利用這些結果去建立起石墨烯在包含不同線缺陷下的物理模型。結果顯示當線缺陷的型態為「之」字形(zigzag type)，當外加電壓差平行線缺陷，電子容易沿著線缺陷傳播就像是一個一維通道一樣。而當外加電壓差跨過「之」字形線缺陷，線缺陷像是一個屏障，限制電子傳遞。當考慮線缺陷附近有自旋軌道偶和效應(spin-orbit coupling)時，自旋密度分布的結果顯示「之」字形線缺陷有能力限制某一種自旋電子。而我們所建立的其中一種線缺陷，5-7 線缺陷的結果與吳教授所作的實驗結果相符合。在基本 電子傳輸與電流與電壓曲線中，石墨烯或石墨烯奈米緞帶包含 5-7 線缺陷時為 半導體特性，這是因為外加電壓差跨過 5-7 線缺陷，「之」字形線缺陷發揮阻擋 的效應。而磁阻則為正磁阻行為，這是因為「之」字形線缺陷容易限制某一種 自旋訊號，而外加磁場會造成該種自旋方向更容易被限制，所以這些實驗結果 都可以由「之」字形線缺陷特性解釋。而在波包隨著時間在實空間演化的模擬 中，5-5-8 線缺陷的石墨烯像是一個準穩定態。波包帶著 300 公尺/秒的速度沿著 5-5-8 線缺陷傳播，而且從模擬的最長時間 6 奈米秒結果可知，波包依然沿著線缺陷沒有因為時間而湮滅。而波包的傳播速度恰恰等於能帶結構所預測出 來的結果，所以 5-5-8 線缺陷就像是一個獨立的量子態。進一步，當我們考慮 外加磁場的時候，波包所帶的自旋行為如同自由電子結果一樣，會因為外加磁 場而使得自旋方向周而復始的從自旋向上轉成自旋向下再轉回自旋向上。根據 波包傳遞的行為以及外加磁場造成的自旋方向改變的結果，可以預測，有足夠 的時間去控制在 5-5-8 缺陷上的波包自旋方向。又因為自旋向上跟向下可視為 兩個量子態系統，也就是量子資訊中的量子位元(qbit)，所以 5-5-8 線缺陷的 石墨烯系統可以被預測作為自旋元件或是實現量子電腦的重要物質。
並列摘要
In this thesis, we established all possible structures of line defect in graphene system. Using non-equilibrium Green function obtains the band structure, transmission, charge density and spin density distribution in graphene nano ribbon with a line defect in different types. Using these results establish the reasonable physics picture for the electron and spin propagating in the line defect. The zigzag type line defect is like as a one dimensional channel when the current passes parallel with the line defect. However when the electron tries to cross through the zigzag type line defect, the line defect is like as barrier and blocks the electron. The spin density distribution results show that the zigzag type line defect has the ability for trapping one of kind spin when the local spin orbit coupling is considered. All of the results in 5-7 line defect is corresponded with the experiment result which is done by Prof. Wu group. The transmission and I-V behaviors show that if graphene or graphene nano ribbon contains 5 − 7 line defects, the electric property is semiconductor like. The magnetoresistance shows the positive behaviors, and it can be explained by the argument of that the zigzag type line defect has the ability to select and trap one kind of spin. In wave packet simulation result show that the wave packet moving along the 5 − 5 − 8 line defect is a quasi stable state. The wave packet moves along the line defect even after 6ns without dispersion and the velocity of the wave packet is about 300m/s and the result is corresponded to the band calculation. If an external magnetic field is considered, the spin of the wave packet rotates in cycle from spin up to down, and the result is satisfied with free electron case. According previous results it can be predicted that the electron trapped and moving along line defect can be operated the spin signal by the external magnetic field with enough time. And the spin signal can be considered the two quantum state system (one is spin up and another spin down). Therefore, the line defect graphene can be a candidate material for the device of spintronics and quantum computer.