在磁場中, 於一存在位能障的量子通道中的同調傳輸

Abstract

在本論文中，我們試著將所能得到的在量子導線的磁導率增促到高磁場的範圍。我們使用了兩種不同的方法、模態匹配近似法及Lippmann-Schwinger方程式的部分富立葉轉換近似方法、來交互比對確定我們的結果。接著我們對對穿透率、波函數、及電流密度作圖並解釋其中邊緣態的現象。經由比較比較磁場的迴旋半徑及通道的等效寬度，提供了一個簡單度量邊緣態產生的方法。

在通道含有一個排斥力的雜質時，我們在次能帶底部之上可以發現一個凹陷。而在吸引的雜質時，則在入射能量低於次能帶底部的地方發現兩個凹陷。我們也會討論邊緣態跟衰減態的現象。

In this thesis, we try to push our theoretical description of magnetotransport in a quantum wire to the high magnetic field regime. Two different approaches, namely, the mode matching approach and the partial Fourier transformation of the Lippmann-Schwinger equation approach, have been employed to cross check our results. We have plotted the transmission, the wavefunction, and the current density patterns and have interpreted them in light of the edge states. A simple criteria for the formation of edge states is reached, which is arisen from the comparison of the cyclotron radius and the effective width of the wire. For the case of a single repulsive barrier, a transmission dip is found at the threshold of a subband. For the case of a single attractive barrier, two transmission dips are found for incident energy that lies below a subband threshold. These are discussed in terms of the edge states and the evanescent modes.