以廣義弗羅奎茲(Floquet)方法處理奈米尺度下時變電子傳輸

Abstract

時變電子傳輸的過程，通常考慮在寬帶極限下並由週期性外加場驅動。在此論文中，我們以廣義弗羅奎茲(Floquet)方法處理由單一或雙外加場驅動的電子傳輸。為了處理雙外加場中不相稱的(incommensurate)頻率問題，我們採用多模弗羅奎茲理論(many-mode Floquet theory)將時變且非週期性的哈密爾敦量(Hamiltonian)，轉變成非時變的弗羅奎茲矩陣(Floquet matrix)，從原本的偏微分方程簡化成解特徵值的問題。這個方法可用來分析由外加場驅動的電子傳輸在電極─量子點─電極系統下的直流電流。由週期性外加場的驅動下，探討對稱型式(Λ-type)三量子點的同調 穿隧截止現象。此外，在雙頻率外加場的影響下，發現直流電流對於兩頻率的可公度性(commensurability)非常靈敏。這些有趣的物理現象，提供製作量子裝置一種輕易控制電流的方法。

Time-dependent electron transport processes are often driven by a periodic field and studied in the wide-band limit. In this thesis, we extend the generalized Floquet approach beyond wide-band limit for the nonperturbative treatment of electron transport driven by monochromatic or bichromatic fields. In order to deal with the case of bichromatically driven fields with incommensurate frequencies, we adopt the many-mode Floquet theory to reduce the non-periodically time-dependent Hamiltonian into an equivalent time-independent infinite-dimensional generalized Floquet matrix eigenvalue problem. The approach is used to perform a detailed analysis of the electron-transport dc current in the electrode-quantum dots-electrode system driven by external fields, including periodic and bichromatic fields. The coherent destruction of tunneling phenomenon is studied in the case of symmetric Λ-type triple quantum dots driven by a periodic field. Besides, we show that the dc current depends sensitively on the commensurability of the driving frequencies. These interesting physical phenomena may provide a convenient way to control the current by fabricating a quantum device.