- 學位論文
量子點系統中電子傳輸的條件式統計
Conditional counting statistics of electron transport in quantum dot systems
摘要
計數統計(Full counting statistics)是一種提供我們了解介觀電子系統的量子傳輸統計行為的方法。藉由number-resolved master equation的理論描述，計數統計已被有效落實於理論計算的研究上。但截至目前為止，大多研究主要都專注在非條件式計數統計來探討分析電子在奈米元件中的傳輸性質，即使是較為複雜的雙電流耦合導體系統中的電流與電流之間擾動（fluctuation）的交互關聯(cross correlation)也已經有理論計算的成果。條件式計數統計(conditional counting statistics)所計算的是雙電流耦合奈米元件中其中一個導體的電流統計，條件於來自該元件另一個導體所被觀測到的某一個特定輸出電流訊號。不同於一般的計數統計所涉及的面向，條件式計數統計提供了更多介觀系統內電子傳輸的訊息和物理內涵。近年來，單量子點傳輸系統耦合到量子點接觸(quantum point contac)的條件式計數統計已經在實驗上量測到。但是，理論上依然缺乏了一個系統化的方式來計算更為複雜的系統的條件式電流與電流擾動統計性質。因此，在這篇論文內，我們從number-resolved master equation出發，進一步發展一個較系統化且有效率的方法來計算條件式計數統計。我們將使用雙量子點傳輸系統耦合到量子點接觸的模型為一個範例來展示我們的方法。我們預期這樣的方法將可以被用來處理許多不同的奈米元件中電子的傳輸的計數統計問題。
並列摘要
Full counting statistics (FCS) can provide information of quantum statistical properties of electron transport phenomena. A theoretical approach called n-resolved master equation approach has been applied to calculate FCS of electron transport properties in nanostructure device. But so far this approach has mainly been applied to calculate the unconditional FCS even through the cross correlation between current fluctuation in two coupled conductors each connected to its own leads has also been investigated. The conditional counting statistics that is the statistical current fluctuation of one conductor conditioned on a particular current observed in the other could be substantially different from its unconditional counterparts. Furthermore, the conditional counting statistics can provide more information and more insight into the electron transport properties than the unconditional one. The conditional counting statistics of electron transport for a system of a quantum dot (QD) coupled to a quantum point contact (QPC) has been measured experimentally recently. Since a systematic method to calculate the conditional FCS for more complicated nanostructure dvice is still lacking, we aim to develop and provide such a method based on n-resolved master equation approach in this thesis. We will take a system of two coupled quantum dots measured by a QPC as an example to demonstrate our method. It is expected that our method can be applied to electron transport problems for many different nanostructure devices.