單量子點在含時偏壓與閘極電壓下的非馬可夫量子傳輸研究

Abstract

在此篇論文中, 我們研究了在兩個電極(electrodes)中間單量子點的非馬可夫動力行為。在過去的理論當中, 一般用約化密度矩陣主方程式(reduced master equation)在處理奈米元件下電子傳輸行為時, 通常使用寬能帶極限近似和馬可夫近似。但我們可以從非馬可夫量子態擴散方程式(non-Markovian quantum state diffusion equation)的理論架構出發而進一步地得到精確的約化密度矩陣主方程式,以及經由海森堡方程式, 推導出通過單量子點系統的電流方程式。另外我們也顯示從非馬可夫量子態擴散狀態方程式推導出的精確約化主方程式和精確的電流方程式裡的函時係數與從非平衡態量子理論用Feynman-Vernon泛函路徑積分方法所得到的相同。此外, 我們推廣非馬可夫量子態擴散方程式理論來研究在同時外加含時偏壓以及含時閘級電壓的單量子點電子傳輸問題。我們採用左右兩邊電極的譜密度(spectral density)為勞倫茲型式來對通過單量子點系統量子傳輸動力行為進行探討。在外加偏壓以及閘極電壓為與時間無關以及與時間相關這兩個情況之下, 我們研究勞倫茲型譜密度的能帶寬度(bandwidth)以及中心(center of spectral density)對有效穿遂率和平均電流的影響。

In this thesis, we investigate the non-Markovian dynamics of a quantum dot system between two electrodes. Going beyond the wideband limit (WBL) and the Markovian approximation usually employed in the theoretical study for the electron transport in the nanostructure devices, we use the exact reduced master equation derived from the non-Markovian quantum state diffusion (NMQSD) approach. We start from the Heisenberg equation and further derive the reduced master equation and the current equation for the quantum dot system by NMQSD. Then, we show that the time-dependent coefficients in both of the reduced master equation and the current equation can be exactly expressed in terms of the time-dependent coefficients calculated by the non-equilibrium theory based on Feynman-Vernon influence functional approach. Furthermore, we generalize NMQSD formalism to treat the transport problem of a single quantum dot with time-dependent bias voltage and time-dependent gate voltage. Taking the spectral densities of the two electrodes as Lorentzian-type shapes, we study the quantum transport dynamics through the quantum dot system. We set the bias voltage and gate voltage to be time-independent or/and time-dependent. The dependence of the width and center of the Lorentzian-type electrode spectral density and the behavior of the gate voltage and bias voltage on the effectively tunneling rates and average current are investigated.