單量子點在與電極之耦合強度隨時間變化下的非馬可夫量子傳輸研究

Abstract

在此篇論文中，我們討論通過兩個電極之間的單量子點(single quantum dot) 的電子 傳輸行為，亦即特別在考慮電極對量子點上電子的非馬可夫效應情況下通過單量子點的 電流。傳統上研究通過單量子點的電流，大部分使用馬可夫近似，馬可夫近似是指電子 的傳輸行為不會受到環境過去的資訊影響，只和當下的環境產生交互作用，而得到近 似後的馬可夫約化密度矩陣主方程式(reduced density matrix master equation )。而在 研究非馬可夫環境下，通過量子點的電流，主要有Feynman Vernon in uence functional theory、Non-equilibrium Green function method、Quantum state di usion equation幾 種方法。此篇論文中，我們使用非馬可夫量子態擴散方程式(non-Markovian quantum state di usion equation , NMQSD) 去推導出在外加時變偏壓與時變閘極電壓，且單量 子點和電極之間耦合常數亦為時變下精確的約化密度矩陣主方程式。然後用約化密度算 出量子點的平均粒子數，再經由海森堡方程式，進而得到通過量子點的電流。

In this thesis, we discuss the electron transport behavior of the single quantum dot between two electrodes, that is, the current owing into the single quantum dot, especially under the non-Markovian e ect of the electrodes. Traditionally, the study on the current owing into the quantum dot is under Markovian approximation. Markovian approximation means that the electron transport behavior will not be a ected by the past information of the environment, which we call it the bath in this thesis. It is a ected only by the environment at the present time. The main research method on transient current owing into the quantum dot are Feynman- Vernon in uence functional theory, non-equilibrium Green function method, quantum state di usion equation. In this thesis, we use non-Markovian quantum state di usion equation (NMQSD) to derive the master equation under time-dependent bias voltage, time-dependent gate voltage and time-dependent transmission coe cient controlled by the left and the right gate voltage. Finally, by Heisenberg equation, we get the transient current owing into the single quantum dot.