在有限環中側接量子點的Kondo效應

Abstract

這篇論文利用平均場論研究在雙量子點系統中，Kondo 效應和反鐵磁耦合間的競爭。這個雙量子點系統中，包含一個介觀環和兩個量子點，其中一個量子點(dot1)埋在環的兩端間且利用環上的傳導電子和dot1上幾乎被固定住的電子之間的Kondo耦合連接，而另一個量子點(dot2)從側邊利用電子與電子間的反鐵磁耦合連接在dot1上。反鐵磁耦合趨向使dot1和dot2上的電子形成local spin-singlet，而Kondo耦合趨向使環和dot1形成一個導通的線路。兩種耦合在系統中彼此競爭。當反鐵磁耦合的強度增加時，Kondo耦合的強度因此被削弱。我們透過改變系統大小取代改變溫度來看在Kondo以及反鐵磁耦合造成的過度區裡的物理。在論文中，我們展示我們從平均場中得到的相變圖，相變圖會隨著系統大小L而有所不同 (L mod 4)。相變圖中說明兩個效應之間的競爭。並且，我們計算三個物理量，有效Kondo溫度(或是Kondo屏蔽雲大小的倒數)、態密度和恆定電流，可以幫助我們了解當環的大小改變或是反鐵磁耦合強度改變時，系統的狀態。其中，對有效Kondo 溫度做scaling，能夠幫助我們更了解在熱力學極限時，發生的Kondo態和單重態間量子相變。Kondo態指的是，在系統中，只有Kondo耦合存在；單重態指的是，在系統中，只有反鐵磁耦合存在。在結果的部分，我們幸運的發現，在熱力學極限所發生的量子相變為擁有有限值Kc (臨界點)的Kosterlitz-Thouless相變。

In this thesis, we use large-N slave-boson mean-field theory to study the competition between Kondo effect and antiferromagnetic (AF) coupling in a side-coupled doublequantum-dot (DQD) system where one dot (dot 1) is embedded in a mesoscopic ring and the other dot (dot 2) is side-coupled to the dot 1. Kondo effect between terminals of the ring and dot 1 competes with AF coupling between dot1 and dot2. We establish the general phase diagrams which presents the results of the competition in different system size or in different AF coupling strength and can be classified into two cases by system size L (mod 4). For a further understanding these phase diagrams, three observables, effective Kondo temperature, density of state, and persistent current, are calculated. For fixed K > Kc, we find that all of the observables indicating the system crossover to spin-singlet phase where Kondo effect is blocked with increasing system size; while for a fixed K < Kc, all of the observables imply the system toward Kondo phase where AF coupling does not exist with increasing size. Especially, we apply finite size scaling to effective Kondo temperature and find the system following Kosterlitz Thouless transition with finite critical point, Kc > 0, in thermodynamic limit. Our results at zero temperature but finite sizes offer an alternative route to study the crossover behaviors between Kondo and spin-singlet phase in a DQD system. The relevance of our system to the experiments is discussed.