含砷化銦量子點的砷化鎵二維電子氣之傳輸

Abstract

本論文探討的是摻雜砷化銦量子點之砷化鎵二維電子系統在低溫下之磁傳輸(magnetotransport)性質，內容包含下列二部分：

1. 低磁場下的侷域化，藍道能階量子化，與絕緣–量子霍爾相變

我們研究二維電子系統在外加垂直磁場下的電子傳輸性質。低磁場下，在絕緣態中所觀察到的SdH震盪代表藍道能階量子化能調變能譜的狀態密度，卻不會形成量子霍爾液體；隨著垂直磁場的增加，當能譜上藍道能帶間距足夠時，我們的實驗顯示出絕緣–量子霍爾相變：在相變點，系統從低磁場絕緣態轉變至一個填充因子ν大於等於3的量子霍爾狀態，然而霍爾電值與縱向電阻二者數值並不相同。根據SdH震盪的數學式，我們可以估計二維電子的量子遷移率，並發現μB ~ 1的關係式在相變點依然成立，此顯示能譜上不同藍道能帶間之可解析的必要性。

2. 在摻雜砷化銦量子點之砷化鎵二維電子系統中的溫度驅策流線與相變

我們從一個具閘極且含砷化銦量子點之砷化鎵二維電子系統的縱向與橫向電導率(σxx , σxy)建構一溫度驅策流線，進而研究系統的相變化。透過重整化群函數(renormalization-group functions)的效應，溫度驅策流線可以理論上的實現。在自旋簡併的區域，溫度驅策流線圖上的垂直線σxy = me2/h ( m是一奇數)分隔開兩個量子霍爾態。此外，隨著溫度降低，分析結果顯出溫度流線併入量子霍爾態的行為偏離了預期的半圓關係(semicircle relation)，此可能由於非彈性散射(電子-聲子、電子-電子等)的存在對侷域效應造成影響。

The thesis describes the low temperature magnetotransport properties in a GaAs two-dimensional electron gas containing self-assembled InAs quantum dots. This thesis comprises the following two parts.

1. Localization, Landau quantization, and insulator-quantum Hall transition at low magnetic fields

We present a magnetotransport study of a two-dimensional electron system. Shubnikov-de Haas (SdH) oscillations are observed in the insulator, indicating that Landau quantization can modulate the density of states without causing the formation of the QH liquid. With increasing the perpendicular magnetic field, from our study the insulator-quantum Hall (I-QH) transition from the low-B insulator to a filling factor ν which is greater than or equal to 3 QH state does occur as Landau bands become well-separated while the Hall and longitudinal resistivities may be different at the transition point. We can estimate the quantum mobility according to the expression of SdH oscillations. At the transition point, the relation μB ~ 1 is still valid, which represents a necessity of well-separated Landau bands in the energy spectrum.

2. Temperature driven flow lines and “phase” transitions in a GaAs two-dimensional electron system containing InAs quantum dots

We have constructed temperature driven flow lines from the longitudinal and transverse conductivities (σxx , σxy) in a gated two-dimensional GaAs electron gas containing InAs quantum dots, which allowed us to study the phase transition in our system. The flow lines could be realized theoretically from the effect of the renormalization-group functions. In the spin-degenerate regime, the separatrix σxy = me2/h ( m is an odd integer) separates a quantum Hall state from another. Moreover, the merging into these quantum Hall states with decreasing temperature appears to deviate from a semicircle relation. This could be due to the fact that the presence of inelastic scatterings (electron-phonon, electron-electron, etc.) is known to affect the localization effect.