二維砷化鎵電子系統之傳輸特性

Transport properties in two-dimensional GaAs electron systems

黃才育(Tsai-Yu Huang)

指導教授 ： 梁啟德

國立臺灣大學/理學院/物理研究所/博士(2005年)

https://doi.org/10.6342/NTU.2005.10360

摘要

我們研究了二維砷化鎵電子系統在磁場下之傳輸的量測。本論文包含下列四個主題：
1.低磁場下“絕緣體-量子霍爾”相變的研究
我們利用了具有閘極且含有自身聚集形成的砷化銦量子點的二維砷化鎵電子系統來研究“絕緣體-量子霍爾導體”的相變；此相變是分離了低磁場的絕緣體和填充係數為4的量子霍爾態。為了從低磁場的絕緣體直接地進入填充係數為4的量子霍爾態，此系統會經過一個從低磁場之侷域化到藍道之量子化的交點。事實上，此交點涵蓋了很廣的磁場範圍，並非只靠近在發生“絕緣體-量子霍爾導體”相變的臨界點的一小範圍。

2.不同的霍爾絕緣體之研究
我們利用了具有閘極且含有自身聚集形成的砷化銦量子點的二維砷化鎵電子系統來研究不同的霍爾絕緣體。實驗結果顯示在發生量子化的霍爾絕緣體時，並不需要伴隨著發生“絕緣體-量子霍爾”的相變。由我們的實驗結果可知，因為半圓理論(semicircle law)在量子霍爾態中可以是不符合的，所以在發生“絕緣體-量子霍爾”轉變時量子化的霍爾平台可以不存在。當量子霍爾態被無序破壞時，在絕緣態中可同時觀察到半圓理論的出現與崩潰。

3.直接量測一具閘極的二維砷化鎵電子氣之自旋能隙
我們研究了具閘極的砷化鎵二維電子氣之磁傳輸。從能量(E)-磁場(B)的圖形來探討具有自旋分裂的藍道能階時，我們可以對於不同的藍道能階之自旋能隙進行直接的量測。所量測出來的g-係數會大大地超過其在砷化鎵塊材的值(0.44)，這是由於電子-電子交互作用所造成的。當藍道能階的指數減少時，則g-係數會增加；這是由於當被佔據的藍道能階的數目減少時，則電子-電子交互作用的強度會增加的緣故。而且，由傳統活化能方式所得到的g-係數要比由直接量測所得的值約小2.5倍。

4.具自旋分裂的砷化鎵二維電子系統之“遷移率能隙”
我們進行了對於二維砷化鎵電子氣之電子的g-係數的磁傳輸量測。為了得知自旋能隙，我們量測了具自旋分裂的縱向電阻率的最小值，因其顯示了可被活化的行為。由不同奇數的填充係數的自旋能隙，我們可以得到有效的g-係數，且其值大大地超過了砷化鎵塊材的值(0.44)。這個增加的效應是由於多體的電子-電子交互作用所引起的。我們的實驗結果提供了可信服的證據，說明了由傳統的的活化能方式所得到的是“遷移率能隙”，這與真實的自旋能隙有很大的不同。

關鍵字

砷化鎵 ； 量子霍爾效應 ； 相變 ； 霍爾絕緣體 ； 電子自旋

並列摘要

We have investigated the low-temperature magnetotransport measurements in two-dimensional GaAs electron systems. This dissertation consists of the following four topics.

1. On the low-field insulator-quantum Hall transitions

We studied the insulator-quantum Hall conductor transition which separates the low-field insulator from the quantum Hall state of the filling factor /nu=4 on a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. To enter the /nu=4 quantum Hall state directly from the low-field insulator, the system undergoes a crossover from the low-field localization to Landau quantization. The crossover, in fact, covers a wide range with respect to the magnetic field rather than only a small region near the critical point of the insulator-quantum Hall conductor transition.

2. On the various Hall insulators

We have studied the various Hall insulators (HIs) in a gated two-dimensional GaAs electron system containing self-assembled InAs quantum dots. It is shown that the quantized HI is not necessarily accompanied by the insulator-quantum Hall (I-QH) transition. From our study, the semicircle law can become invalid in the QH liquid so that the quantized Hall plateau is absent at the I-QH transition. The appearance and breakdown of the semicircle law in the insulating phase can be both observed when the QH liquid is destroyed by disorder.

3. Direct measurement of the spin gaps in a gated two-dimensional GaAs electron gas

We have investigated magneto transport in gated GaAs two-dimensional electron gases. From the evolution of spin-split Landau levels (LLs) in the Energy (E)-magnetic field (B) plane, we can perform direct measurements of the spin gap for different LLs. The measured g-factor is greatly enhanced over its bulk value in GaAs (0.44) due to electron-electron (e-e) interactions. As the LL index decreases, the g-factor increases, suggesting that the strength of e-e interactions increases as the number of occupied LL decreases. Moreover, the g-factor determined from the conventional activation energy studies is ~ 2.5 times smaller than that deduced from the direct measurements.

4. “Mobility gap” of a spin-split GaAs two- dimensional electron system

We have performed magnetotransport measurements of the electron g-factor in a two-dimensional GaAs electron gas. In order to obtain the spin gap△S, we measure the spin-split longitudinal resistivity minimum which shows an activated behavior. From the spin gaps at different odd filling factors, we can obtain the effective g-factor which is greatly enhanced over its bare value (0.44) in GaAs. This enhancement is due to many-body electron-electron interactions. Our experimental results provide compelling evidence that conventional activation energy studies yield a “mobility gap” which can be very different from the real spin gap in the energy spectrum.

並列關鍵字

GaAs ； quantum Hall effect ； phase transition ； Hall insulator ； spin

參考文獻

References for chapter 1

[1] D. Stein, K. v. Klitzing, and G. Weimann, Phys. Rev. Lett. 51, 130 (1983).

[2] H. L. Störmer, R. Dingle, A. C. Gossard, W. Wiegmann, and M. D. Struge, Solid State Commun. 29, 705 (1979).

[3] R. Dingle, H. L. Störmer, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 33, 665 (1978).

References for chapter 2