本研究的目的是解決一個量子線中的懸題：局域性的磁性雜質是否能存在一個開放性且彈道傳輸的系統中？根據Cronenwett以及其研究團隊的研究成果[1]，在量子點接觸中觀察到的零偏壓非尋常效應代表著在這個量子線中存在著一個磁性雜質，前提是這個零偏壓非尋常效應遵循著近藤效應理論中的溫度變化以及磁場的影響。在本論文中，我們探討具有Rashba自旋軌道耦合效應的量子點接觸中的零偏壓非尋常效應，自旋軌道耦合效應提供我們操控電子自旋的途徑，藉此來找到量子線中懸題的答案。
在三次降溫過程中，零偏壓非尋常效應皆被觀察到，這意味著零偏壓非尋常效應不是由二維電子氣形成時產生的非序性導致的。單峰零偏壓非尋常效應遵循著近藤效應理論中的溫度變化：溫度上升時，電導下降。除此之外，在不同侷限偏壓情況下所得到的零偏壓非尋常效應之近藤溫度符合歸一化的關係。
值得一提的是，雙峰零偏壓非尋常效應在外加磁場為零時亦被觀察到，符合預期中自旋軌道耦合效應等效磁場的影響。在我同事的碩士論文中有近藤效應與Rashba自旋軌道耦合效應之間關係的詳細探討。
本研究的結果指出：在量子點接觸的彈道傳輸通道中，存在一個磁性雜質。由於量子點接觸的製造便利性與操控容易程度，使得我們可以利用量子點接觸來取代量子點來當作量子電腦中的基礎元件。

The project of this thesis is to find the clues to resolve one controversy over the quantum wire: does localized magnetic impurity exist in an open and ballistic system? According to the research done by Cronenwett [1], the zero-bias anomaly (ZBA) observed in the quantum point contact (QPC) is the signature of magnetic impurity embedded in the quantum wire as the ZBA peaks obeys the temperature and magnetic field dependence of the Kondo theory. In this thesis, we investigate the ZBA in the QPC with Rashba spin-orbit interaction, which provides us methods to control the electron spin, trying to find the solution to the controversy.
ZBA peaks are separately observed in three repeated cool-down process, suggesting that it was not caused by the disorder generated when the two dimensional gas is formed. The single ZBA peaks are found to obey the temperature dependence of Kondo theory: the conductance decreases as the temperature increases. Besides, the Kondo temperature, Tk, is extracted and the conductance of the different ZBA peaks follow the universal relationship of T/Tk.
It is worth noting that double peaks arise at zero external magnetic field, as expected that the effective magnetic field induce the peak splitting. The interaction between the Rashba SOI and the Kondo effect is fully investigated in my coworker’s thesis.
The result of our work indicates that magnetic impurities forms in the ballistic transport channel of the QPC, makes it a promising candidate to replace the quantum dots (QD) as the basic element of quantum computing as we can precisely control such localized spin in the quantum wire.

[1] S. M. Cronenwett et al., Phys. Rev. Lett. 88, 226805 (2002).
[2] J. Kondo, Prog. Theor. Phys. 32, 37-49 (1964)
[3] P. W. Anderson, J. Phys. C 3, 2439 (1970)
[4 K. G. Wilson, Rev. Mod. Phys. 47, 773 (1975)
[5] D. Goldhaber-Gordon et al., Nature 391, 156 (1998)
[6] A. Kristensen et al., Phys. Rev. B 62, 10 950 (2000).
[7] A. Das, Y. Ronen et al., Nat. Phys. 8, 887 (2012).
[8] F. Bauer, et al., Nature (London) 501, 73 (2013)
[9] T. Koga, et al., Phys. Rev. Lett. 89, 046801 (2002)
[10] C. Ford, C. Barnes, and T.-M. Chen, Mesoscopics, 1.
[11] S. D. Ganichev, et al., Phys. Rev. Lett. 92, 256601 (2004)
[12] F. D. M. Haldane. Phys. Rev. Lett. 40, 911 (1978)
[13] L. Kouwenhoven and L. Glazman, Phys. World 14, No. 1, 33–38 (2001)
[14] W.G. van der Wiel, et al., Science, 289, 2105-2108 (2000)
[15] P. J. Simmonds, et al., Applied Physics Letters, 92, 152108 (2008)
[16] Aguado, et al., Phys. Rev. Lett. 85, 1946-1949 (2000)