碎形結構上的自旋傳輸

Spin Transport on Multiply Connected Fractal Conductors

李柏叡(Bo-Ray Lee)

指導教授 ： 張慶瑞

國立臺灣大學/理學院/物理研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.10679

摘要

本篇論文主要探討在碎形結構上的電子自旋傳輸，希望藉由碎形結構的的自我相似性來找出特殊現象。計算上使用了非平衡格林函數和緊束縛近似模型，模擬在不同的碎形程度和偏壓下，電子自旋密度、電荷密度和遷移率的演變。我們發現隨著碎形程度的增強，遷移率會有共振變化，更在謝爾賓斯基地毯的二階碎形結構中，發現了自旋-電赫不相依的現象。論文中利用等效位能井、量子線模態和自旋極化距離的概念，解釋了上述的物理圖像。
此外，我們也探討了自旋傳輸上的滲透理論。以往的滲透理論，當媒介的密度達到某一臨界值時，滲透物可從媒介一端到達另一端，所以當一個金屬導體的密度低於極值時，將會轉變為絕緣體。然而，自旋和電荷的滲透臨界值可能不同，意味著電荷上的絕緣體有可能是自旋上的導體。其中，遷移率的計算符合了二維滲透理論的預測。

關鍵字

自旋 ； 量子傳輸 ； 碎形結構 ； 非平衡格林函數 ； 自旋霍爾效應

並列摘要

We consider spin and charge transport on a Sierpinski planar carpet; the interest here is its unique fractal geometry. Analyzing a fractal conductor as a combination of multiply connected quantum wires we observe the evolution of the transmission envelope in different generations of the fractal conductor. For a fractal conductor dominated by resonant modes the transmission is characterized by strong fluctuations and conducting gaps. We show that charge and spin transport have different responses to the presence of defects and to applied bias. At a high bias, or in a high-order fractal generation, spin accumulation is separated from charge accumulation because the larger drift velocity needs a longer polarization length, and the sample may turn into an insulator by the action of the defects.
Furthermore, we also discuss the percolation theory in spin transport. In the old percolation theory a metal can be turned into an insulator if its site ratio is lower than the percolation ratio. However, the percolation of charges and spin may be different. It means a charge insulator is possible to be a “spin conductor”. Our results are calculated numerically using the Keldysh Green function in the tight-binding framework.

Keywords: Spin, Quantum Transport, Fractal Structure, Landau-Keldysh Formalism, Non-Equilibrium Green Function, Spin Hall Effect

並列關鍵字

Spin ； Quantum Transport ； Fractal Structure ； Landau-Keldysh Formalism ； Non-Equilibrium Green Function ； Spin Hall Effect

參考文獻

[1] Tang, C. S. and Mal’shukov, A. G. and Chao, K. A., Phys. Rev. B 71, 195314 (2005).

[4] Seki, Takeshi and Hasegawa, Yu and Mitani, Seiji and Takahashi, Saburo and Imamura, Hiroshi and Maekawa, Sadamichi and Nitta, Junsaku and Takanashi, Koki, Nat. Matter 7, 125 (2008).

[9] Sheng P. and Tao R., Phys. Rev. B 31, 6131 (1985).

[12] Grimmett, Geoffrey, Percolation, Springer (1999).

[16] Supriyo Datta, Electronic Transport in Mesoscopic Systems (First edition, 1998).