自旋電子於二維類碎形結構的傳輸行為

本論文中，我們利用蘭道方程式計算電荷與其自旋在規則碎形和隨機碎形中的傳輸行為，除此之外，我們考慮兩種裝置在這兩種情況，一個連接兩個極版，另一個連接四個極版。在規則碎形中，我們發現當樣本中的晶格缺陷數達到某一定值，電荷和電子只會被侷限在較高的電位處，且此傳輸係數的值與導體中可穿過的路徑有著公式化的規則；在隨機碎形中，我們不只更深入地尋找三種不同晶格結構的臨界機率，並探討電荷與其自旋的特性，它們表現出與參考數值相同的現象；正方形晶格、正三角形晶格和六角形蜂巢晶格的臨界機率分別是0.59，0.50和0.70。

關鍵字

蘭道方程式；碎形；傳輸係數；臨界機率

並列摘要

In the thesis, we calculate transmission coefficients of charge and spin in deterministic and random fractals by using Landau-Keldysh formalism. Besides, consider two setups, two leads and four leads, in both of cases. In the deterministic fractals, we find out that charge and spin are only accumulated in the beginning of the applied bias when the amount of defects increase to a designated value. And, transmission coefficients are followed a formula which is related with opened tunnels in the conductor. In the random fractals, we not only do a deeply studying to seek that values of threshold probability in three kind lattices but also are looking for the properties of charge and spin. They express the same as our reference values. The square lattice, triangular lattice and honeycomb lattice are 0.59, 0.50 and 0.70 for each.

並列關鍵字

Landau-Keldysh formalism ； fractals ； transmission coefficients ； threshold probability

參考文獻

[1] D. Sophin Seeli. “A Study on Fractal Image Compression using Soft Computing Techniques”. IJCSI, 9, No. 2. 420-430 ( Nov, 2012)

[2] J. J. SANKURAI. “Modern Quantum Mechanics”. Addison-Wesley, New York, revised edition (1994). 5, 54, 61, 119

[5] B. MANDELBROT. “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension”. Science, New Series. 156, No. 3775. 636-638 (May 5, 1967)

[6] M. ALI OMAR. “Elementary Solid State Physics: Principles and Applications”. Addison-Wesley (Jan 10, 1994)

[10] T. A. Witten, Jr. and L. M. Sander. “Diffusion-limited aggregation, a kinetic critical phenomenon”. Phys. Rev. Lett. 47, 1400-1403 (1981)

國際替代計量

自旋電子於二維類碎形結構的傳輸行為

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