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系統識別號 U0026-0307201309175500
論文名稱(中文) 磁性雜質對碳膜的狀態密度修正
論文名稱(英文) Studies on Density of state Correction Induced by Magnetic Impurity on Graphene
校院名稱 成功大學
系所名稱(中) 物理學系碩博士班
系所名稱(英) Department of Physics
學年度 101
學期 2
出版年 102
研究生(中文) 陳玉清水
研究生(英文) Tran Ngoc Thanh Thuy
學號 L26007020
學位類別 碩士
語文別 英文
論文頁數 44頁
口試委員 指導教授-陳家駒
口試委員-包健華
口試委員-蔡錦俊
中文關鍵字 none 
英文關鍵字 mean field approximation  density of state 
學科別分類
中文摘要 none
英文摘要 Based on the mean field approximation and the Green’s function techniques, we have reviewed the paper “Localized Magnetic states in Graphene” published by Uchoa et al. In this thesis, we have extended their work by applying the mean field approximation to the equation of motion instead of applying it directly to the hamiltonian as Uchoa’s work and obtained the density of state correction induced by magnetic impurity on graphene.
論文目次 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Review on Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Lattice structure of Graphene . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Graphene stacking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Bilayer graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Trilayer graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Electronic properties of Graphene . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Band structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Cyclotron mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.3 Density of states . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.4 Dirac fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Green’s Function and the Mean Field Approximation . . . . . . . . . . . . . . . 18
3.1 Time-independent Green’s functions . . . . . . . . . . . . . . . . . . . . . 18
3.2 Time-dependent Green’s functions . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Equation of motion method . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 The mean field approximation . . . . . . . . . . . . . . . . . . . . . . . . 23
4 The Density of State of Localized Magnetic Impurity . . . . . . . . . . . . . . . 24
4.1 Localized Magnetic States in Metals . . . . . . . . . . . . . . . . . . . . . 24
4.2 Localized magnetic states in graphene . . . . . . . . . . . . . . . . . . . . 26
5 Beyond the standard Mean Field Approximation . . . . . . . . . . . . . . . . . . 35
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
參考文獻 [1] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys., vol. 81, pp. 109–162, Jan 2009.
[2] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature, vol. 438, no. 7065, pp. 197–200, 2005.
[3] K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Communications,
vol. 146, pp. 351 – 355, 2008.
[4] K. Kim, J.-Y. Choi, T. Kim, S.-H. Cho, and H.-J. Chung, “A role for graphene in siliconbased semiconductor devices,” Nature, vol. 479, no. 7373, pp. 338–344, 2011.
[5] B. Uchoa, V. N. Kotov, N. M. R. Peres, and A. H. Castro Neto, “Localized magnetic states in graphene,” Phys. Rev. Lett., vol. 101, p. 026805, Jul 2008.
[6] P.W. Anderson, “Localized magnetic states in metals,” Phys. Rev., vol. 124, pp. 41–53, Oct 1961.
[7] E. Jomehzadeh, A. Saidi, and N. Pugno, “Large amplitude vibration of a bilayer graphene embedded in a nonlinear polymer matrix,” Physica E: Low-dimensional Systems
and Nanostructures, vol. 44, no. 10, pp. 1973 – 1982, 2012.
[8] M. Hanfland, H. Beister, and K. Syassen, “Graphite under pressure: Equation of state and first-order raman modes,” Phys. Rev. B, vol. 39, pp. 12 598–12 603, Jun 1989.
[9] P. R. Wallace, “The band theory of graphite,” Phys. Rev., vol. 71, pp. 622–634, May 1947.
[10] C. Kittel, Introduction to solid state physics. Hoboken, NJ: Wiley, 2005.
[11] G. Dresselhaus, A. F. Kip, and C. Kittel, “Cyclotron resonance of electrons and holes in silicon and germanium crystals,” Phys. Rev., vol. 98, pp. 368–384, Apr 1955.
[12] N. Ashcroft, Solid state physics. New York: Holt, Rinehart and Winston, 1976.
[13] C. Kittel, Quantum theory of solids. New York: Wiley, 1987.
[14] E. N. Economou, Green’s functions in quantum physics. Berlin London: Springer, 2010.
[15] S. Doniach, Green’s functions for solid state physicists. London River Edge, NJ: Imperial College Press Distributed by World Scientific Pub, 1998.
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