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研究生:陳冠伊
研究生(外文):Kuan-Yi Chen
論文名稱:自旋霍爾效應設置下在微結構附近產生的殘餘電阻偶極和電子自旋偶極的共振現象
論文名稱(外文):Resonant generation of residual resistivity dipole and spin dipole around microstructures in a spin-Hall configuration
指導教授:朱仲夏
指導教授(外文):Chon-Saar Chu
學位類別:碩士
校院名稱:國立交通大學
系所名稱:電子物理系所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:99
中文關鍵詞:電子自旋自旋電子學自旋堆積自旋霍爾效應殘餘電阻偶極非平衡電子分佈自旋軌道交互作用共振散射
外文關鍵詞:electron spinspintronicsspin accumulationspin Hall effectresidual resistivity dipolenonequlibrium electron distributionspin-orbit interactionresonant scattering
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此論文的焦點放在一個有外加電場的微結構附近,自旋軌道交互作用對電荷和電子自旋的堆積的影響。透過一個環形的微結構所可能造成的量子共振效應,我們進一步探討放大自旋軌道交互作用的可能性。
  最重要的發現是,以往一直被忽略的,由電位梯度產生的自旋軌道耦合可以使一個微結構附近造成可觀的電子自旋堆積。藉由把在一個外電場中非平衡電自分佈裡所有電子波的空間機率加總,我們可以在量子彈道範圍內的微結構附近得到一個狀似偶極的電子自旋分佈,也就是自旋偶極。伴隨著量子散射的共振,此交互作用可以提供我們一個調控自旋偶極的方法。特別的是,隨著系統費米能的改變,自旋偶極會表現出方向的反轉和強度的放大。
  藉由引入一個與自旋相關的非平衡電子分佈,材料背景雜質所產生的外秉自旋軌道耦合效應已經包含在我們的考慮裡面。此效應在共振時對自旋偶極的修正並沒有值得注意的貢獻。
This thesis focuses on spin-orbit interaction effect on
charge and spin accumulation around a microstructure in an external electric field. Furthermore, a ring type microstructure is
introduced to explore possible amplification of the spin-orbit interaction effect from quantum resonances allowed by such microstructures.

A major finding in this thesis is that the mostly overlooked
spin-orbit interaction arising from in-plane potential gradient can contribute to significant spin accumulation around a microstructure. By considering quantum-mechanical scattering of individual electrons in a nonequilibrium distribution acted upon by an external electric field, we obtain a spin dipole, or spin accumulation of a dipole-like spatial variation, around a microstructure within the ballistic range. The subsequent quantum scattering resonance
provides and additional knob for the manipulation of spin dipole. Specifically, the spin dipole manifests both sign reversal and large amplification when the Fermi energy crosses a resonance.

We have included the extrinsic spin-orbit interaction effects from background spin-orbit scatterers by invoking a spin dependent nonequilibrium electron distribution. The correction of the spin dipole is found to be insignificant in the resonant region.
Contents

Abstract in Chinese i
Abstract in English ii
Acknowledgement iii

1 Introduction 1

1.1 Introduction to Landauer’s residual resistivity dipole . . . . . . . . . . . . 3

1.2 Spin-orbit coupling in solid-state systems . . . . . . . . . . . . . . . . . . . 4

1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 A guiding tour to this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Landauer’s residual resistivity dipole around a ring-shaped microstructure
9

2.1 Quantum-mechanical scattering in two dimensions . . . . . . . . . . . . . . 9

2.1.1 Method of partial waves . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Phase shift and the unitarity relation . . . . . . . . . . . . . . . . . 12

2.1.3 Asymptotic expansion of scattering wave and the differential cross
section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 Nonequilibrium distribution of electrons: Theory of the Boltzmann kinetic
equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Relaxation time approximation . . . . . . . . . . . . . . . . . . . . 15

2.2.2 The linear response to the uniform electric field . . . . . . . . . . . 16

2.3 Landauer’s residual resistivity dipole . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Charge accumulation due to nonequilibrium incident distribution . 16

2.3.2 Screening effect and potential induced by charge accumulation . . . 18

2.3.3 Thomas-Fermi screening in two dimensions . . . . . . . . . . . . . . 19

2.3.4 Definition of the strength of the residual resistivity dipole . . . . . . 21

2.4 Resonance generation of RRD around a ring-shaped structure . . . . . . . 22

2.5 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Residual resistivity dipole and spin dipole in the presence of spin-orbit
interaction arising from in-plain potential gradient of a microstructure 28

3.1 Spin dependent asymmetric scattering in the presence of SOI . . . . . . . . 29

3.1.1 Two useful relations . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2 Residual resistivity dipole in the presence of local structure SOI . . . . . . 32

3.3 Spin dipole due to spin-independent nonequilibrium incident distribution . 33

3.3.1 Second-order correction to the spin dipole strength at resonance . . 35

3.4 Resonance of charge and spin dipole in the presence of the SOI from the
microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.1 Resonant asymmetric skew scattering . . . . . . . . . . . . . . . . . 37

3.4.2 Resonant RRD in the presence of the SOI . . . . . . . . . . . . . . 39

3.4.3 Resonance of spin dipole . . . . . . . . . . . . . . . . . . . . . . . . 40

3.5 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Spin dipole correction due to effect of extrinsic spin-orbit interaction 46

4.1 Differential cross section in terms of spin density operator . . . . . . . . . . 46

4.1.1 Density operator formalism . . . . . . . . . . . . . . . . . . . . . . 46

4.1.2 Spin dependent scattering cross section in terms of spin density
operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 The spin dependent nonequilibrium distribution . . . . . . . . . . . . . . . 50

4.3 The correction to the spin dipole due to the term h(k) · σ . . . . . . . . . 54

4.4 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 Numerical calculation for smooth potential variation 61

5.1 Variable phase approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.3 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6 Conclusion and future work 70

Appendix

A Derivation of charge accumulation 72

B Derivation of spin accumulation 75

C Derivation of transport cross section 78

D Derivation of transverse transport cross section 81

E Asymmetric Mott skew scattering 84

F Asymptotic expansion of residual resistivity dipole and charge dipole
strength 89

G Asymptotic expansion of spin dipole and spin dipole strength 92

H Collision integrals in detail 95
[1] M. Baibich et al., Phys. Rev. Lett. 61, 1472 (1988).
[2] E. I. Rashba, Fiz. Tverd. Tela (Leningrad) 2, 1224 (1960) [Sov. Phys. Solid State 2,
1109 (1960)]; Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[3] G. Dresselhaus, Phys. Rev. 100, 580 (1955).
[4] N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, 3rd ed., (Oxford
University Press, 1965).
[5] M. I. Dyakonov and V. I. Perel, JETP Lett. 13, 467 (1971); Phys. Lett. 35A, 459
(1971).
[6] J. E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999).
[7] S. Murakami, N. Nagaosa, and S.-C. Zhang, Science 301, 1348 (2003); J. Sinova et
al., Phys. Rev. Lett. 92, 126603 (2004); D. Culcer et al., Phys. Rev. Lett. 93, 046602
(2004).
[8] H.-A. Engel, B. I. Halperin, and E. I. Rashba, Phys. Rev. Lett. 95, 166605 (2005).
[9] J. Wunderlich et al., Phys. Rev. Lett. 94, 047204 (2005).
[10] Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science 306, 1910
(2004).
[11] J. Shi, P. Zhang, D. Xiao, and Q. Niu, Phys. Rev. Lett. 96, 076604 (2006).
[12] P.-Q. Jin, Y.-Q. Li, and F.-C. Zhang, cond-mat/0502231.
[13] S. Murakami, N. Nagaosa, and S.-C. Zhang, Phys. Rev. B 69, 235206 (2004).
[14] A. G. Mal’shukov and C. S. Chu, Phys. Rev. Lett. 97, 076601 (2006).
[15] A. O. Govorov, A. V. Kalameitsev, and J. P. Dulka, Phys. Rev. B 70, 145310 (2004).
[16] H. Chen et al., Appl. Phys. Lett. 86, 32113 (2005).
[17] J. D. Walls et al., Phys. Rev. B 73, 35325 (2006).
[18] J. Y. Yeh, M. C. Chang, and C. Y. Mou, Phys. Rev. B 73, 35313 (2006).
[19] A. P´alyi, C. P´eterfalvi, and J. Cserti, Phys. Rev. B 74, 73305 (2006).
[20] R. Landauer, IBM J. Res. Dev. 1, 223 (1957); R. Landauer, Z. Phys.
[21] R. S. Sorbello and C. S. Chu, IBM J. Res. Dev. 32, 58 (1988); C. S. Chu and R. S.
Sorbello, Phys. Rev. B 38, 7260 (1988).
[22] W. Zwerger, L. B¨onig, and K. Schonhammer, Phys. Rev. B 43, 6434 (1991).
[23] R. M. Feenstra, B. G. Briner, T. P. Chin, and J. M. Woodall, Phys. Rev. B 54,
R5283 (1996); R. M. Feenstra and B. G. Briner, Superlattices and Microstructures
23, 699 (1998).
[24] Topics in advanced quantum mechanics, Barry R. Holstein (Addison Wesley).
[25] Spin-Orbit Coupling in Two-Dimensional Electron and Hole systems, Roland Winkler
(Springer, 2003).
[26] E. I. Rashba, Physica E 34, 31 (2006).
[27] Mathematical Methods for Physicists, 4th ed., G. B. Arfkan and H. J. Weber (Academic
Press, 1995).
[28] S. K. Adhikari, Am. J. Phys. 54, 362 (1986).
[29] Solid State Physics, N. W. Ashcroft and N. D. Mermin (Saunders College, 1976).
[30] Modern Quantum Mechanics, Revised ed., J. J. Sakurai (Addison-Wesley, 1994).
[31] V. Sih, W. H. Lau, R. C. Myers, V. R. Horowitz, A. C. Gossard, and D. D.
Awschalom, Phys. Rev. Lett. 97, 096605 (2006).
[32] T. Hada, T. Goto, J. Yanagisawa, F. Wakaya, Y. Yuba, and K. Gamo, J. Vac. Sci.
Technol. B 18, 3158 (2000).
[33] Scattering Theory, A. G. Sitenko (Springer-Verlag, 1991).
[34] Variable phase approach to potential scattering, F. Calogero (New York Academic,
1967).
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