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Based on the previous work (Li P, Deng W J 2009 Acta Phys. Sin. 58 02713), the quantum transportation of electron through arbitrary equilateral polygons quantum rings with Rashba spin-orbit interaction is studied. With the typical method of quantum network and the Landauer-Büttiker formalism, we analytically solve the scattering problem of electron through equilateral polygonal quantum ring, and obtain the relevant formula for spin transportation conductance. The characteristics of the conductance varying with the wave-vector of electron, the strength of spin-orbit interaction, the number of polygon edges, and the ways of leads connecting to quantum rings are discussed. In the limit of infinite number of edges of polygon, we prove that the formula is consistent with the results obtained directly from the circular model of quantum rings.
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Keywords:
- Rashba spin-orbit interaction /
- Aharonov-Casher phase /
- quantum network /
- quantum transportation
[1] ［1］Winkler R 2003 Spin-orbit Coupling Effects in Two-dimensional Electron and Hole Systems (Berlin/Heidelberg：Springer-Verlag) p69
[2] ［2］Grundler D 2000 Phys. Rev. Lett. 84 6074
[3] ［3］Sato Y, Kita T, Gozu S, Yamada S 2001 J. Appl. Phys. 89 8017
[4] ［4］Qiu Z J, Gui Y S, Shu X Z, Dai N, Guo S L, Chu J H 2004 Acta Phys. Sin. 53 1186 (in Chinese) ［仇志军、桂永胜、疏小舟、戴宁、郭少令、褚君浩 2004 53 1186］［5］Song H Z, Zhang P, Duan S Q, Zhao X G 2006 Chin. Phys. 15 3019
[5] ［6］Zhu B, Gui Y S, Qiu Z J, Zhou W Z, Yao W, Guo S L, Chu J H, Zhang F J 2006 Acta Phys. Sin. 55 786 (in Chinese)
[6] ［朱博、桂永胜、仇志军、周文政、姚炜、郭少令、褚君浩、张福甲 2006 55 786］
[7] ［7］Zhou W Z, Lin T, Shang L Y, Huang Z M, Cui L J, Li D L, Gao H L, Zeng Y P, Guo S L, Gui Y S, Chu J H 2007 Acta Phys. Sin. 56 4099 (in Chinese) ［周文政、林铁、商丽燕、黄志明、崔利杰、李东临、高宏玲、曾一平、郭少令、桂永胜、褚君浩 2007 56 4099］
[8] ［8］Xu T N, Wu H Z, Sui C H 2008 Acta Phys. Sin. 57 7865 (in Chinese) ［徐天宁、吴惠桢、隋成华 2008 57 7865]
[9] ［9］Nitta J, Akazaki T, Takayanagi H, Enoki T 1997 Phys. Rev. Lett. 78 1335
[10] ］Koga T, Sekine Y, Nitta J 2006 Phys. Rev. B 74 041302R
[11] ］Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323
[12] ］Xia J B 1992 Phys. Rev. B 45 3593
[13] ］Nitta J, Meijer F E, Takayanagi H 1999 Appl. Phys. Lett. 75 695
[14] ］Frustaglia D, Richter K 2004 Phys. Rev. B 69 235310
[15] ］Molnar B, Peeters F M, Vasilopoulos P 2004 Phys. Rev. B 69 155335
[16] ］Foldi P, Molnar B, Benedict M G, Peeters F M 2005 Phys. Rev. B 71 033309
[17] ］Citro R, Romeo F 2007 Phys. Rev. B 75 073306
[18] ］Zhang X H, Xiong S J 2008 Chin. Phys. Lett. 25 5
[19] ］Wang J M, Wang R, Liang J Q 2007 Chin. Phys. 16 2075
[20] ］Dong Y K, Li Y X 2008 J. Appl. Phys. 103 113716
[21] ］Du J, Li C G, Qin F 2009 Acta Phys. Sin. 58 3448 (in chinese) ［杜坚、李春光、秦芳 2009 58 3448］
[22] ］Koga T, Nitta J, van Veenhuizen M J 2004 Phys. Rev. B 70 161302R
[23] ］Bercioux D, Governale M, Cataudella V, Ramaglia V M 2004 Phys. Rev. Lett. 93 056802
[24] ］Bercioux D, Governale M, Cataudella V, Ramaglia V M 2005 Phys. Rev. B 72 075305
[25] ］Bercioux D, Frustaglia D, Governale M 2005 Phys. Rev. B 72 113310
[26] ］Van Veenhuizen M J, Koga T, Nitta J 2006 Phys. Rev. B 73 235315
[27] ］Ramaglia V M, Cataudella V, Filippis G D, Perroni C A 2006 Phys. Rev. B 73 155328
[28] ］Li P, Deng W J 2009 Acta Phys. Sin. 58 2713 （In Chinese）［李鹏、邓文基 2009 58 2713］［29］Bergsten T, Kobayashi T, Sekine Y, Nitta J 2006 Phys. Rev. Lett. 97 196803
[29] ］Konig M, Tschetschetkin A, Hankiewicz E M， Sinova J, Hock V, Daumer V, Schfer M, Becker C R, Buhmann H, Molenkamp L W 2006 Phys. Rev. Lett. 96 076804
[30] ］Grbic B, Leturcq R, Ihn T, Ensslin K, Reuter D, Wieck A D 2007 Phys. Rev. Lett. 99 176803
[31] ］Zhu Z Y, Wang Y, Xia K, Xie X C, Ma Z S 2007 Phys. Rev. B 76 125311
[32] ］Kalman O, Foldi P, Benedict M G, Peeters F M 2008 Phys. Rev. B 78 125306
[33] ］Datta S 1997 Electronic Transport in Mesoscopic Systems (Cambridge: Cambridge University Press) p57
[34] ］Aharonov Y, Casher A, Cimmino A, Opat G I 1984 Phys. Rev. Lett. 53 319
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[1] ［1］Winkler R 2003 Spin-orbit Coupling Effects in Two-dimensional Electron and Hole Systems (Berlin/Heidelberg：Springer-Verlag) p69
[2] ［2］Grundler D 2000 Phys. Rev. Lett. 84 6074
[3] ［3］Sato Y, Kita T, Gozu S, Yamada S 2001 J. Appl. Phys. 89 8017
[4] ［4］Qiu Z J, Gui Y S, Shu X Z, Dai N, Guo S L, Chu J H 2004 Acta Phys. Sin. 53 1186 (in Chinese) ［仇志军、桂永胜、疏小舟、戴宁、郭少令、褚君浩 2004 53 1186］［5］Song H Z, Zhang P, Duan S Q, Zhao X G 2006 Chin. Phys. 15 3019
[5] ［6］Zhu B, Gui Y S, Qiu Z J, Zhou W Z, Yao W, Guo S L, Chu J H, Zhang F J 2006 Acta Phys. Sin. 55 786 (in Chinese)
[6] ［朱博、桂永胜、仇志军、周文政、姚炜、郭少令、褚君浩、张福甲 2006 55 786］
[7] ［7］Zhou W Z, Lin T, Shang L Y, Huang Z M, Cui L J, Li D L, Gao H L, Zeng Y P, Guo S L, Gui Y S, Chu J H 2007 Acta Phys. Sin. 56 4099 (in Chinese) ［周文政、林铁、商丽燕、黄志明、崔利杰、李东临、高宏玲、曾一平、郭少令、桂永胜、褚君浩 2007 56 4099］
[8] ［8］Xu T N, Wu H Z, Sui C H 2008 Acta Phys. Sin. 57 7865 (in Chinese) ［徐天宁、吴惠桢、隋成华 2008 57 7865]
[9] ［9］Nitta J, Akazaki T, Takayanagi H, Enoki T 1997 Phys. Rev. Lett. 78 1335
[10] ］Koga T, Sekine Y, Nitta J 2006 Phys. Rev. B 74 041302R
[11] ］Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323
[12] ］Xia J B 1992 Phys. Rev. B 45 3593
[13] ］Nitta J, Meijer F E, Takayanagi H 1999 Appl. Phys. Lett. 75 695
[14] ］Frustaglia D, Richter K 2004 Phys. Rev. B 69 235310
[15] ］Molnar B, Peeters F M, Vasilopoulos P 2004 Phys. Rev. B 69 155335
[16] ］Foldi P, Molnar B, Benedict M G, Peeters F M 2005 Phys. Rev. B 71 033309
[17] ］Citro R, Romeo F 2007 Phys. Rev. B 75 073306
[18] ］Zhang X H, Xiong S J 2008 Chin. Phys. Lett. 25 5
[19] ］Wang J M, Wang R, Liang J Q 2007 Chin. Phys. 16 2075
[20] ］Dong Y K, Li Y X 2008 J. Appl. Phys. 103 113716
[21] ］Du J, Li C G, Qin F 2009 Acta Phys. Sin. 58 3448 (in chinese) ［杜坚、李春光、秦芳 2009 58 3448］
[22] ］Koga T, Nitta J, van Veenhuizen M J 2004 Phys. Rev. B 70 161302R
[23] ］Bercioux D, Governale M, Cataudella V, Ramaglia V M 2004 Phys. Rev. Lett. 93 056802
[24] ］Bercioux D, Governale M, Cataudella V, Ramaglia V M 2005 Phys. Rev. B 72 075305
[25] ］Bercioux D, Frustaglia D, Governale M 2005 Phys. Rev. B 72 113310
[26] ］Van Veenhuizen M J, Koga T, Nitta J 2006 Phys. Rev. B 73 235315
[27] ］Ramaglia V M, Cataudella V, Filippis G D, Perroni C A 2006 Phys. Rev. B 73 155328
[28] ］Li P, Deng W J 2009 Acta Phys. Sin. 58 2713 （In Chinese）［李鹏、邓文基 2009 58 2713］［29］Bergsten T, Kobayashi T, Sekine Y, Nitta J 2006 Phys. Rev. Lett. 97 196803
[29] ］Konig M, Tschetschetkin A, Hankiewicz E M， Sinova J, Hock V, Daumer V, Schfer M, Becker C R, Buhmann H, Molenkamp L W 2006 Phys. Rev. Lett. 96 076804
[30] ］Grbic B, Leturcq R, Ihn T, Ensslin K, Reuter D, Wieck A D 2007 Phys. Rev. Lett. 99 176803
[31] ］Zhu Z Y, Wang Y, Xia K, Xie X C, Ma Z S 2007 Phys. Rev. B 76 125311
[32] ］Kalman O, Foldi P, Benedict M G, Peeters F M 2008 Phys. Rev. B 78 125306
[33] ］Datta S 1997 Electronic Transport in Mesoscopic Systems (Cambridge: Cambridge University Press) p57
[34] ］Aharonov Y, Casher A, Cimmino A, Opat G I 1984 Phys. Rev. Lett. 53 319
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