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題名 介觀自旋軌道耦合系統中的量子傳輸之數值研究
Numerical study of quantum transport in mesoscopic spin-orbit coupled systems作者 劉于綺
Liu, Yu-Chi貢獻者 許琇娟
Hsu, Hsiu-Chuan
劉于綺
Liu, Yu-Chi關鍵詞 量子傳輸
Rashba自旋軌道耦合
自旋霍爾效應
自旋霍爾傳導率
量子傳導率
雜質效應
Quantum transport
Quantum conductance
Rashba spin-orbit coupling
Spin–Hall effect
Spin–Hall conductivity
Disorder effect日期 2022 上傳時間 5-Oct-2022 09:31:07 (UTC+8) 摘要 在本篇論文中我們以數值計算討論幾種Rashba自旋軌道耦合介觀系\n統，由文獻指出在這些系統設置下所計算的量子傳導率和自旋霍爾傳導\n率會受到Rashba自旋軌道耦合強度及雜質之影響，在本論文中會針對幾個\n系統之結果做討論及介紹。論文中所有的結果皆由kwant一個由多國研究\n員共同研發來計算量子傳輸效應進行數值計算。Kwant以Landauer–B ̈uttiker 形式及格林函數（Green’s function）去計算一緊束緮模型（Tight–binding model）。\n\n在研究系統幾何的例子中，我們設置了圓形環、方形環以及實心方形\n系統，而傳導率在圓形環的結果出現震盪現象，且系統傳導率會受到自旋\n軌道耦合強度的影響。當我們在圓形環、方形環系統中施加一平面內塞曼\n場（Zeeman field）時，傳導率及自旋霍爾傳導率結果皆呈現一些干涉紋特徵。\n\n在研究雜質（隨機亂數）效應的例子，我們發現只要Rashba自旋軌道\n耦合強度不為零便能誘發自旋霍爾傳導率的產生。介觀下的自旋霍爾傳導\n率在雜質強度為零時（乾淨系統中）與連續模型所導出的固定常數不同，\n且傳導率會受雜質強度影響。在某些雜質添加方式下雜質強度不為零時\n（隨機雜質系統中），雜質會削弱自旋霍爾傳導率且隨強度增加而減弱。\n根據文獻與我們的結果顯示自旋霍爾傳導率震盪週期顯示此震盪現象係由\n有限系統下之自旋進動結果。
We numerically study quantum transport in mesoscopic two-dimensional electron systems (2DESs) with Rashba spin–orbit coupling (SOC), particularly the effect of disorder and Rashba SOC on spin-Hall conductivities (SHCs) and charge\nconductance in different limits. The numerical simulations are performed with Kwant, an open–source package for numerically calculating quantum transport for discretized tight-binding models based on the Landauer–B ̈uttiker approach and Green’s function formalism.\n\nIn this thesis, the geometric structures are rings, square loops and square shapes. For a Rashba ring, the quantum conductance oscillates and depends on\nthe strength of Rashba SOC. When an in–plane Zeeman field is applied to a ring or a square–loop system, the quantum conductance and SHC show interference pattern characteristics.\n\nFor disorder effects, in the disordered limit, the on–site and Rashba type disorders weaken SHC. Notably, we found that in a system without SOC, SHC can be induced by random Rashba SOC. We show that in the clean limit (W = 0), in contrast to the continuum model, SHC is not universal for a mesoscopic structure. This finding agrees with previous numerical studies. Moreover, the period of SHC indicates that oscillation patterns result from the spin precessional effect in finite–size systems.參考文獻 [1] Jairo Sinova, Sergio O Valenzuela, J ̈org Wunderlich, CH Back, and T Jung-wirth. Spin hall effects. Reviews of modern physics, 87(4):1213, 2015.\n[2] Igor ˇZuti ́c, Jaroslav Fabian, and S Das Sarma. Spintronics: Fundamentals and applications. Reviews of modern physics, 76(2):323, 2004.\n[3] Atsufumi Hirohata, Keisuke Yamada, Yoshinobu Nakatani, Ioan-Lucian Pre-jbeanu, Bernard Di ́eny, Philipp Pirro, and Burkard Hillebrands. Review on spintronics: Principles and device applications. Journal of Magnetism and\nMagnetic Materials, 509:166711, 2020.\n[4] Supriyo Datta and Biswajit Das. Electronic analog of the electro-optic modulator. Applied Physics Letters, 56(7):665–667, 1990.\n[5] Supriyo Datta. Electronic transport in mesoscopic systems. Cambridge university press, 1997.\n[6] Edwin H Hall et al. On a new action of the magnet on electric currents. American Journal of Mathematics, 2(3):287–292, 1879.\n[7] Yuichiro K Kato, Roberto C Myers, Arthur C Gossard, and David D Awschalom. Observation of the spin hall effect in semiconductors. science, 306(5703):1910–1913, 2004.\n[8] K Nomura, J Wunderlich, Jairo Sinova, B Kaestner, AH MacDonald, and T Jungwirth. Edge-spin accumulation in semiconductor two-dimensional hole gases. Physical Review B, 72(24):245330, 2005.\n[9] Tsung-Wei Chen. Conserved spin current with a perpendicular magnetic field. Physics Letters A, 384(24):126454, 2020.\n[10] Emmanuel I Rashba. Spin–orbit coupling and spin transport. Physica E: Low-dimensional Systems and Nanostructures, 34(1-2):31–35, 2006.\n[11] Christoph W Groth, Michael Wimmer, Anton R Akhmerov, and Xavier Waintal. Kwant: a software package for quantum transport. New Journal of\nPhysics, 16(6):063065, 2014.\n[12] Rohit Subbarayan Chandramouli, Rohit Kumar Srivastav, and Santosh Kumar. Electronic transport in chaotic mesoscopic cavities: A kwant and random matrix theory based exploration. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12):123120, 2020.\n[13] Sudin Ganguly and Saurabh Basu. Spin dependent disorder in a junction device with spin orbit couplings. In Journal of Physics: Conference Series, volume 759, page 012028. IOP Publishing, 2016.\n[14] Sverre A Gulbrandsen, Camilla Espedal, and Arne Brataas. Spin hall effect\nin antiferromagnets. Physical Review B, 101(18):184411, 2020.\n[15] Minmin Wang, H Saarikoski, Andres Alejandro Reynoso, JP Baltan ́as, D Frustaglia, and J Nitta. Geometry-assisted topological transitions in spin interferometry. Physical review letters, 123(26):266804, 2019.\n[16] Henri Saarikoski, J Enrique V ́azquez-Lozano, Jos ́e Pablo Baltan ́as, Fumiya Nagasawa, Junsaku Nitta, and Diego Frustaglia. Topological transitions in spin interferometers. Physical Review B, 91(24):241406, 2015.\n[17] Francisco Mireles and George Kirczenow. Ballistic spin-polarized transport\nand rashba spin precession in semiconductor nanowires. Physical Review B, 64(2):024426, 2001.\n[18] M Buttiker. Symmetry of electrical conduction. IBM Journal of Research\nand Development, 32(3):317–334, 1988.\n[19] Rolf Landauer. Conductance from transmission: common sense points.\nPhysica Scripta, 1992(T42):110, 1992.\n[20] H-L Engquist and PW Anderson. Definition and measurement of the electri-\ncal and thermal resistances. Physical Review B, 24(2):1151, 1981.\n[21] Yoseph Imry. Physics of mesoscopic systems. In Directions in Condensed\nMatter Physics: Memorial Volume in Honor of Shang-keng Ma, pages 101–\n163. World Scientific, 1986.\n[22] Robert Landauer. Spatial variation of currents and fields due to localized\nscatterers in metallic conduction. IBM Journal of Research and Development,\n32(3):306–316, 1988.\n[23] Lingjie Du, Ivan Knez, Gerard Sullivan, and Rui-Rui Du. Robust helical edge\ntransport in gated inas/gasb bilayers. Physical review letters, 114(9):096802,\n2015.\n[24] AG Mal’shukov, VV Shlyapin, and Koung-An Chao. Quantum oscillations\nof spin current through a iii-v semiconductor loop. Physical Review B, 6(8):081311, 2002.\n[25] Francisco Mireles and George Kirczenow. Ballistic spin-polarized transport\nand rashba spin precession in semiconductor nanowires. Physical Review B, 64(2):024426, 2001.\n[26] Gary A Prinz. Magnetoelectronics. science, 282(5394):1660–1663, 1998.\n[27] SA Wolf, DD Awschalom, RA Buhrman, JM Daughton, von S von Moln ́ar, ML Roukes, A Yu Chtchelkanova, and DM Treger. Spintronics: a spin-based electronics vision for the future. science, 294(5546):1488–1495, 2001.\n[28] Tsuneya Ando, Yasuhiko Arakawa, Kazuhito Furuya, Susumu Komiyama,\nand Hisao Nakashima. Mesoscopic physics and electronics. Springer Science\n& Business Media, 2012.\n[29] Michael Victor Berry. Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 392(1802):45–57, 1984.\n[30] Cheng-Hung Chang, Anatoly G Mal’shukov, and Koung-An Chao. Spin transmission through quantum dots with strong spin–orbit interaction. Physics Letters A, 326(5-6):436–441, 2004.\n[31] Supriyo Datta and Biswajit Das. Electronic analog of the electro-optic modulator. Applied Physics Letters, 56(7):665–667, 1990.\n[32] Diego Frustaglia and Klaus Richter. Spin interference effects in ring conductors subject to rashba coupling. Physical Review B, 69(23):235310, 2004.\n[33] AG Mal’shukov, VV Shlyapin, and KA Chao. Effect of the spin-orbit geometric phase on the spectrum of aharonov-bohm oscillations in a semiconductor mesoscopic ring. Physical Review B, 60(4):R2161, 1999.\n[34] FE Meijer, AF Morpurgo, and TM Klapwijk. One-dimensional ring in the presence of rashba spin-orbit interaction: Derivation of the correct hamiltonian. Physical Review B, 66(3):033107, 2002.\n[35] Junsaku Nitta, Frank E Meijer, and Hideaki Takayanagi. Spin-interference device. Applied Physics Letters, 75(5):695–697, 1999.\n[36] Han-Zhao Tang, Li-Xue Zhai, and Jian-Jun Liu. Spin conductance in three-terminal rings subject to rashba and dresselhaus spin-orbit coupling. Current\nApplied Physics, 18(1):122–126, 2018.\n[37] Shuichi Murakami, Naoto Nagaosa, and Shou-Cheng Zhang. Dissipationless\nquantum spin current at room temperature. Science, 301(5638):1348–1351, 2003.\n[38] Jairo Sinova, Dimitrie Culcer, Qian Niu, NA Sinitsyn, T Jungwirth, and Allan H MacDonald. Universal intrinsic spin hall effect. Physical review letters, 92(12):126603, 2004.\n[39] AA Burkov, Alvaro S N ́u ̃nez, and AH MacDonald. Theory of spin-charge-coupled transport in a two-dimensional electron gas with rashba spin-orbit interactions. Physical Review B, 70(15):155308, 2004.\n[40] John Schliemann and Daniel Loss. Dissipation effects in spin-hall transport\nof electrons and holes. Physical Review B, 69(16):165315, 2004.\n[41] L Sheng, DN Sheng, and CS Ting. Spin-hall effect in two-dimensional electron systems with rashba spin-orbit coupling and disorder. Physical review letters, 94(1):016602, 2005.\n[42] TP Pareek and P Bruno. Spin coherence in a two-dimensional electron gas with rashba spin-orbit interaction. Physical Review B, 65(24):241305, 2002.\n[43] DN Sheng and ZY Weng. Disappearance of integer quantum hall effect. Physical review letters, 78(2):318, 1997. 描述 碩士
國立政治大學
應用物理研究所
109755001資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109755001 資料類型 thesis dc.contributor.advisor 許琇娟 zh_TW dc.contributor.advisor Hsu, Hsiu-Chuan en_US dc.contributor.author (Authors) 劉于綺 zh_TW dc.contributor.author (Authors) Liu, Yu-Chi en_US dc.creator (作者) 劉于綺 zh_TW dc.creator (作者) Liu, Yu-Chi en_US dc.date (日期) 2022 en_US dc.date.accessioned 5-Oct-2022 09:31:07 (UTC+8) - dc.date.available 5-Oct-2022 09:31:07 (UTC+8) - dc.date.issued (上傳時間) 5-Oct-2022 09:31:07 (UTC+8) - dc.identifier (Other Identifiers) G0109755001 en_US dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=161563 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用物理研究所 zh_TW dc.description (描述) 109755001 zh_TW dc.description.abstract (摘要) 在本篇論文中我們以數值計算討論幾種Rashba自旋軌道耦合介觀系\n統，由文獻指出在這些系統設置下所計算的量子傳導率和自旋霍爾傳導\n率會受到Rashba自旋軌道耦合強度及雜質之影響，在本論文中會針對幾個\n系統之結果做討論及介紹。論文中所有的結果皆由kwant一個由多國研究\n員共同研發來計算量子傳輸效應進行數值計算。Kwant以Landauer–B ̈uttiker 形式及格林函數（Green’s function）去計算一緊束緮模型（Tight–binding model）。\n\n在研究系統幾何的例子中，我們設置了圓形環、方形環以及實心方形\n系統，而傳導率在圓形環的結果出現震盪現象，且系統傳導率會受到自旋\n軌道耦合強度的影響。當我們在圓形環、方形環系統中施加一平面內塞曼\n場（Zeeman field）時，傳導率及自旋霍爾傳導率結果皆呈現一些干涉紋特徵。\n\n在研究雜質（隨機亂數）效應的例子，我們發現只要Rashba自旋軌道\n耦合強度不為零便能誘發自旋霍爾傳導率的產生。介觀下的自旋霍爾傳導\n率在雜質強度為零時（乾淨系統中）與連續模型所導出的固定常數不同，\n且傳導率會受雜質強度影響。在某些雜質添加方式下雜質強度不為零時\n（隨機雜質系統中），雜質會削弱自旋霍爾傳導率且隨強度增加而減弱。\n根據文獻與我們的結果顯示自旋霍爾傳導率震盪週期顯示此震盪現象係由\n有限系統下之自旋進動結果。 zh_TW dc.description.abstract (摘要) We numerically study quantum transport in mesoscopic two-dimensional electron systems (2DESs) with Rashba spin–orbit coupling (SOC), particularly the effect of disorder and Rashba SOC on spin-Hall conductivities (SHCs) and charge\nconductance in different limits. The numerical simulations are performed with Kwant, an open–source package for numerically calculating quantum transport for discretized tight-binding models based on the Landauer–B ̈uttiker approach and Green’s function formalism.\n\nIn this thesis, the geometric structures are rings, square loops and square shapes. For a Rashba ring, the quantum conductance oscillates and depends on\nthe strength of Rashba SOC. When an in–plane Zeeman field is applied to a ring or a square–loop system, the quantum conductance and SHC show interference pattern characteristics.\n\nFor disorder effects, in the disordered limit, the on–site and Rashba type disorders weaken SHC. Notably, we found that in a system without SOC, SHC can be induced by random Rashba SOC. We show that in the clean limit (W = 0), in contrast to the continuum model, SHC is not universal for a mesoscopic structure. This finding agrees with previous numerical studies. Moreover, the period of SHC indicates that oscillation patterns result from the spin precessional effect in finite–size systems. en_US dc.description.tableofcontents 誌謝 i\n摘要 ii\nAbstract iii\nList of Figures v\nAcronyms ix\n\n1 Introduction 1\n1.1 Spintronics 1\n1.2 Spin Hall effect (SHE) 2\n1.2.1 Rashba Spin-orbit coupling 4\n1.3 Characteristic length in a mesoscopic conductor 6\n1.3.1 Two dimensional electron gas 6\n1.3.2 Fermi wavelength 8\n1.3.3 Mean free path/ momentum relaxation length 9\n1.4 Kwant 10\n\n2 Methodology 11\n2.1 Tight-binding model 11\n2.2 Landauer-B ̈uttiker formalism 15\n2.2.1 Landauer formula 15\n2.2.2 B ̈uttiker formula 19\n2.2.3 Multiterminal conductor in the Landauer–B ̈uttiker formalism 20\n\n3 Numerical calculation and discussion 24\n3.1 Conductance on Rashba ring 24\n3.1.1 Analytical calculation 25\n3.1.2 Zero-temperature conductance and relevant parameters 27\n3.1.3 Conductance as function of Rashba spin-orbit coupling 28\n3.2 Spin-Hall effect in two-dimensional electron systems with Rashba spin-orbit coupling and disorder 29\n3.2.1 The system 31\n3.2.2 Spin-Hall Conductance as a function of Rashba spin-orbit coupling 35\n3.2.3 Spin-Hall Conductance as a function of Fermi energy 37\n3.3 The field texture subject to Rashba spin-orbit coupling and Zeeman field 41\n3.3.1 The Hamiltonian 41\n3.3.2 The field texture 42\n\n4 Conclusion 44\n\nReferences 46 zh_TW dc.format.extent 4195971 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109755001 en_US dc.subject (關鍵詞) 量子傳輸 zh_TW dc.subject (關鍵詞) Rashba自旋軌道耦合 zh_TW dc.subject (關鍵詞) 自旋霍爾效應 zh_TW dc.subject (關鍵詞) 自旋霍爾傳導率 zh_TW dc.subject (關鍵詞) 量子傳導率 zh_TW dc.subject (關鍵詞) 雜質效應 zh_TW dc.subject (關鍵詞) Quantum transport en_US dc.subject (關鍵詞) Quantum conductance en_US dc.subject (關鍵詞) Rashba spin-orbit coupling en_US dc.subject (關鍵詞) Spin–Hall effect en_US dc.subject (關鍵詞) Spin–Hall conductivity en_US dc.subject (關鍵詞) Disorder effect en_US dc.title (題名) 介觀自旋軌道耦合系統中的量子傳輸之數值研究 zh_TW dc.title (題名) Numerical study of quantum transport in mesoscopic spin-orbit coupled systems en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Jairo Sinova, Sergio O Valenzuela, J ̈org Wunderlich, CH Back, and T Jung-wirth. Spin hall effects. Reviews of modern physics, 87(4):1213, 2015.\n[2] Igor ˇZuti ́c, Jaroslav Fabian, and S Das Sarma. Spintronics: Fundamentals and applications. Reviews of modern physics, 76(2):323, 2004.\n[3] Atsufumi Hirohata, Keisuke Yamada, Yoshinobu Nakatani, Ioan-Lucian Pre-jbeanu, Bernard Di ́eny, Philipp Pirro, and Burkard Hillebrands. Review on spintronics: Principles and device applications. Journal of Magnetism and\nMagnetic Materials, 509:166711, 2020.\n[4] Supriyo Datta and Biswajit Das. Electronic analog of the electro-optic modulator. Applied Physics Letters, 56(7):665–667, 1990.\n[5] Supriyo Datta. Electronic transport in mesoscopic systems. Cambridge university press, 1997.\n[6] Edwin H Hall et al. On a new action of the magnet on electric currents. American Journal of Mathematics, 2(3):287–292, 1879.\n[7] Yuichiro K Kato, Roberto C Myers, Arthur C Gossard, and David D Awschalom. Observation of the spin hall effect in semiconductors. science, 306(5703):1910–1913, 2004.\n[8] K Nomura, J Wunderlich, Jairo Sinova, B Kaestner, AH MacDonald, and T Jungwirth. Edge-spin accumulation in semiconductor two-dimensional hole gases. Physical Review B, 72(24):245330, 2005.\n[9] Tsung-Wei Chen. Conserved spin current with a perpendicular magnetic field. Physics Letters A, 384(24):126454, 2020.\n[10] Emmanuel I Rashba. Spin–orbit coupling and spin transport. Physica E: Low-dimensional Systems and Nanostructures, 34(1-2):31–35, 2006.\n[11] Christoph W Groth, Michael Wimmer, Anton R Akhmerov, and Xavier Waintal. Kwant: a software package for quantum transport. New Journal of\nPhysics, 16(6):063065, 2014.\n[12] Rohit Subbarayan Chandramouli, Rohit Kumar Srivastav, and Santosh Kumar. Electronic transport in chaotic mesoscopic cavities: A kwant and random matrix theory based exploration. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(12):123120, 2020.\n[13] Sudin Ganguly and Saurabh Basu. Spin dependent disorder in a junction device with spin orbit couplings. In Journal of Physics: Conference Series, volume 759, page 012028. IOP Publishing, 2016.\n[14] Sverre A Gulbrandsen, Camilla Espedal, and Arne Brataas. Spin hall effect\nin antiferromagnets. Physical Review B, 101(18):184411, 2020.\n[15] Minmin Wang, H Saarikoski, Andres Alejandro Reynoso, JP Baltan ́as, D Frustaglia, and J Nitta. Geometry-assisted topological transitions in spin interferometry. Physical review letters, 123(26):266804, 2019.\n[16] Henri Saarikoski, J Enrique V ́azquez-Lozano, Jos ́e Pablo Baltan ́as, Fumiya Nagasawa, Junsaku Nitta, and Diego Frustaglia. Topological transitions in spin interferometers. Physical Review B, 91(24):241406, 2015.\n[17] Francisco Mireles and George Kirczenow. Ballistic spin-polarized transport\nand rashba spin precession in semiconductor nanowires. Physical Review B, 64(2):024426, 2001.\n[18] M Buttiker. Symmetry of electrical conduction. IBM Journal of Research\nand Development, 32(3):317–334, 1988.\n[19] Rolf Landauer. Conductance from transmission: common sense points.\nPhysica Scripta, 1992(T42):110, 1992.\n[20] H-L Engquist and PW Anderson. Definition and measurement of the electri-\ncal and thermal resistances. Physical Review B, 24(2):1151, 1981.\n[21] Yoseph Imry. Physics of mesoscopic systems. In Directions in Condensed\nMatter Physics: Memorial Volume in Honor of Shang-keng Ma, pages 101–\n163. World Scientific, 1986.\n[22] Robert Landauer. Spatial variation of currents and fields due to localized\nscatterers in metallic conduction. IBM Journal of Research and Development,\n32(3):306–316, 1988.\n[23] Lingjie Du, Ivan Knez, Gerard Sullivan, and Rui-Rui Du. Robust helical edge\ntransport in gated inas/gasb bilayers. Physical review letters, 114(9):096802,\n2015.\n[24] AG Mal’shukov, VV Shlyapin, and Koung-An Chao. Quantum oscillations\nof spin current through a iii-v semiconductor loop. Physical Review B, 6(8):081311, 2002.\n[25] Francisco Mireles and George Kirczenow. Ballistic spin-polarized transport\nand rashba spin precession in semiconductor nanowires. Physical Review B, 64(2):024426, 2001.\n[26] Gary A Prinz. Magnetoelectronics. science, 282(5394):1660–1663, 1998.\n[27] SA Wolf, DD Awschalom, RA Buhrman, JM Daughton, von S von Moln ́ar, ML Roukes, A Yu Chtchelkanova, and DM Treger. Spintronics: a spin-based electronics vision for the future. science, 294(5546):1488–1495, 2001.\n[28] Tsuneya Ando, Yasuhiko Arakawa, Kazuhito Furuya, Susumu Komiyama,\nand Hisao Nakashima. Mesoscopic physics and electronics. Springer Science\n& Business Media, 2012.\n[29] Michael Victor Berry. Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 392(1802):45–57, 1984.\n[30] Cheng-Hung Chang, Anatoly G Mal’shukov, and Koung-An Chao. Spin transmission through quantum dots with strong spin–orbit interaction. Physics Letters A, 326(5-6):436–441, 2004.\n[31] Supriyo Datta and Biswajit Das. Electronic analog of the electro-optic modulator. Applied Physics Letters, 56(7):665–667, 1990.\n[32] Diego Frustaglia and Klaus Richter. Spin interference effects in ring conductors subject to rashba coupling. Physical Review B, 69(23):235310, 2004.\n[33] AG Mal’shukov, VV Shlyapin, and KA Chao. Effect of the spin-orbit geometric phase on the spectrum of aharonov-bohm oscillations in a semiconductor mesoscopic ring. Physical Review B, 60(4):R2161, 1999.\n[34] FE Meijer, AF Morpurgo, and TM Klapwijk. One-dimensional ring in the presence of rashba spin-orbit interaction: Derivation of the correct hamiltonian. Physical Review B, 66(3):033107, 2002.\n[35] Junsaku Nitta, Frank E Meijer, and Hideaki Takayanagi. Spin-interference device. Applied Physics Letters, 75(5):695–697, 1999.\n[36] Han-Zhao Tang, Li-Xue Zhai, and Jian-Jun Liu. Spin conductance in three-terminal rings subject to rashba and dresselhaus spin-orbit coupling. Current\nApplied Physics, 18(1):122–126, 2018.\n[37] Shuichi Murakami, Naoto Nagaosa, and Shou-Cheng Zhang. Dissipationless\nquantum spin current at room temperature. Science, 301(5638):1348–1351, 2003.\n[38] Jairo Sinova, Dimitrie Culcer, Qian Niu, NA Sinitsyn, T Jungwirth, and Allan H MacDonald. Universal intrinsic spin hall effect. Physical review letters, 92(12):126603, 2004.\n[39] AA Burkov, Alvaro S N ́u ̃nez, and AH MacDonald. Theory of spin-charge-coupled transport in a two-dimensional electron gas with rashba spin-orbit interactions. Physical Review B, 70(15):155308, 2004.\n[40] John Schliemann and Daniel Loss. Dissipation effects in spin-hall transport\nof electrons and holes. Physical Review B, 69(16):165315, 2004.\n[41] L Sheng, DN Sheng, and CS Ting. Spin-hall effect in two-dimensional electron systems with rashba spin-orbit coupling and disorder. Physical review letters, 94(1):016602, 2005.\n[42] TP Pareek and P Bruno. Spin coherence in a two-dimensional electron gas with rashba spin-orbit interaction. Physical Review B, 65(24):241305, 2002.\n[43] DN Sheng and ZY Weng. Disappearance of integer quantum hall effect. Physical review letters, 78(2):318, 1997. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202201608 en_US
