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Nuclear-Electron Spin Interactions in the Quantum Hall Regime

  • Chapter
Spin Physics in Semiconductors

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 157))

Abstract

The discoveries of the integer and fractional quantum Hall effects [1, 2] in the early 1980s opened an exciting field for condensed matter physics. The continuous effort in this area during the past quarter century has been particularly rewarding. The interplay between Landau quantization, disorder, electron-electron and spin interactions gives rise to a large variety of fascinating electronic states [36]. Some examples are incompressible quantum fluids with quasi-particles carrying fractional charge [711], compressible metallic states composed of composite particles [1214], insulating Wigner crystal electron solids [15, 16], Bose-Einstein condensates [17], Skyrmion spin textures in quantum Hall ferromagnets [18, 19], non-Abelian states [2022], electron liquid crystal phases [2328], and so forth. Indeed, this list is incomplete.

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References

  1. K. von Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980)

    Article  ADS  Google Scholar 

  2. D.C. Tsui, H.L. Stornier, A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)

    Article  ADS  Google Scholar 

  3. R.E. Prange, S.M. Girvin (eds.), The Quantum Hall Effect (Springer, New York, 1987)

    Google Scholar 

  4. T. Chakraborty, The Quantum Hall Effects (Springer, Berlin, 1995)

    Google Scholar 

  5. S. Das Sarma (ed.), Perspectives in Quantum Hall Effects (Wiley, New York, 1997)

    Google Scholar 

  6. Z.F. Ezawa, Quantum Hall Effects—Field Effect Approach and Related Topics (World Scientific, Singapore, 2000)

    Google Scholar 

  7. R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

    Article  ADS  Google Scholar 

  8. R. dePicciotto et al., Nature 389, 162 (1997)

    Article  ADS  Google Scholar 

  9. L. Saminadayar et al., Phys. Rev. Lett. 79, 2526 (1997)

    Article  ADS  Google Scholar 

  10. M. Reznikov et al., Nature 399, 328 (1999)

    Google Scholar 

  11. J. Martin et al., Science 305, 980 (2004)

    Article  ADS  Google Scholar 

  12. J.K. Jain, Phys. Today 53(4), 39 (2000)

    Article  Google Scholar 

  13. O. Heinonen (ed.), Composite Fermions (World Scientific, Singapore, 1998)

    Google Scholar 

  14. J.K. Jain, Composite Fermions (Cambridge University Press, Cambridge, 2007)

    Book  MATH  Google Scholar 

  15. R.L. Willett et al., Phys. Rev. B 37, 8476 (1988)

    Article  ADS  Google Scholar 

  16. H.W. Jiang et al., Phys. Rev. Lett. 65, 633 (1990)

    Article  ADS  Google Scholar 

  17. J.P. Eisenstein, A.H. MacDonald, Nature 432, 691 (2004)

    Article  ADS  Google Scholar 

  18. S.L. Sondhi et al., Phys. Rev. B 47, 16419 (1993)

    Article  ADS  Google Scholar 

  19. S.E. Barrett et al., Phys. Rev. Lett. 74, 5112 (1995)

    Article  ADS  Google Scholar 

  20. G. Moore, N. Read, Nucl. Phys. B 360, 362 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  21. M. Greiter, X.G. Wen, E. Wilczek, Nucl. Phys. B 374, 567 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. S. Das Sarma, M. Freedman, C. Nayak, Phys. Today 59, 32 (2006)

    Article  Google Scholar 

  23. A.A. Koulakov, M.M. Fogler, B.I. Shklovskii, Phys. Rev. Lett. 76, 499 (1996)

    Article  ADS  Google Scholar 

  24. R. Moessner, J.T. Chalker, Phys. Rev. B 54, 5006 (1996)

    Article  ADS  Google Scholar 

  25. S.A. Kivelson, E. Fradkin, V.J. Emery, Nature 393, 550 (1998)

    Article  ADS  Google Scholar 

  26. R.R. Du et al., Solid State Commun. 109, 389 (1999)

    Article  ADS  Google Scholar 

  27. E. Fradkin, S.A. Kivelson, Phys. Rev. B 59, 8065 (1999)

    Article  ADS  Google Scholar 

  28. E. Fradkin et al., Phys. Rev. Lett. 84, 1982 (2000)

    Article  ADS  Google Scholar 

  29. A. Hartland et al., Phys. Rev. Lett. 66, 969 (1991)

    Article  ADS  Google Scholar 

  30. A.M. Chang et al., Phys. Rev. B 28, 6133 (1983)

    Article  ADS  Google Scholar 

  31. G.S. Boebinger et al., Phys. Rev. B 36, 7919 (1987)

    Article  ADS  Google Scholar 

  32. A. Usher et al., Phys. Rev. B 41, 1129 (1990)

    Article  ADS  Google Scholar 

  33. M. Dobers, K. von Klitzing, G. Weimann, Phys. Rev. B 38, 5453 (1988)

    Article  ADS  Google Scholar 

  34. R.B. Laughlin, Phys. Rev. B 23, 5632 (1981)

    Article  ADS  Google Scholar 

  35. S.H. Simon, in Composite Fermions, ed. by O. Heinonen (World Scientific, Singapore, 1998)

    Google Scholar 

  36. B.I. Halperin, P.A. Lee, N. Read, Phys. Rev. B 47, 7312 (1993)

    Article  ADS  Google Scholar 

  37. W. Kang et al., Phys. Rev. Lett. 71, 3850 (1993)

    Article  ADS  Google Scholar 

  38. R.L. Willett et al., Phys. Rev. Lett. 71, 3846 (1993)

    Article  ADS  Google Scholar 

  39. V.J. Goldman, B. Su, J.K. Jain, Phys. Rev. Lett. 72, 2065 (1994)

    Article  ADS  Google Scholar 

  40. J.H. Smet et al., Phys. Rev. Lett. 77, 2272 (1996)

    Article  ADS  Google Scholar 

  41. I.V. Kukushkin et al., Nature 415, 409 (2002)

    Article  ADS  Google Scholar 

  42. B.I. Halperin, Phys. Rev. B 25, 2185 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  43. M. Büttiker, Phys. Rev. B 38, 9375 (1988)

    Article  ADS  Google Scholar 

  44. A.H. MacDonald, P. Streda, Phys. Rev. B 29, 1616 (1984)

    Article  ADS  Google Scholar 

  45. T.J. Thornton et al., Phys. Rev. Lett. 56, 1198 (1986)

    Article  ADS  Google Scholar 

  46. H.Z. Zheng et al., Phys. Rev. B 34, 5635 (1986)

    Article  ADS  Google Scholar 

  47. B.J. van Wees et al., Phys. Rev. Lett. 62, 1181 (1989)

    Article  ADS  Google Scholar 

  48. B.J. van Wees et al., Phys. Rev. B 43, 12431 (1991)

    Article  ADS  Google Scholar 

  49. D. Yoshioka, The Quantum Hall Effect (Springer, Berlin, 2002)

    MATH  Google Scholar 

  50. K. von Klitzing, 25 Years of Quantum Hall Effects. Séminar Poincaré (Vol. 2, p. 1) (2004)

    Google Scholar 

  51. H.L. Stormer, Rev. Mod. Phys. 71, 875 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  52. D.C. Tsui, Rev. Mod. Phys. 71, 891 (1999)

    Article  ADS  Google Scholar 

  53. R.B. Laughlin, Rev. Mod. Phys. 71, 863 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  54. S.M. Girvin, Introduction to the Fractional Quantum Hall Effect. Séminar Poincaré (Vol. 2, p. 53) (2004)

    Google Scholar 

  55. B.I. Halperin, Helv. Phys. Acta 56, 75 (1983)

    Google Scholar 

  56. T. Chakraborty, F.C. Zhang, Phys. Rev. B 29, 7032 (1984)

    Article  ADS  Google Scholar 

  57. F.C. Zhang, T. Chakraborty, Phys. Rev. B 30, 7320 (1984)

    Article  ADS  Google Scholar 

  58. X.C. Xie, Y. Guo, F.C. Zhang, Phys. Rev. B 40, 3487 (1989)

    Article  ADS  Google Scholar 

  59. J.P. Eisenstein et al., Phys. Rev. Lett. 62, 1540 (1989)

    Article  ADS  Google Scholar 

  60. R.G. Clark et al., Phys. Rev. Lett. 62, 1536 (1989)

    Article  ADS  Google Scholar 

  61. J.P. Eisenstein et al., Phys. Rev. B 41, 7910 (1990)

    Article  ADS  Google Scholar 

  62. L.W. Engel et al., Phys. Rev. B 45, 3418 (1992)

    Article  ADS  Google Scholar 

  63. H. Cho, J.B. Young, W. Kang, K.L. Campman, A.C. Gossard, M. Bichler, W. Wegscheider, Phys. Rev. Lett. 81, 2522 (1998)

    Article  ADS  Google Scholar 

  64. R.R. Du et al., Phys. Rev. Lett. 75, 3926 (1995)

    Article  ADS  Google Scholar 

  65. J.H. Smet et al., Phys. Rev. Lett. 86, 2412 (2001)

    Article  ADS  Google Scholar 

  66. I.V. Kukushkin, K. von Klitzing, K. Eberl, Phys. Rev. Lett. 82, 3665 (1999)

    Article  ADS  Google Scholar 

  67. A.E. Dementyev et al., Phys. Rev. Lett. 83, 5074 (1999)

    Article  ADS  Google Scholar 

  68. S. Melinte et al., Phys. Rev. Lett. 84, 354 (2000)

    Article  ADS  Google Scholar 

  69. T. Jungwirth et al., Phys. Rev. Lett. 81, 2328 (1998)

    Article  ADS  Google Scholar 

  70. A.S. Yeh, H.L. Stornier, D.C. Tsui, Phys. Rev. Lett. 82, 592 (1999)

    Article  ADS  Google Scholar 

  71. M.A. Ruderman, C. Kittel, Phys. Rev. 96, 99 (1954)

    Article  ADS  Google Scholar 

  72. T. Machida et al., Physica E 21, 921 (2004)

    Article  ADS  Google Scholar 

  73. A. Berg et al., Phys. Rev. Lett. 64, 2563 (1990)

    Article  ADS  Google Scholar 

  74. O.V. Lounasmaa, Phys. Today 42(10), 26 (1989)

    Article  Google Scholar 

  75. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, London, 1961)

    Google Scholar 

  76. D.R. Lide (ed.), CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, 2008)

    Google Scholar 

  77. D. Paget, G. Lampel, B. Sapoval, V.I. Safarov, Phys. Rev. B 15, 5780 (1977)

    Article  ADS  Google Scholar 

  78. M.I. Dyakonov, V.I. Perel, in Optical Orientation, ed. byF. Meier, B.P. Zakharchenya (Elsvier, New York, 1984)

    Google Scholar 

  79. F. Meier, B.P. Zakharchenya (eds.), Optical Orientation (Elsevier, New York, 1984)

    Google Scholar 

  80. M. Dobers et al., Phys. Rev. Lett. 61, 1650 (1988)

    Article  ADS  Google Scholar 

  81. J. Strand et al., Phys. Rev. Lett. 91, 036602 (2003)

    Article  ADS  Google Scholar 

  82. C.P. Slichter, Principles of Magnetic Resonance (Harper & Row Publishers, New York, 1963)

    Google Scholar 

  83. J. Korringa, Physica 16, 601 (1950)

    Article  MATH  ADS  Google Scholar 

  84. K. Hashimoto et al., Phys. Rev. Lett. 94, 146601 (2005)

    Article  ADS  Google Scholar 

  85. J.H. Kim, I.D. Vagner, L. Xing, Phys. Rev. B 49, 16777 (1994)

    Article  ADS  Google Scholar 

  86. R. Côté et al., Phys. Rev. Lett. 78, 4825 (1997)

    Article  ADS  Google Scholar 

  87. C.X. Deng, X.D. Hu, Phys. Rev. B 72, 165333 (2005)

    Article  ADS  Google Scholar 

  88. D. Paget, Phys. Rev. B 25, 4444 (1982)

    Article  ADS  Google Scholar 

  89. K.R. Wald et al., Phys. Rev. Lett. 73, 1011 (1994)

    Article  ADS  Google Scholar 

  90. H. Sanada et al., Phys. Rev. Lett. 96, 067602 (2006)

    Article  ADS  Google Scholar 

  91. I.L. Chuang et al., Nature 393, 143 (1998)

    Article  ADS  Google Scholar 

  92. L.M.K. Vandersypen et al., Nature 414, 883 (2001)

    Article  ADS  Google Scholar 

  93. R. Tycko et al., Science 268, 1460 (1995)

    Article  ADS  Google Scholar 

  94. D.C. Dixon et al., Phys. Rev. B 56, 4743 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  95. S. Kronmüller et al., Phys. Rev. Lett. 82, 4070 (1999)

    Article  ADS  Google Scholar 

  96. J.H. Smet et al., Nature 415, 281 (2002)

    Article  ADS  Google Scholar 

  97. K. Hashimoto et al., Phys. Rev. Lett. 88, 176601 (2002)

    Article  ADS  Google Scholar 

  98. W. Desrat et al., Phys. Rev. Lett. 88, 256807 (2002)

    Article  ADS  Google Scholar 

  99. A. Würtz et al., Phys. Rev. Lett. 95, 056802 (2005)

    Article  ADS  Google Scholar 

  100. G. Gervais et al., Phys. Rev. Lett. 94, 196803 (2005)

    Article  ADS  Google Scholar 

  101. J.M. Kikkawa, D.D. Awschalom, Science 287, 473 (2000)

    Article  ADS  Google Scholar 

  102. D. Rugar et al., Nature 430, 329 (2004)

    Article  ADS  Google Scholar 

  103. I.D. Vagner, T. Maniv, Phys. Rev. Lett. 61, 1400 (1988)

    Article  ADS  Google Scholar 

  104. E. Olshanetsky et al., Phys. Rev. B 67, 165325 (2003)

    Article  ADS  Google Scholar 

  105. S.V. Iordanskii, S.V. Meshkov, I.D. Vagner, Phys. Rev. B 44, 6554 (1991)

    Article  ADS  Google Scholar 

  106. D. Antoniou, A.H. MacDonald, Phys. Rev. B 43, 11686 (1991)

    Article  ADS  Google Scholar 

  107. B.E. Kane, L.N. Pfeiffer, K.W. West, Phys. Rev. B 46, 7264 (1992)

    Article  ADS  Google Scholar 

  108. T. Machida et al., Physica E 25, 142 (2004)

    Article  ADS  Google Scholar 

  109. T. Machida et al., Phys. Rev. B 65, 233304 (2002)

    Article  ADS  Google Scholar 

  110. H.A. Fertig et al., Phys. Rev. B 50, 11018 (1994)

    Article  ADS  Google Scholar 

  111. X.C. Xie, S. He, Phys. Rev. B 53, 1046 (1996)

    Article  ADS  Google Scholar 

  112. S.M. Girvin, Phys. Today 53(6), 39 (2000)

    Article  Google Scholar 

  113. T.H.R. Skyrme, Nucl. Phys. 31, 556 (1962)

    Article  MathSciNet  Google Scholar 

  114. A. Schmeller et al., Phys. Rev. Lett. 75, 4290 (1995)

    Article  ADS  Google Scholar 

  115. E.H. Aifer, B.B. Goldberg, D.A. Broido, Phys. Rev. Lett. 76, 680 (1996)

    Article  ADS  Google Scholar 

  116. L. Brey et al., Phys. Rev. Lett. 75, 2562 (1995)

    Article  ADS  Google Scholar 

  117. C. Timm, S.M. Girvin, H.A. Fertig, Phys. Rev. B 58, 10634 (1998)

    Article  ADS  Google Scholar 

  118. V. Bayot et al., Phys. Rev. Lett. 76, 4584 (1996)

    Article  ADS  Google Scholar 

  119. V. Bayot et al., Phys. Rev. Lett. 79, 1718 (1997)

    Article  ADS  Google Scholar 

  120. L.A. Tracy et al., Phys. Rev. B 73, 121306 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  121. R.G. Clark et al., Surf. Sci. 229, 25 (1990)

    Article  ADS  Google Scholar 

  122. K. Hashimoto, T. Saku, Y. Hirayama, Phys. Rev. B 69, 153306 (2004)

    Article  ADS  Google Scholar 

  123. V. Piazza et al., Nature 402, 638 (1999)

    Article  ADS  Google Scholar 

  124. K. Vyborny et al., Phys. Rev. B 75, 045434 (2007)

    Article  ADS  Google Scholar 

  125. O. Stern et al., Phys. Rev. B 70, 075318 (2004)

    Article  ADS  Google Scholar 

  126. S. Kraus et al., Phys. Rev. Lett. 89, 266801 (2002)

    Article  ADS  Google Scholar 

  127. S. Kronmüller et al., Phys. Rev. Lett. 81, 2526 (1998)

    Article  ADS  Google Scholar 

  128. G. Yusa et al., Nature 434, 1001 (2005)

    Article  ADS  Google Scholar 

  129. N. Kumada et al., Phys. Rev. Lett. 94, 096802 (2005)

    Article  ADS  Google Scholar 

  130. N. Kumada, K. Muraki, Y. Hirayama, Science 313, 329 (2006)

    Article  ADS  Google Scholar 

  131. J.H. Smet et al., Phys. Rev. Lett. 92, 086802 (2004)

    Article  ADS  Google Scholar 

  132. V. Kalmeyer, S.C. Zhang, Phys. Rev. B 46, 9889 (1992)

    Article  ADS  Google Scholar 

  133. J.H. Smet et al., Phys. Rev. Lett. 83, 2620 (1999)

    Article  ADS  Google Scholar 

  134. R.L. Willett, K.W. West, L.N. Pfeiffer, Phys. Rev. Lett. 83, 2624 (1999)

    Article  ADS  Google Scholar 

  135. J.K. Jain, R.K. Kamilla, Phys. Rev. B 55, R4895 (1997)

    Article  ADS  Google Scholar 

  136. J.K. Jain, R.K. Kamilla, Intern. J. Mod. Phys. B 11, 2621 (1997)

    Article  ADS  Google Scholar 

  137. K. Park, J.K. Jain, Phys. Rev. Lett. 80, 4237 (1998)

    Article  ADS  Google Scholar 

  138. N. Freytag et al., Phys. Rev. Lett. 89, 246804 (2002)

    Article  ADS  Google Scholar 

  139. R. Shankar, G. Murthy, Phys. Rev. Lett. 79, 4437 (1997)

    Article  ADS  Google Scholar 

  140. R. Shankar, Phys. Rev. B 63, 085322 (2001)

    Article  ADS  Google Scholar 

  141. G. Murthy, R. Shankar, Rev. Mod. Phys. 75, 1101 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  142. F.C. Zhang, S. Das Sarma, Phys. Rev. B 33, 2903 (1986)

    Article  ADS  Google Scholar 

  143. R. Shankar, Phys. Rev. Lett. 84, 3946 (2000)

    Article  ADS  Google Scholar 

  144. I.B. Spielman et al., Phys. Rev. Lett. 94, 076803 (2005)

    Article  ADS  Google Scholar 

  145. L.A. Tracy et al., Phys. Rev. Lett. 98, 086801 (2007)

    Article  ADS  Google Scholar 

  146. A.D. Mirlin, D.G. Polyakov, P. Wölfle, Phys. Rev. Lett. 80, 2429 (1998)

    Article  ADS  Google Scholar 

  147. G. Murthy, R. Shankar, Phys. Rev. B 76, 075341 (2007)

    Article  ADS  Google Scholar 

  148. G. Ebert, K. von Klitzing, K. Ploog, G. Weimann, J. Phys. C 16, 5441 (1983)

    Article  ADS  Google Scholar 

  149. M.E. Cage et al., Phys. Rev. Lett. 51, 1374 (1983)

    Article  ADS  Google Scholar 

  150. A.M. Martin et al., Phys. Rev. Lett. 91, 126803 (2003)

    Article  ADS  Google Scholar 

  151. S. Komiyama et al., Solid State Commun. 54, 479 (1985)

    Article  ADS  Google Scholar 

  152. O. Heinonen, P.L. Taylor, S.M. Girvin, Phys. Rev. B 30, 3016 (1984)

    Article  ADS  Google Scholar 

  153. L. Eaves, F.W. Sheard, Semicond. Sci. Technol. 1, 346 (1986)

    Article  ADS  Google Scholar 

  154. A.M. Song, P. Omling, Phys. Rev. Lett. 84, 3145 (2000)

    Article  ADS  Google Scholar 

  155. M. Kawamura, H. Takahashi et al., Appl. Phys. Lett. 90, 022102 (2007)

    Article  ADS  Google Scholar 

  156. P.K. Lam, S.M. Girvin, Phys. Rev. B 30, 473 (1984)

    Article  ADS  Google Scholar 

  157. D. Levesque, J.J. Weis, A.H. MacDonald, Phys. Rev. B 30, 1056 (1984)

    Article  ADS  Google Scholar 

  158. X.J. Zhu, S.G. Louie, Phys. Rev. B 52, 5863 (1995)

    Article  ADS  Google Scholar 

  159. P.D. Ye et al., Phys. Rev. Lett. 89, 176802 (2002)

    Article  ADS  Google Scholar 

  160. Y.P. Chen et al., Phys. Rev. Lett. 93, 206805 (2007)

    Article  ADS  Google Scholar 

  161. G. Gervais et al., Phys. Rev. B 72, 041310 (2005)

    Article  ADS  Google Scholar 

  162. Y.B. Lyanda-Geller, I.L. Aleiner, B.L. Altshuler, Phys. Rev. Lett. 89, 107602 (2002)

    Article  ADS  Google Scholar 

  163. X.C. Zhang, D.R. Faulhaber, H.W. Jiang, Phys. Rev. Lett. 95, 216801 (2005)

    Article  ADS  Google Scholar 

  164. X.C. Zhang, G.D. Scott, H.W. Jiang, Phys. Rev. Lett. 98, 246802 (2007)

    Article  ADS  Google Scholar 

  165. N. Kumada, K. Muraki, Y. Hirayama, Phys. Rev. Lett. 99, 076805 (2007)

    Article  ADS  Google Scholar 

  166. P. Weitz et al., Surf. Sci. 362, 542 (1996)

    Article  ADS  Google Scholar 

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Li, Y.Q., Smet, J.H. (2008). Nuclear-Electron Spin Interactions in the Quantum Hall Regime. In: Dyakonov, M.I. (eds) Spin Physics in Semiconductors. Springer Series in Solid-State Sciences, vol 157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78820-1_12

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