Вышедшие номера
Home » Физика и техника полупроводников » Год 2008, выпуск 8 » Статья стр. 1007
<<<
Relaxation processes in a disordered Luttinger liquid
Bagrets D.A.1, Gornyi I.V.1,2, Mirlin A.D.1,3, Polyakov D.G.1
1Institut fur Nanotechnologie, Forschungszentrum Karlsruhe, Karlsruhe, Germany
2Ioffe Physicotechnical Institute, St. Petersburg, Russia
3Petersburg Nuclear Physics Institute, Russian Academy of Sciences, St. Petersburg, Russia
Поступила в редакцию: 6 февраля 2008 г.
Выставление онлайн: 20 июля 2008 г.
PDF версия
The Luttinger liquid model, which describes interacting electrons in a single-channel quantum wire, is completely integrable in the absence of disorder and as such does not exhibit any relaxation to equilibrium. We consider relaxation processes induced by inelastic electron-electron interactions in a disordered Luttinger liquid, focusing on the equilibration rate and its essential differences from the electron-electron scattering rate as well as the rate of phase relaxation. In the first part of the paper, we review the basic concepts in the disordered Luttinger liquid at equilibrium. These include the elastic renormalization, dephasing, and interference-induced localization. In the second part, we formulate a conceptually important framework for systematically studying the nonequilibrium properties of the strongly correlated (non-Fermi) Luttinger liquid. We derive a coupled set of kinetic equations for the fermionic and bosonic distribution functions that describe the evolution of the nonequilibrium Luttinger liquid. Remarkably, the energy equilibration rate in the conducting disordered quantum wire (at sufficiently high temperature, when the localization effects are suppressed by dephasing) is shown to be of the order of the rate of elastic scattering off disorder, independent of the interaction constant and temperature. PACS: 71.10.Pm, 73.20.Jc, 73.21.-b, 73.63.-b
  1. O.M. Auslaender, A. Yacoby, R. de Picciotto, K.W. Baldwin, L.N. Pfeiffer, and K.W. West. Phys. Rev. Lett., 84, 1764 (2000); Science, 295, 825 (2002); O.M. Auslaender, H. Steinberg, A. Yacoby, Y. Tserkovnyak, B.I. Halperin, K.W. Baldwin, L.N. Pfeiffer, and K.W. West. Science, 308, 88 (2005)
  2. E. Levy, A. Tsukernik, M. Karpovski, A. Palevski, B. Dwir, E. Pelucchi, A. Rudra, E. Kapon, and Y. Oreg. Phys. Rev. Lett., 97, 196 802 (2006)
  3. S.V. Zaitsev-Zotov, Y.A. Kumzerov, Y.A. Firsov, and P. Monceau. J. Phys.: Condens. Matter, 12, L303 (2000); Pis'ma Zh. Eksp. Teor. Fiz., 77, 162 (2003) [JETP Lett., 77, 135 (2003)]
  4. W. Kang, H.L. Stormer, L.N. Pfeiffer, K.W. Baldwin, and K.W. West. Nature, 403, 59 (2000); I. Yang, W. Kang, K.W. Baldwin, L.N. Pfeiffer, and K.W. West. Phys. Rev. Lett., 92, 056 802 (2004)
  5. M. Grayson, D. Schuh, M. Huber, M. Bichler, and G. Abstreiter. Appl. Phys. Lett., 86, 032 101 (2005); M. Grayson, L. Steinke, D. Schuh, M. Bichler, L. Hoeppel, J. Smet, K. v. Klitzing, D.K. Maude, and G. Abstreiter. Phys. Rev. B, 76, 201 304 (2007).
  6. For recent work see, e. g.: S. Li, Z. Yu, C. Rutherglen, and P.J. Burke. Nano Letters, 4, 2003 (2004); H.T. Man and A.F. Morpurgo. Phys. Rev. Lett., 95, 026 801 (2005); J. Wei, M. Shimogawa, Z. Wang, I. Radu, R. Dormaier, and D.H. Cobden. Phys. Rev. Lett., 95, 256 601 (2005); P.J. Leek, M.R. Buitelaar, V.I. Talyanskii, C.G. Smith, D. Anderson, G.A.C. Jones, J. Wei, and D.H. Cobden. Phys. Rev. Lett., 95, 256 802 (2005); H.T. Man, I.J.W. Wever, and A.F. Morpurgo. Phys. Rev. B, 73, 241 401 (2006); M. Purewal, B.H. Hong, A. Ravi, B. Chandra, J. Hone, and P. Kim. Phys. Rev. Lett., 98, 186 808 (2007)
  7. A.N. Aleshin, H.J. Lee, Y.W. Park, and K. Akagi. Phys. Rev. Lett., 93, 196 601 (2004); A.N. Aleshin. Adv. Mat., 18, 17 (2006), and references therein
  8. E. Slot, M.A. Holst, H.S.J. van der Zant, and S.V. Zaitsev-Zotov. Phys. Rev. Lett., 93, 176 602 (2004)
  9. L. Venkataraman, Y.S. Hong, and P. Kim. Phys. Rev. Lett., 96, 076 601 (2006)
  10. T. Giamarchi. Quantum Physics in One Dimension (Oxford University Press, Oxford, 2004)
  11. C.L. Kane and M.P.A. Fisher. Phys. Rev. B, 46, 15 233 (1992)
  12. I.V. Gornyi, A.D. Mirlin, and D.G. Polyakov. Phys. Rev. B, 75, 085 421 (2007)
  13. P.W. Anderson. Phys. Rev., 109, 1492 (1958)
  14. M.E. Gertsenshtein and V.B. Vasil'ev. Radiotekhnika i Elektronika, 4, 611 (1959); Teor. Veroyatn. Primen., 4, 424 (1959) [Theor. Probab. Appl., 4, 391 (1959)]; N.F. Mott and W.D. Twose. Adv. Phys., 10, 107 (1961); V.L. Berezinskii. Zh. Eksp. Teor. Fiz., 65, 1251 (1973) [Sov. Phys. JETP, 38, 620 (1974)]; A.A. Gogolin, V.I. Mel'nikov, and E.I. Rashba. Zh. Eksp. Teor. Fiz., 69, 327 (1975) [Sov. Phys. JETP, 42, 168 (1975); D.J. Thouless. Phys. Rev. Lett., 39, 1167 (1977); A.A. Abrikosov and I.A. Ryzhkin. Adv. Phys., 27, 147 (1978); V.L. Berezinskii and L.P. Gor'kov. Zh. Eksp. Teor. Fiz., 77, 2498 (1979) [Sov. Phys. JETP, 50, 1209 (1979)]; A.A. Gogolin. Phys. Rep., 86, 1 (1982); L.P. Gor'kov, O.N. Dorokhov, and F.V. Prigara. Zh. Eksp. Teor. Fiz., 84, 1440 (1983) [Sov. Phys. JETP, 57, 838 (1983); V.I. Perel and D.G. Polyakov. Zh. Eksp. Teor. Fiz., 86, 352 (1984) [Sov. Phys. JETP, 59, 204 (1984)]; I.M. Lifshitz, S.A. Gredeskul, and L.A. Pastur. Introduction to the Theory of Disordered Systems (New York, Wiley, 1988)
  15. I.V. Gornyi, A.D. Mirlin, and D.G. Polyakov. Phys. Rev. Lett., 95, 046 404 (2005)
  16. D.A. Bagrets, I.V. Gornyi, and D.G. Polyakov (unpublished)
  17. A.G. Yashenkin, I.V. Gornyi, A.D. Mirlin, and D.G. Polyakov (unpublished)
  18. A.I. Larkin. Zh. Eksp. Teor. Fiz., 58, 1466 (1970) [Sov. Phys. JETP, 31, 784 (1970)]
  19. A.D. Mirlin, D.G. Polyakov, and V.M. Vinokur. Phys. Rev. Lett., 99, 156 405 (2007)
  20. D.G. Polyakov and I.V. Gornyi. Phys. Rev. B, 68, 035 421 (2003)
  21. T. Giamarchi and H.J. Schulz. Phys. Rev. B, 37, 325 (1988)
  22. J.T. Chalker, Y. Gefen, and M.Y. Veillette. Phys. Rev. B, 76, 085 320 (2007)
  23. B.L. Altshuler, A.G. Aronov, and D.E. Khmelnitskii. J. Phys. C, 15, 7367 (1982)
  24. B.N. Narozhny, G. Zala, and I.L. Aleiner. Phys. Rev. B, 65, 180 202(R) (2002).
  25. H.C. Fogedby. J. Phys. C, 9, 3757 (1976); D.K.K. Lee and Y. Chen. J. Phys. A, 21, 4155 (1988); P. Kopietz. Bosonization of Interacting Electrons in Arbitrary Dimensions (Springer, Berlin, 1997); V. Fernandez, K. Li, and C. Naon. Phys. Lett. B, 452, 98 (1999); V.I. Fernandez and C.M. Naon. Phys. Rev. B, 64, 033 402 (2001); I.V. Yurkevich. In: Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems, ed. by I.V. Lerner, B.L. Altshuler, and V.I. Fal'ko (Kluwer, Dordrecht, 2002), cond-mat/0112270; A. Grishin, I.V. Yurkevich, and I.V. Lerner. Phys. Rev. B, 69, 165 108 (2004)
  26. I.V. Lerner and I.V. Yurkevich. In: Nanophysics: Coherence and Transport, ed. by H. Bouchiat, Y. Gefen, S. Gu\`eron, G. Montambaux, and J. Dalibard (Elsevier, Amsterdam, 2005); cond-mat/0508223.
  27. I.E. Dzyaloshinskii and A.I. Larkin. Zh. Eksp. Teor. Fiz., 65, 411 (1973) [Sov. Phys. JETP, 38, 202 (1974)]
  28. L. Fleishman and P.W. Anderson. Phys. Rev. B, 21, 2366 (1980); I.V. Gornyi, A.D. Mirlin, and D.G. Polyakov. Phys. Rev. Lett., 95, 206 603 (2005); D.M. Basko, I.L. Aleiner, and B.L. Altshuler. Ann. Phys. (N.Y.), 321, 1126 (2006)
  29. A.M. Lunde, K. Flensberg, and L.I. Glazman. Phys. Rev. B, 75, 245 418 (2007)
  30. R. Egger and H. Grabert. Phys. Rev. Lett., 77, 538 (1996); F. Dolcini, B. Trauzettel, I. Safi, and H. Grabert. Phys. Rev. B, 71, 165 309 (2005)
  31. P. Fendley, A.W.W. Ludwig, and H. Saleur. Phys. Rev. B, 52, 8934 (1995); U. Weiss. Solid State Commun., 100, 281 (1996); R. Egger and H. Grabert. Phys. Rev. B, 58, 10 761 (1998)
  32. G. Catelani and I.L. Aleiner. Zh. Eksp. Teor. Fiz., 127, 372 (2005) [JETP, 100 331 (2005)]
  33. D.B. Gutman, Y. Gefen, and A.D. Mirlin. Phys. Rev. Lett., 100, 086 801 (2008)
  34. D.B. Gutman, Y. Gefen, and A.D. Mirlin. arXiv:0804.4294
  35. B.A. Muzykantskii and D.E. Khmelnitskii. JETP Lett., 62, 76 (1995)
  36. A. Kamenev and A. Andreev. Phys. Rev. B, 60, 2218 (1999)
  37. A.L. Shelankov. J. Low Temp. Phys., 60, 29 (1985)
  38. G. Eilenberger. Z. Phys., 214, 195 (1968)
  39. J. Rammer and H. Smith. Rev. Mod. Phys., 58, 323 (1986)
  40. A. Kamenev. In: Nanophysics: Coherence and Transport, ed. by H. Bouchiat, Y. Gefen, S. Gueron, G. Montambaux, and J. Dalibard (Elsevier, Amsterdam, 2005); cond-mat/0412296
  41. U. Eckern and P. Schwab. Phys. Status Solidi B, 244, 2343 (2007)
  42. L.S. Levitov, A.V. Shytov, and B.I. Halperin. Phys. Rev. B, 64, 075 322 (2001).

Подсчитывается количество просмотров абстрактов ("html" на диаграммах) и полных версий статей ("pdf"). Просмотры с одинаковых IP-адресов засчитываются, если происходят с интервалом не менее 2-х часов.

Дата начала обработки статистических данных - 27 января 2016 г.

Учредители

Издатель

© 2024 Физико-технический институт им. А.Ф. Иоффе Российской академии наук
Powered by webapplicationthemes.com - High quality HTML Theme