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Pair spin–orbit interaction in low-dimensional electron systems

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Abstract

The pair spin–orbit interaction (PSOI) is the spin–orbit component of the electron–electron interaction that originates from the Coulomb fields of the electrons. This relativistic component, which has been commonly assumed small in the low-energy approximation, appears large and very significant in materials with the strong SOI The PSOI, being determined by the spins and momenta of electrons, has highly unusual properties among which of most interest is the mutual attraction of the electrons in certain spin configurations. We review the nature of the PSOI in solids and its manifestations in low-dimensional systems that have been studied to date. The specific results depend on the configuration of the Coulomb fields in a particular structure. The main actual structures are considered: one-dimensional quantum wires and two-dimensional layers, both suspended and placed in various dielectric media, as well as in the presence of a metallic gate. We discuss the possible types of the two-electron bound states, the conditions of their formation, their spectra together with the spin and orbital structure. In a many-particle system, the PSOI breaks the spin-charge separation as a result of which spin and charge degrees of freedom are mixed in the collective excitations. At sufficiently strong PSOI, one of the collective modes softens. This signals of the instability, which eventually leads to the reconstruction of the homogeneous state of the system.

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References

  1. G. Breit, Phys. Rev. 34, 553 (1929)

    Article  ADS  Google Scholar 

  2. G. Breit, Phys. Rev. 36, 383 (1930)

    Article  ADS  Google Scholar 

  3. G. Breit, Phys. Rev. 39, 616 (1932)

    Article  ADS  Google Scholar 

  4. Y. Gindikin, V.A. Sablikov, Phys. Rev. B 95, 045138 (2017)

    Article  ADS  Google Scholar 

  5. Y. Gindikin, Phys. Status Solidi Rapid Res. Lett. 11, 1700256 (2017)

    Article  ADS  Google Scholar 

  6. Y. Gindikin, V.A. Sablikov, Phys. Status Solidi Rapid Res. Lett. 12, 1700313 (2018)

    Article  ADS  Google Scholar 

  7. Y. Gindikin, V.A. Sablikov, Phys. Status Solidi Rapid Res. Lett. 12, 1800209 (2018)

    Article  ADS  Google Scholar 

  8. Y. Gindikin, V.A. Sablikov, Phys. Rev. B 98, 115137 (2018)

    Article  ADS  Google Scholar 

  9. Y. Gindikin, V.A. Sablikov, Physica E 108, 187 (2019)

    Article  ADS  Google Scholar 

  10. Y. Gindikin, V. Vigdorchik, V.A. Sablikov, https://arXiv:1904.09510 (2019)

  11. H.A. Bethe, E.E. Salpeter,Quantum mechanics of one- and two-electron atoms (Springer, Berlin, 1957)

  12. R. Winkler, Spin-orbit coupling effects in two-dimensional electron and hole systems, Vol. 191 ofSpringer Tracts in Modern Physics (Springer, Berlin, 2003)

  13. J. Voit, Rep. Prog. Phys. 58, 977 (1995)

    Article  ADS  Google Scholar 

  14. A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)

    Article  ADS  Google Scholar 

  15. M.S. Dresselhaus, G. Dresselhaus, P. Eklund, A. Rao, The physics of fullerene-based and fullerene-related materials, Vol. 23 ofPhysics and Chemistry of Materials with Low-Dimensional Structures (Springer, Dordrecht, 2000)

  16. F. Ortmann, S. Roche, S.O. Valenzuela,Topological insulators: fundamentals and perspectives (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2015)

  17. A. Bansil, H. Lin, T. Das, Rev. Mod. Phys. 88, 021004 (2016)

    Article  ADS  Google Scholar 

  18. S.Q. Shen,Topological insulators: Dirac equation in condensed matter (Springer, Singapore, 2017)

  19. N.P. Armitage, E.J. Mele, A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018)

    Article  ADS  Google Scholar 

  20. S. Manzeli, D. Ovchinnikov, D. Pasquier, O.V. Yazyev, A. Kis, Nat. Rev. Mater. 2, 17033 (2017)

    Article  ADS  Google Scholar 

  21. P.A.M. Dirac, Proc. R. Soc. Lond. A 117, 610 (1928)

    Article  ADS  Google Scholar 

  22. M.I. Dyakonov, Spin physics in semiconductors, Vol. 157 ofSpringer Series in Solid-State Sciences (Springer International Publishing, Cham, 2017)

  23. W. Pauli,General principles of quantum mechanics (Springer-Verlag, Berlin, 1980)

  24. G. Dresselhaus, Phys. Rev. 100, 580 (1955)

    Article  ADS  Google Scholar 

  25. E.I. Rashba, V.I. Sheka, Fiz. Tverd. Tela: Collected Papers 2, 162 (1959)

    Google Scholar 

  26. G. Bir, G. Pikus,Symmetry and strain-induced effects in semiconductors (Wiley, New York, 1974)

  27. M.M. Glazov, Electron & nuclear spin dynamics in semiconductor nanostructures, Vol. 23 ofSeries on Semiconductor Science and Technology (Oxford University Press, Oxford, 2018)

  28. L.C.L.Y.Voon, M. Willatzen,The k ⋅ p method: electronic properties of semiconductors (Springer Science & Business Media, Berlin, 2009)

  29. Y.A. Bychkov, E.I. Rashba, JETP Lett. 39, 78 (1984)

    ADS  Google Scholar 

  30. G. Bihlmayer, O. Rader, R. Winkler, New J. Phys. 17, 050202 (2015)

    Article  ADS  Google Scholar 

  31. A. Manchon, H.C. Koo, J. Nitta, S.M. Frolov, R.A. Duine, Nat. Mater. 14, 871 (2015)

    Article  ADS  Google Scholar 

  32. J. Smit, Physica 24, 39 (1958)

    Article  ADS  Google Scholar 

  33. M.I. Dyakonov, V.I. Perel, ZhETF Pis. Red. 13, 657 (1971)

    ADS  Google Scholar 

  34. L. Berger, Phys. Rev. B 2, 4559 (1970)

    Article  ADS  Google Scholar 

  35. P. Nozières, C. Lewiner, J. Phys. 34, 901 (1973)

    Article  Google Scholar 

  36. A. Crépieux, P. Bruno, Phys. Rev. B 64, 014416 (2001)

    Article  ADS  Google Scholar 

  37. H.A. Engel, B.I. Halperin, E.I. Rashba, Phys. Rev. Lett. 95, 166605 (2005)

    Article  ADS  Google Scholar 

  38. J. Sinova, S.O. Valenzuela, J. Wunderlich, C.H. Back, T. Jungwirth, Rev. Mod. Phys. 87, 1213 (2015)

    Article  ADS  Google Scholar 

  39. T. Giamarchi,Quantum physics in one dimension (Clarendon press, Oxford, 2003), Vol. 121

  40. R.M. Martin, L. Reining, D.M. Ceperley,Interacting electrons: theory and computational approaches (Cambridge University Press, Cambridge, 2016)

  41. E.O. Kane, J. Phys. Chem. Solids 1, 249 (1957)

    Article  ADS  Google Scholar 

  42. J.R. McLaughlan, E.M. Llewellyn-Samuel, S. Crampin, J. Phys. Condens. Matter 16, 6841 (2004)

    Article  ADS  Google Scholar 

  43. T. Nakazawa, N. Takagi, M. Kawai, H. Ishida, R. Arafune, Phys. Rev. B 94, 115412 (2016)

    Article  ADS  Google Scholar 

  44. S. Tognolini, S. Achilli, L. Longetti, E. Fava, C. Mariani, M.I. Trioni, S. Pagliara, Phys. Rev. Lett. 115, 046801 (2015)

    Article  ADS  Google Scholar 

  45. M.M. Glazov, M.A. Semina, S.M. Badalyan, G. Vignale, Phys. Rev. B 84, 033305 (2011)

    Article  ADS  Google Scholar 

  46. P.D.C. King et al., Phys. Rev. Lett. 107, 096802 (2011)

    Article  ADS  Google Scholar 

  47. K. Ishizaka et al., Nat. Mater. 10, 521 (2011)

    Article  ADS  Google Scholar 

  48. S. Singh, A.H. Romero, Phys. Rev. B 95, 165444 (2017)

    Article  ADS  Google Scholar 

  49. M.M. Otrokov et al., 2D Mater. 5, 035029 (2018)

    Article  Google Scholar 

  50. A. López, L. Colmenárez, M. Peralta, F. Mireles, E. Medina, Phys. Rev. B 99, 085411 (2019)

    Article  ADS  Google Scholar 

  51. D. Niesner, M. Wilhelm, I. Levchuk, A. Osvet, S. Shrestha, M. Batentschuk, C. Brabec, T. Fauster, Phys. Rev. Lett. 117, 126401 (2016)

    Article  ADS  Google Scholar 

  52. J. Varignon, L. Vila, A. Barthelemy, M. Bibes, Nat. Phys. 14, 322 (2018)

    Article  Google Scholar 

  53. L. Keldysh, Sov. Phys. JETP 29, 658 (1979)

    Google Scholar 

  54. G. Wang, A. Chernikov, M.M. Glazov, T.F. Heinz, X. Marie, T. Amand, B. Urbaszek, Rev. Mod. Phys. 90, 021001 (2018)

    Article  ADS  Google Scholar 

  55. N. Rytova, Moscow Univ. Phys. Bull. 3, 30 (1967)

    Google Scholar 

  56. C. Rössler, M. Herz, M. Bichler, S. Ludwig, Solid State Commun. 150, 861 (2010)

    Article  ADS  Google Scholar 

  57. D.A. Pokhabov, A.G. Pogosov, E.Y. Zhdanov, A.A. Shevyrin, A.K. Bakarov, A.A. Shklyaev, Appl. Phys. Lett. 112, 082102 (2018)

    Article  ADS  Google Scholar 

  58. H. Allami, O.A. Starykh, D.A. Pesin, Phys. Rev. B 99, 104505 (2019)

    Article  ADS  Google Scholar 

  59. F.W.J. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark,NIST handbook of mathematical functions (Cambridge University Press, Cambridge, 2010)

  60. P. Cudazzo, I.V. Tokatly, A. Rubio, Phys. Rev. B 84, 085406 (2011)

    Article  ADS  Google Scholar 

  61. S.A. Mikhailov, APL Photon. 4, 034501 (2019)

    Article  Google Scholar 

  62. T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, Phys. Rev. B 88, 045318 (2013)

    Article  ADS  Google Scholar 

  63. M. Combescot, S.Y. Shiau,Excitons and Cooper pairs: two composite bosons in many-body physics (Oxford University Press, Oxford, 2015)

  64. M.Y. Kagan, Modern trends in superconductivity and superfluidity, Vol. 874 ofLecture Notes in Physics (Springer, Berlin, 2013)

  65. B. Simon, Ann. Phys. 97, 279 (1976)

    Article  ADS  Google Scholar 

  66. W.M. Frank, D.J. Land, R.M. Spector, Rev. Mod. Phys. 43, 36 (1971)

    Article  ADS  Google Scholar 

  67. V.N. Efimov, Sov. J. Nucl. Phys. 12, 589 (1971)

    Google Scholar 

  68. J.M. Lévy-Leblond, Phys. Rev. 153, 1 (1967)

    Article  ADS  Google Scholar 

  69. J. Denschlag, G. Umshaus, J. Schmiedmayer, Phys. Rev. Lett. 81, 737 (1998)

    Article  ADS  Google Scholar 

  70. K.M. Case, Phys. Rev. 80, 797 (1950)

    Article  ADS  MathSciNet  Google Scholar 

  71. L.D. Landau, E.M. Lifshitz, Course of theoretical physics, Vol. 3 of Quantum Mechanics (Pergamon Press, Oxford, 1958)

  72. Y. Wang et al., Science 340, 734 (2013)

    Article  ADS  Google Scholar 

  73. K. Meetz, II Nuovo Cim. (1955-1965) 34, 690 (1964)

    MathSciNet  Google Scholar 

  74. H.E. Camblong, L.N. Epele, H. Fanchiotti, C.A. García Canal, Phys. Rev. Lett. 85, 1590 (2000)

    Article  ADS  Google Scholar 

  75. S.R. Beane, P.F. Bedaque, L. Childress, A. Kryjevski, J. McGuire, U. van Kolck, Phys. Rev. A 64, 042103 (2001)

    Article  ADS  Google Scholar 

  76. D. Bouaziz, M. Bawin, Phys. Rev. A 76, 032112 (2007)

    Article  ADS  Google Scholar 

  77. K.S. Gupta, S.G. Rajeev, Phys. Rev. D 48, 5940 (1993)

    Article  ADS  Google Scholar 

  78. G. Cuniberti, M. Sassetti, B. Kramer, J. Phys. Condens. Matter 8, L21 (1996)

    Article  ADS  Google Scholar 

  79. G. Cuniberti, M. Sassetti, B. Kramer, Phys. Rev. B 57, 1515 (1998)

    Article  ADS  Google Scholar 

  80. Y.M. Blanter, F.W.J. Hekking, M. Büttiker, Phys. Rev. Lett. 81, 1925 (1998)

    Article  ADS  Google Scholar 

  81. V.A. Sablikov, B.S. Shchamkhalova, Phys. Rev. B 58, 13847 (1998)

    Article  ADS  Google Scholar 

  82. V.A. Sablikov, B.S. Shchamkhalova, J. Low Temp. Phys. 118, 485 (2000)

    Article  ADS  Google Scholar 

  83. V.A. Sablikov, Y. Gindikin, Phys. Rev. B 61, 12766 (2000)

    Article  ADS  Google Scholar 

  84. Z. Zhong, N.M. Gabor, J.E. Sharping, A.L. Gaeta, P.L. McEuen, Nature Nanotechnology 3, 201 (2008)

    Article  Google Scholar 

  85. D.F. Santavicca, D.E. Prober, Terahertz resonances and bolometric response of a single-walled carbon nanotube, in2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves, 2008, pp. 1–3

  86. J.D. Chudow, D.F. Santavicca, D.E. Prober, Nano Lett. 16, 4909 (2016)

    Article  ADS  Google Scholar 

  87. E. Bocquillon, V. Freulon, J.M. Berroir, P. Degiovanni, B. Plaçais, A. Cavanna, Y. Jin, G. Fève, Nat. Commun. 4, 1839 (2013)

    Article  ADS  Google Scholar 

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  1. Fryazino Branch of the Kotelnikov Institute of Radio Engineering and Electronics of Russian Academy of Sciences, Fryazino, Moscow District, 141190, Russia

    Yasha Gindikin & Vladimir A. Sablikov

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  1. Yasha Gindikin
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  2. Vladimir A. Sablikov
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Correspondence to Yasha Gindikin.

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Gindikin, Y., Sablikov, V.A. Pair spin–orbit interaction in low-dimensional electron systems. Eur. Phys. J. Spec. Top. 229, 503–525 (2020). https://doi.org/10.1140/epjst/e2019-900086-6

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