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Few-Body Systems

, 60:52 | Cite as

Few-Body Systems in Condensed Matter Physics

  • Roman Ya. KezerashviliEmail author
Article
Part of the following topical collections:
  1. Ludwig Faddeev Memorial Issue

Abstract

This review focuses on the studies and computations of few-body systems of electrons and holes in condensed matter physics. We analyze and illustrate the application of a variety of methods for description of two- three- and four-body excitonic complexes such as an exciton, trion and biexciton in three-, two- and one-dimensional configuration spaces in various types of materials. We discuss and analyze the contributions made over the years to understanding how the reduction of dimensionality affects the binding energy of excitons, trions and biexcitons in bulk and low-dimensional semiconductors and address the challenges that still remain.

Notes

Acknowledgements

This work is supported by the U.S. Department of Defense under Grant No. W911NF1810433 and PSC CUNY under Grant No. 62261-00.

References

  1. 1.
    G.V. Skorniakov, K.A. Ter-Martirosian, ZhETF 31, 775 (1957); [Sov. Phys. JETP 4, 648 (1957)] Google Scholar
  2. 2.
    L.D. Faddeev, ZhETF 39, 1459 (1961); [Sov. Phys. JETP 12, 1014 (1961)]Google Scholar
  3. 3.
    L. Eyges, Phys. Rev. 115, 1643 (1959)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    V.N. Gribov, ZhETF 38, 553 (1960); [Sov. Phys. JETP 11, 400 (1960)]Google Scholar
  5. 5.
    L.D. Faddeev, Mathematical problems of the quantum theory of scattering for a system of three particles. Proc. Math. Inst. Acad. Sciences USSR 69, 1–122 (1963)Google Scholar
  6. 6.
    V. Efimov, Few-Body Syst. 60, 15 (2019)ADSCrossRefGoogle Scholar
  7. 7.
    V. Efimov, Yad. Fiz. 12, 1080 (1970)Google Scholar
  8. 8.
    V. Efimov, Phys. Lett. 33B, 563 (1970)ADSCrossRefGoogle Scholar
  9. 9.
    O.A. Yakubovsky, Sov. J. Nucl. Phys. 5, 937 (1967)Google Scholar
  10. 10.
    S.P. Merkuriev, C. Gignoux, A. Laverne, Ann. Phys. 99, 30 (1976)ADSCrossRefGoogle Scholar
  11. 11.
    L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Nauka, Moscow, 1985)zbMATHGoogle Scholar
  12. 12.
    L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer Academic, Dordrecht, 1993)zbMATHCrossRefGoogle Scholar
  13. 13.
    Y. Suzuki, K. Varga, Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems (Springer, Berlin, 1998)zbMATHGoogle Scholar
  14. 14.
    J. Mitroy, S. Bubin, W. Horiuchi, Y. Suzuki, L. Adamowicz, W. Cencek, K. Szalewicz, J. Komasa, D. Blume, K. Varga, Rev. Mod. Phys. 85, 693 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    G. Morpurgo, Nuovo Cim. 9, 461 (1952)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    L.M. Delves, Nucl. Phys. 9, 391 (1959)CrossRefGoogle Scholar
  17. 17.
    L.M. Delves, Nucl. Phys. 20, 276 (1960)CrossRefGoogle Scholar
  18. 18.
    L.M. Delves, Nucl. Phys. 29, 268 (1962)CrossRefGoogle Scholar
  19. 19.
    F.T. Smith, Phys. Rev. 120, 1058 (1960)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    YuA Simonov, Yad. Fiz. 3, 630 (1966)Google Scholar
  21. 21.
    YuA Simonov, Sov. J. Nucl. Phys. 3, 461 (1966)Google Scholar
  22. 22.
    A.M. Badalyan, YuA Simonov, Yad. Fiz. 3, 1032 (1966)Google Scholar
  23. 23.
    J. Avery, Hyperspherical Harmonics: Applications in Quantum Theory (Kluwer, Dordrecht, 1989)zbMATHCrossRefGoogle Scholar
  24. 24.
    R.I. Jibuti, K.V. Shitikova, Method of Hyperspherical Functions in Atomic and Nuclear Physics (Energoatomizdat, Moscow, 1993). (in Russian) Google Scholar
  25. 25.
    J. Frenkel, Phys. Rev. 37, 17 (1931)ADSCrossRefGoogle Scholar
  26. 26.
    G. Wannier, Phys. Rev. 52, 191 (1937)ADSCrossRefGoogle Scholar
  27. 27.
    K.N. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  28. 28.
    G.R. Bhimanapati et al., ACS Nano 9, 11509 (2015)CrossRefGoogle Scholar
  29. 29.
    K.S. Novoselov, A. Mishchenko, A. Carvalho, A.H. Castro Neto, Science 353, 9439 (2016)CrossRefGoogle Scholar
  30. 30.
    M. Velický, P.S. Toth, Appl. Mater. Today 8, 68 (2017)CrossRefGoogle Scholar
  31. 31.
    D. Jariwala, T.J. Marks, M.C. Hersam, Nat. Mater. 16, 170 (2017)ADSCrossRefGoogle Scholar
  32. 32.
    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)ADSCrossRefGoogle Scholar
  33. 33.
    A. Kormányos, G. Burkard, M. Gmitra, J. Fabian, V. Zolyomi, N.D. Drummond, V. Fal’ko, 2D Mater. 2, 022001 (2015)CrossRefGoogle Scholar
  34. 34.
    J.O. Island et al., 2D Mater. 4, 022003 (2017)CrossRefGoogle Scholar
  35. 35.
    L. Li, Y. Yu, G.J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X.H. Chen, Y. Zhang, Nat. Nanotechnol. 9, 372 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    H. Liu, A.T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, P.D. Ye, ACS Nano 8, 4033 (2014)CrossRefGoogle Scholar
  37. 37.
    A.H. Woomer, T.W. Farnsworth, J. Hu, R.A. Wells, C.L. Donley, S.C. Warren, ACS Nano 9, 8869 (2015)CrossRefGoogle Scholar
  38. 38.
    C.R. Dean et al., Nat. Nanotechnol. 5, 722 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    L. Matthes, P. Gori, O. Pulci, F. Bechstedt, Phys. Rev. B 87, 035438 (2013)ADSCrossRefGoogle Scholar
  40. 40.
    A. Molle, J. Goldberger, M. Houssa, Y. Xu, S.C. Zhang, D. Akinwande, Nat. Mater. 16, 163 (2017)ADSCrossRefGoogle Scholar
  41. 41.
    M.N. Brunetti, O.L. Berman, R.Ya. Kezerashvili, Phys. Rev. B 98, 125406 (2018)ADSCrossRefGoogle Scholar
  42. 42.
    N.D. Drummond, V. Zólyomi, V.I. Falko, Phys. Rev. B 85, 075423 (2012)ADSCrossRefGoogle Scholar
  43. 43.
    M.E. Dávila, L. Xian, S. Cahangirov, A. Rubio, G. Le Lay, N. J. Phys. 16, 095002 (2014)CrossRefGoogle Scholar
  44. 44.
    F.-F. Zhu, W.-J. Chen, Y. Xu, C.-L. Gao, D.-D. Guan, C.-H. Liu, D. Qian, S.-C. Zhang, J.-F. Jia, Nat. Mater. 14, 1020 (2015)ADSCrossRefGoogle Scholar
  45. 45.
    A.J. Mannix et al., Science 350, 1513 (2015)ADSCrossRefGoogle Scholar
  46. 46.
    A. Geim, I. Grigorieva, Nature 499, 419 (2014)CrossRefGoogle Scholar
  47. 47.
    N.S. Rytova, Proc. Moscow State University, Phys. Astron. 3, 30 (1967)Google Scholar
  48. 48.
    L.V. Keldysh, JETP Lett. 29, 658 (1979) ; [Pis’ma. Zh. Eksp. Teor. Fiz. 29, 716 (1979)]Google Scholar
  49. 49.
    B. Scharf, D. Van Tuan, I. Žutić, H. Dery, J. Phys. Condens. Matter. 31, 203001 (2019)ADSCrossRefGoogle Scholar
  50. 50.
    Yu.E. Lozovik, V.N. Nishanov, Sov. Phys. Solid State 18, 1905 (1976)Google Scholar
  51. 51.
    S.A. Moskalenko, D.W. Snoke, Bose-Einstein Condensation of Excitons and Biexcitons and Coherent Nonlinear Optics with Excitons (Cambridge University Press, New York, 2000)CrossRefGoogle Scholar
  52. 52.
    Yu.E Lozovik, V.I. Yudson, Sov. Phys. JETP 44, 389 (1976)Google Scholar
  53. 53.
    Yu.E. Lozovik, V.I. Yudson, Zh Eksp, Teor. Fiz. 71, 738 (1976)Google Scholar
  54. 54.
    D. Snoke, Spontaneous Bose coherence of excitons and polaritons. Science 298, 1368 (2002)ADSCrossRefGoogle Scholar
  55. 55.
    L.V. Butov, J. Phys. Condens. Matter 16, R1577 (2004)ADSCrossRefGoogle Scholar
  56. 56.
    M. Combescot, R. Combescot, F. Dubin, Rep. Prog. Phys. 80, 066501 (2017)ADSCrossRefGoogle Scholar
  57. 57.
    M. Danovich, D.A. Ruiz-Tijerina, R.J. Hunt, M. Szyniszewski, N.D. Drummond, V.I. Fal’ko, Phys. Rev. 97, 195452 (2018)ADSCrossRefGoogle Scholar
  58. 58.
    O.L. Berman, R.Ya. Kezerashvili, Few-Body Syst. 50, 407 (2011)ADSCrossRefGoogle Scholar
  59. 59.
    O.L. Berman, R.Ya. Kezerashvili, K. Ziegler, Phys. Rev. B 85, 035418 (2012)ADSCrossRefGoogle Scholar
  60. 60.
    O.L. Berman, R.Ya. Kezerashvili, Phys. Rev. B 93, 245410 (2016)ADSCrossRefGoogle Scholar
  61. 61.
    O.L. Berman, R.Ya. Kezerashvili, Phys. Rev. B 96, 245410 (2017)CrossRefGoogle Scholar
  62. 62.
    A.H. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  63. 63.
    M.A.H. Vozmediano, M.I. Katsnelson, F. Guinea, Phys. Rep. 496, 109 (2010)ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    D. Xiao, G.B. Liu, W. Feng, X. Xu, W. Yao, Phys. Rev. Lett. 108, 094502 (2012)Google Scholar
  65. 65.
    C.J. Tabert, E.J. Nicol, Phys. Rev. B 89, 195410 (2014)ADSCrossRefGoogle Scholar
  66. 66.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd edn. (Elsevier, Oxford, 1977)zbMATHGoogle Scholar
  67. 67.
    R.L. Liboff, Introductory Quantum Mechanics, 2nd edn. (Addison-Wesley, Reading, 1992)zbMATHGoogle Scholar
  68. 68.
    D.J. Griffiths, Introduction to Quantum Mechanics, 2nd edn. (Prentice-Hall, New York, 2005)Google Scholar
  69. 69.
    O.L. Berman, R.Ya. Kezerashvili, K. Ziegler, Phys. Rev. A 87, 042513 (2013)ADSCrossRefGoogle Scholar
  70. 70.
    D. Alba, H.W. Crater, L. Lusanna, J. Phys. A Math. Theor. 40, 9585 (2007)ADSCrossRefGoogle Scholar
  71. 71.
    J. Sabio, F. Sols, F. Guinea, Phys. Rev. B 81, 045428 (2010)ADSCrossRefGoogle Scholar
  72. 72.
    A. Ramasubramaniam, Phys. Rev. B 86, 115409 (2012)ADSCrossRefGoogle Scholar
  73. 73.
    D.Y. Qiu, F.H. da Jornada, S.G. Louie, Phys. Rev. Lett. 111, 216805 (2013)ADSCrossRefGoogle Scholar
  74. 74.
    M.M. Fogler, L.V. Butov, K.S. Novoselov, Nat. Commun. 5, 4555 (2014)ADSCrossRefGoogle Scholar
  75. 75.
    E.V. Calman, C.J. Dorow, M.M. Fogler, L.V. Butov, S. Hu, A. Mishchenko, A.K. Geim, Appl. Phys. Lett. 108, 101901 (2016)ADSCrossRefGoogle Scholar
  76. 76.
    M. Van der Donck, F.M. Peeters, Phys. Rev. B 98, 115104 (2018)ADSCrossRefGoogle Scholar
  77. 77.
    T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, Phys. Rev. B 88, 045318 (2013)ADSCrossRefGoogle Scholar
  78. 78.
    P. Cudazzo, I.V. Tokatly, A. Rubio, Phys. Rev. B 84, 085406 (2011)ADSCrossRefGoogle Scholar
  79. 79.
    G. Wang, A. Chernikov, M.M. Glazov, T.F. Heinz, X. Marie, T. Amand, B. Urbaszek, Rev. Mod. Phys. 90, 021001 (2018)ADSCrossRefGoogle Scholar
  80. 80.
    I. Kylänpää, H.-P. Komsa, Phys. Rev. B 92, 205418 (2015)ADSCrossRefGoogle Scholar
  81. 81.
    M.N. Brunetti, O.L. Berman, R.Ya. Kezerashvili, J. Phys. Condens. Matter 30, 225001 (2018)ADSGoogle Scholar
  82. 82.
    X. Wang et al., Nat. Nanotechnol. 10, 517 (2015)ADSCrossRefGoogle Scholar
  83. 83.
    A.S. Rodin, A. Carvalho, A.H. Neto, Phys. Rev. B 90, 075429 (2014)ADSCrossRefGoogle Scholar
  84. 84.
    E. Prada, J.V. Alvarez, K.L. Narasimha-Acharya, F.J. Bailen, J.J. Palacios, Phys. Rev. B 91, 245421 (2015)ADSCrossRefGoogle Scholar
  85. 85.
    R.J. Hunt, M. Szyniszewski, G.I. Prayogo, R. Maezono, N.D. Drummond, Phys. Rev. 98, 075122 (2018)CrossRefGoogle Scholar
  86. 86.
    O.L. Berman, G. Gumbs, R.Ya. Kezerashvili, Phys. Rev. B 96, 014505 (2017)ADSCrossRefGoogle Scholar
  87. 87.
    M.N. Brunetti, O.L. Berman, R.Ya. Kezerashvili, Phys. Lett. A 383, 482 (2019)ADSMathSciNetCrossRefGoogle Scholar
  88. 88.
    A.C. Bartnik, Al.L. Efros, W.-K. Koh, C.B. Murray, F.W. Wise, Phys. Rev. B 82, 195313 (2010)Google Scholar
  89. 89.
    J. Giblin, F. Vietmeyer, M.P. McDonald, M. Kuno, Nano Lett. 11, 3307 (2011)ADSCrossRefGoogle Scholar
  90. 90.
    T. Ogawa, T. Takagahara, Phys. Rev. B 44, 8138 (1991)ADSCrossRefGoogle Scholar
  91. 91.
    R.Ya. Kezerashvili, Z. Machavariani, B. Beradze, T. Tchelidze, Physica E 109, 228 (2019)ADSCrossRefGoogle Scholar
  92. 92.
    F.C. Zhang, S. Sarma, Phys. Rev. B 33, 2903 (1986)ADSCrossRefGoogle Scholar
  93. 93.
    M.A. Semina, R.A. Sergeev, R.A. Suris, Semiconductors 42, 1427 (2008)ADSCrossRefGoogle Scholar
  94. 94.
    S. Bednarek, B. Szafran, T. Chwiej, J. Adamowski, Phys. Rev. B 68, 045328 (2003)ADSCrossRefGoogle Scholar
  95. 95.
    A.F. Slachmuylders, B. Partoens, W. Magnus, F.M. Peeters, J. Phys. Condens. Matter 18, 3951 (2006)ADSCrossRefGoogle Scholar
  96. 96.
    R. Loudon, Am. J. Phys. 27, 649 (1959)ADSCrossRefGoogle Scholar
  97. 97.
    R.J. Elliott, R. Loudon, J. Phys. Chem. Solids 8, 382 (1959)ADSCrossRefGoogle Scholar
  98. 98.
    R.J. Elliott, R. Loudon, J. Phys. Chem. Solids 15, 196 (1960)ADSCrossRefGoogle Scholar
  99. 99.
    M.A. Lampert, Phys. Rev. Lett. 1, 450 (1958)ADSCrossRefGoogle Scholar
  100. 100.
    B. Stébé, E. Feddi, G. Munschy, Phys. Rev. B 35, 4331 (1987)ADSCrossRefGoogle Scholar
  101. 101.
    B. Stébé, A. Ainane, Superlatt. Microstruct. 5, 545 (1989)ADSCrossRefGoogle Scholar
  102. 102.
    K. Kheng et al., Phys. Rev. Lett. 71, 1752 (1993)ADSCrossRefGoogle Scholar
  103. 103.
    I.N. Filikhin, A. Gal, V.M. Suslov, Phys. Rev. C 68, 024002 (2003)ADSCrossRefGoogle Scholar
  104. 104.
    R.Ya. Kezerashvili, S.M. Tsiklauri, I. Filikhin, V.M. Suslov, B. Vlahovic, J. Phys. G Nucl. Part. Phys. 43, 065104 (2016)ADSCrossRefGoogle Scholar
  105. 105.
    I. Filikhin, R.Ya. Kezerashvili, B. Vlahovic, Phys. Lett. A 382, 787 (2018)ADSCrossRefGoogle Scholar
  106. 106.
    G. Finkelstein, H. Shtrikman, I. Bar-Joseph, Phys. Rev. Lett. 74, 976 (1995)ADSCrossRefGoogle Scholar
  107. 107.
    A.J. Shields, M. Pepper, D.A. Ritchie, M.Y. Simmons, G.A.C. Jones, Phys. Rev. B 51, 18049 (1995)ADSCrossRefGoogle Scholar
  108. 108.
    H. Buhmann, L. Mansouri, J. Wang, P.H. Beton, N. Mori, L. Eaves, M. Henini, M. Potemski, Phys. Rev. B 51, 7969 (1995)ADSCrossRefGoogle Scholar
  109. 109.
    S.A. Brown, J.F. Young, J.A. Brum, P. Hawrylak, Z. Wasilewski, Phys. Rev. B 54, 11082 (1996)ADSCrossRefGoogle Scholar
  110. 110.
    R. Kaur, A.J. Shields, J.L. Osborne, M.Y. Simmons, D.A. Ritchie, M. Pepper, Phys. Stat. Sol. 178, 465 (2000)ADSCrossRefGoogle Scholar
  111. 111.
    V. Huard, R.T. Cox, K. Saminadayar, A. Arnoult, S. Tataremko, Phys. Rev. Lett. 84, 187 (2000)ADSCrossRefGoogle Scholar
  112. 112.
    A. Esser et al., Phys. Status Solidi (a) 178, 489 (2000)ADSCrossRefGoogle Scholar
  113. 113.
    A. Esser et al., Phys. Rev. B 62, 8232 (2000)ADSCrossRefGoogle Scholar
  114. 114.
    A.S. Bracker et al., Phys. Rev. B 72, 035332 (2005)ADSCrossRefGoogle Scholar
  115. 115.
    J. Usukura, Y. Suzuki, K. Varga, Phys. Rev. B 59, 5652 (1999)ADSCrossRefGoogle Scholar
  116. 116.
    C. Riva, F.M. Peeters, K. Varga, Phys. Rev. 61, 873 (2000)CrossRefGoogle Scholar
  117. 117.
    T.F. RØnnow, T.G. Pedersen, B. Partoens, K.K. Berthelsen, Phys. Rev. B 184, 035316 (2011)ADSCrossRefGoogle Scholar
  118. 118.
    W.Y. Ruan, K.S. Chan, H.P. Ho, R.Q. Zhang, E.Y.B. Pun, Phys. Rev. B 60, 5714 (1999)ADSCrossRefGoogle Scholar
  119. 119.
    M. Braun, O.I. Kartavtsev, Nucl. Phys. A 698, 519c (2001)ADSCrossRefGoogle Scholar
  120. 120.
    M. Braun, O.I. Kartavtsev, Phys. Lett. A 331, 437 (2004)ADSCrossRefGoogle Scholar
  121. 121.
    K.F. Mak et al., Nat. Mater. 12, 207 (2013)ADSCrossRefGoogle Scholar
  122. 122.
    J.S. Ross et al., Nat. Commun. 4, 1474 (2013)ADSCrossRefGoogle Scholar
  123. 123.
    A.M. Jones et al., Nat. Nanotechnol. 8, 634 (2013)ADSCrossRefGoogle Scholar
  124. 124.
    G. Wang et al., Phys. Rev. B 90, 075413 (2014)ADSCrossRefGoogle Scholar
  125. 125.
    A. Singh et al., Phys. Rev. Lett. 112, 21680 (2014)Google Scholar
  126. 126.
    C.H. Liu et al., Phys. Rev. Lett. 113, 166801 (2014)ADSCrossRefGoogle Scholar
  127. 127.
    J. Shang et al., ACS Nano 9, 647 (2015)CrossRefGoogle Scholar
  128. 128.
    G. Plechinger et al., Phys. Status Solidi RRL 9, 457 (2015)CrossRefGoogle Scholar
  129. 129.
    Y. Zhang, H. Li, H. Wang, R. Liu, S. Zhang, Z. Qiu, ACS Nano 9, 8514 (2015)CrossRefGoogle Scholar
  130. 130.
    J.W. Christopher, B.B. Goldberg, A.K. Swan, Sci. Rep. 7, 14062 (2017)ADSCrossRefGoogle Scholar
  131. 131.
    E. Courtade et al., Phys. Rev. B 96, 085302 (2017)ADSCrossRefGoogle Scholar
  132. 132.
    M.Z. Bellus, F. Ceballos, H.-Y. Chiu, H. Zhao, ACS Nano 9, 6459 (2015)CrossRefGoogle Scholar
  133. 133.
    J. Shang, X. Shen, C. Cong, N. Peimyoo, B. Cao, M. Eginligil, T. Yu, ACS Nano 9, 647 (2015)CrossRefGoogle Scholar
  134. 134.
    B. Zhu, H. Zeng, J. Dai, Z. Gong, X. Cui, Proc. Natl. Acad. Sci. USA 111, 11606 (2014)ADSCrossRefGoogle Scholar
  135. 135.
    J. Yang et al., ACS Nano 9, 6603 (2015)CrossRefGoogle Scholar
  136. 136.
    T. Godde et al., Phys. Rev. B 94, 165301 (2016)ADSCrossRefGoogle Scholar
  137. 137.
    G. Plechinger et al., Nat. Commun. 7, 12715 (2016)ADSCrossRefGoogle Scholar
  138. 138.
    J. Yang, Y. Lu, Chin. Phys. B 26, 034201 (2017)ADSCrossRefGoogle Scholar
  139. 139.
    R. Xu et al., ACS Nano 10, 2046 (2016)CrossRefGoogle Scholar
  140. 140.
    C. Zhang, H. Wang, W. Chan, C. Manolatou, F. Rana, Phys. Rev. B 89, 205436 (2014)ADSCrossRefGoogle Scholar
  141. 141.
    M. Szyniszewski, E. Mostaani, N.D. Drummond, V.I. Falko, Phys. Rev. B 95, 081301(R) (2017)ADSCrossRefGoogle Scholar
  142. 142.
    E. Mostaani, M. Szyniszewski, C.H. Price, R. Maezono, M. Danovich, R.J. Hunt, N.D. Drummond, V.I. Falko, Phys. Rev. B 96, 075431 (2017)ADSCrossRefGoogle Scholar
  143. 143.
    B. Ganchev, N. Drummond, I. Aleiner, V. Falko, Phys. Rev. Lett. 114, 107401 (2015)ADSCrossRefGoogle Scholar
  144. 144.
    K.A. Velizhanin, A. Saxena, Phys. Rev. B 92, 195305 (2015)ADSCrossRefGoogle Scholar
  145. 145.
    D.W. Kidd, D.K. Zhang, K. Varga, Phys. Rev. B 93, 125423 (2016)ADSCrossRefGoogle Scholar
  146. 146.
    M.Z. Mayers, T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, Phys. Rev. B 92, 161404 (2015)ADSCrossRefGoogle Scholar
  147. 147.
    A. Thilagam, Phys. Rev. B 55, 7804 (1997)ADSCrossRefGoogle Scholar
  148. 148.
    M. Van der Donck, M. Zarenia, F.M. Peeters, Phys. Rev. B 96, 035131 (2017)ADSCrossRefGoogle Scholar
  149. 149.
    R.Ya. Kezerashvili, S.M. Tsiklauri, Few-Body Syst. 58, 18 (2017)Google Scholar
  150. 150.
    I. Filikhin, R.Ya. Kezerashvili, S.M. Tsiklauri, B. Vlahovic, Nanotechnology 29, 124002 (2018)ADSCrossRefGoogle Scholar
  151. 151.
    A. Ramirez-Torres, V. Turkowski, T.S. Rahman, Phys. Rev. B 90, 085419 (2014)ADSCrossRefGoogle Scholar
  152. 152.
    O.L. Berman, R.Ya. Kezerashvili, S.M. Tsiklauri, Int. J. Mod. Phys. B 28, 1450064 (2014)ADSCrossRefGoogle Scholar
  153. 153.
    I.V. Bondarev, M.R. Vladimirova, Phys. Rev. B 97, 165419 (2018)ADSCrossRefGoogle Scholar
  154. 154.
    L.A. Jauregui et al., arXiv:1812.08691 [cond-mat.mes-hall] (2018)
  155. 155.
    O. Witham, R.J. Hunt, N.D. Drummond, Phys. Rev. B 97, 075424 (2018)ADSCrossRefGoogle Scholar
  156. 156.
    T. Baars, W. Braun, M. Bayer, A. Forchel, Phys. Rev. B 58, R1750 (1998)ADSCrossRefGoogle Scholar
  157. 157.
    A. Esser, R. Zimmermann, E. Runge, Phys. Stat. Sol. B 227, 317 (2001)ADSCrossRefGoogle Scholar
  158. 158.
    T. Tsuchiya, Int. J. Mod. Phys. B 15, 3985 (2001)ADSCrossRefGoogle Scholar
  159. 159.
    A. Crottini, J.L. Staehli, B. Deveaud, X.L. Wang, M. Ogura, Solid State Commun. 121, 401 (2002)ADSCrossRefGoogle Scholar
  160. 160.
    T. Otterburg et al., Phys. Rev. B 71, 033301 (2005)ADSCrossRefGoogle Scholar
  161. 161.
    B. Szafran, T. Chwiej, F.M. Peeters, S. Bednarek, J. Adamowski, Phys. Rev. B 71, 235305 (2005)ADSCrossRefGoogle Scholar
  162. 162.
    F.M. Peeters, B. Szafran, T. Chwiej, S. Bednarek, J. Adamowski, Few-Body Syst. 38, 121 (2006)ADSCrossRefGoogle Scholar
  163. 163.
    Y. Sidor, B. Partoens, F.M. Peeters, Phys. Rev. B 77, 205413 (2008)ADSCrossRefGoogle Scholar
  164. 164.
    M.J.A. Schuetz, M.G. Moore, C. Piermarocchi, Nat. Phys. 6, 919 (2010)CrossRefGoogle Scholar
  165. 165.
    L.X. Zhai, Y. Wang, J.J. Liu, Phys. Lett. A 376, 1866 (2012)ADSCrossRefGoogle Scholar
  166. 166.
    T.G. Pedersen, Phys. Rev. B 67, 073401 (2003)ADSCrossRefGoogle Scholar
  167. 167.
    T.G. Pedersen, K. Pedersen, H.D. Cornean, P. Duclos, Nano Lett. 5, 291 (2005)ADSCrossRefGoogle Scholar
  168. 168.
    D. Kammerlander, D. Prezzi, G. Goldoni, E. Molinari, U. Hohenester, Phys. Rev. Lett. 99, 126806 (2007)ADSCrossRefGoogle Scholar
  169. 169.
    D. Kammerlander, D. Prezzi, G. Goldoni, E. Molinari, U. Hohenester, Physica E 40, 1997 (2008)ADSCrossRefGoogle Scholar
  170. 170.
    T.F. Rønnow, T.G. Pedersen, H.D. Cornean, Phys. Rev. B 81, 205446 (2010)ADSCrossRefGoogle Scholar
  171. 171.
    T.F. Rønnow, T.G. Pedersen, B. Partoens, K.K. Berthelsen, Phys. Rev. B 84, 035316 (2011)ADSCrossRefGoogle Scholar
  172. 172.
    R. Matsunaga, K. Matsuda, Y. Kanemitsu, Phys. Rev. Lett. 106, 037404 (2011)ADSCrossRefGoogle Scholar
  173. 173.
    S.M. Santos, B. Yuma, S. Berciaud, J. Shaver, M. Gallart, P. Gilliot et al., Phys. Rev. Lett. 107, 187401 (2011)ADSCrossRefGoogle Scholar
  174. 174.
    I.V. Bondarev, Phys. Rev. B 83, 153409 (2011)ADSCrossRefGoogle Scholar
  175. 175.
    K. Watanabe, K. Asano, Phys. Rev. B 83, 115406 (2011)ADSCrossRefGoogle Scholar
  176. 176.
    K. Watanabe, K. Asano, Phys. Rev. B 85, 035416 (2012)ADSCrossRefGoogle Scholar
  177. 177.
    T.F. Rønnow, T.G. Pedersen, B. Partoens, Phys. Rev. B 85, 045412 (2012)ADSCrossRefGoogle Scholar
  178. 178.
    L. Colombier, J. Selles, E. Rousseau, J.S. Lauret, F. Vialla, C. Voisin, G. Cassabois, Phys. Rev. Lett. 109, 197402 (2012)ADSCrossRefGoogle Scholar
  179. 179.
    B. Yuma, S. Berciaud, J. Besbas, J. Shaver, S. Santos, S. Ghosh et al., Phys. Rev. B 87, 205412 (2013)ADSCrossRefGoogle Scholar
  180. 180.
    I.V. Bondarev, Phys. Rev. B 90, 245430 (2014)ADSCrossRefGoogle Scholar
  181. 181.
    I.V. Bondarev, Mod. Phys. Lett. B 30, 1630006 (2016)ADSCrossRefGoogle Scholar
  182. 182.
    A.F. Slachmuylders, B. Partoens, W. Magnus, F.M. Peeters, Phys. Rev. B 76, 075405 (2007)ADSCrossRefGoogle Scholar
  183. 183.
    A.F. Slachmuylders, B. Partoens, W. Magnus, F.M. Peeters, Physica E 40, 2166 (2008)ADSCrossRefGoogle Scholar
  184. 184.
    T. Deilmann, M. Drüppel, M. Rohlfing, Phys. Rev. Lett. 116, 196804 (2016)ADSCrossRefGoogle Scholar
  185. 185.
    L.N. Ivanov, YuE Lozovik, D.R. Musin, J. Phys. C Solid State Phys. 11, 2527 (1978)ADSCrossRefGoogle Scholar
  186. 186.
    R.C. Miller et al., Phys. Rev. B 25, 6545 (1982)ADSCrossRefGoogle Scholar
  187. 187.
    D. Bressanini, M. Mella, G. Morosi, Phys. Rev. A 55, 200 (1997)ADSCrossRefGoogle Scholar
  188. 188.
    D. Bressanini, M. Mella, G. Morosi, Phys. Rev. A 57, 4956 (1998)ADSCrossRefGoogle Scholar
  189. 189.
    C. Mai et al., Nano Lett. 14, 202 (2014)ADSCrossRefGoogle Scholar
  190. 190.
    Y. You, X.-X. Zhang, T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, T.F. Heinz, Nat. Phys. 11, 477 (2015)CrossRefGoogle Scholar
  191. 191.
    E.J. Sie, A.J. Frenzel, Y.-H. Lee, J. Kong, N. Gedik, Phys. Rev. B 92, 125417 (2015)ADSCrossRefGoogle Scholar
  192. 192.
    K. Hao et al., Nat. Commun. 8, 15552 (2017)ADSCrossRefGoogle Scholar
  193. 193.
    D.K. Zhang, D.W. Kidd, K. Varga, Nano Lett. 15, 7002 (2015)ADSCrossRefGoogle Scholar
  194. 194.
    A. Thilagam, J. Appl. Phys 116, 053523 (2014)ADSCrossRefGoogle Scholar
  195. 195.
    D.V. Tuan, M. Yang, H. Dery, Phys. Rev. B 98, 125308 (2018)ADSCrossRefGoogle Scholar
  196. 196.
    S.-Y. Chen, T. Goldstein, T. Taniguchi, K. Watanabe, J. Yan, Nat. Commun. 9, 3717 (2018)ADSCrossRefGoogle Scholar
  197. 197.
    Z. Ye, L. Waldecker, E.Y. Ma, D. Rhodes, A. Antony, B. Kim et al., Nat. Commun. 9, 3718 (2018)ADSCrossRefGoogle Scholar
  198. 198.
    Z. Li, T. Wang, Z. Lu, C. Jin, Y. Chen, Y. Meng et al., Nat. Commun. 9, 3719 (2018)ADSCrossRefGoogle Scholar
  199. 199.
    M. Barbone, A.R.-P. Montblanch, D.M. Kara, C. Palacios-Berraquero, A.R. Cadore, D. De Fazio et al., Nat. Commun. 9, 3721 (2018)ADSCrossRefGoogle Scholar
  200. 200.
    A. Steinhoff et al., Nat. Phys. 14, 1199 (2018)CrossRefGoogle Scholar
  201. 201.
    A.D. Meyertholen, M.M. Fogler, Phys. Rev. B 78, 235307 (2008)ADSCrossRefGoogle Scholar
  202. 202.
    R.T. Pack, J.O. Hirschfelder, J. Chem. Phys. 52, 521 (1970)ADSCrossRefGoogle Scholar
  203. 203.
    M.Y.J. Tan, N.D. Drummond, R.J. Needs, Phys. Rev. B 71, 033303 (2005)ADSCrossRefGoogle Scholar
  204. 204.
    A. Chaves, M.Z. Mayers, F.M. Peeters, D.R. Reichman, Phys. Rev. B 93, 115314 (2016)ADSCrossRefGoogle Scholar
  205. 205.
    A. Crottinia, J.L. Staehlia, B. Deveauda, X.L. Wang, M. Ogura, Solid State Commun. 121, 401 (2002)ADSCrossRefGoogle Scholar
  206. 206.
    R. Baer, E. Rabani, J. Chem. Phys. 138, 051102 (2013)ADSCrossRefGoogle Scholar
  207. 207.
    C. Herring, M. Flicker, Phys. Rev. 134, A362 (1964)ADSCrossRefGoogle Scholar
  208. 208.
    N.K. Timofeyuk, D. Baye, Few-Body Syst. 58, 157 (2017)ADSCrossRefGoogle Scholar
  209. 209.
    P. Ajayan, P. Kim, K. Banerjee, Phys. Today 69(9), 38 (2016)CrossRefGoogle Scholar
  210. 210.
    A. Kogar et al., Science 358, 1314 (2017)ADSCrossRefGoogle Scholar
  211. 211.
    O. Cotleţ, S. Zeytinoglu, M. Sigrist, E. Demler, A. Imamoglu, Phys. Rev. B 93, 054510 (2016)ADSCrossRefGoogle Scholar
  212. 212.
    K.S. Thygesen, 2D Mater. 4, 022004 (2017)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Physics Department, New York City College of TechnologyThe City University of New YorkBrooklynUSA
  2. 2.The Graduate School and University CenterThe City University of New YorkNew YorkUSA

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