Skip to main content
SpringerLink
Log in

Few-Body Systems in Condensed Matter Physics

  • Published:
Few-Body Systems Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. In the summer of 2016 at the EFB23 conference in Aarhus, Denmark, following the inaugural ceremony establishing the Faddeev Medal, I spoke with L. D. Faddeev and mentioned that I would like to nominate Vitaly Efimov for this distinguished award. A smile touched Faddeev’s face and he said simply, “great choice”. In 2018, Vitaly Efimov and Rudolf Grimm became joint recipients of the Faddeev Medal for the theoretical prediction and ground-breaking experimental confirmation of the Efimov effect.

References

  1. G.V. Skorniakov, K.A. Ter-Martirosian, ZhETF 31, 775 (1957); [Sov. Phys. JETP 4, 648 (1957)]

  2. L.D. Faddeev, ZhETF 39, 1459 (1961); [Sov. Phys. JETP 12, 1014 (1961)]

  3. L. Eyges, Phys. Rev. 115, 1643 (1959)

    ADS  MathSciNet  Google Scholar 

  4. V.N. Gribov, ZhETF 38, 553 (1960); [Sov. Phys. JETP 11, 400 (1960)]

  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. V. Efimov, Few-Body Syst. 60, 15 (2019)

    ADS  Google Scholar 

  7. V. Efimov, Yad. Fiz. 12, 1080 (1970)

    Google Scholar 

  8. V. Efimov, Phys. Lett. 33B, 563 (1970)

    ADS  Google Scholar 

  9. O.A. Yakubovsky, Sov. J. Nucl. Phys. 5, 937 (1967)

    Google Scholar 

  10. S.P. Merkuriev, C. Gignoux, A. Laverne, Ann. Phys. 99, 30 (1976)

    ADS  Google Scholar 

  11. L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Nauka, Moscow, 1985)

    MATH  Google Scholar 

  12. L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer Academic, Dordrecht, 1993)

    MATH  Google Scholar 

  13. Y. Suzuki, K. Varga, Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems (Springer, Berlin, 1998)

    MATH  Google Scholar 

  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)

    ADS  Google Scholar 

  15. G. Morpurgo, Nuovo Cim. 9, 461 (1952)

    ADS  Google Scholar 

  16. L.M. Delves, Nucl. Phys. 9, 391 (1959)

    Google Scholar 

  17. L.M. Delves, Nucl. Phys. 20, 276 (1960)

    Google Scholar 

  18. L.M. Delves, Nucl. Phys. 29, 268 (1962)

    Google Scholar 

  19. F.T. Smith, Phys. Rev. 120, 1058 (1960)

    ADS  MathSciNet  Google Scholar 

  20. YuA Simonov, Yad. Fiz. 3, 630 (1966)

    Google Scholar 

  21. YuA Simonov, Sov. J. Nucl. Phys. 3, 461 (1966)

    Google Scholar 

  22. A.M. Badalyan, YuA Simonov, Yad. Fiz. 3, 1032 (1966)

    Google Scholar 

  23. J. Avery, Hyperspherical Harmonics: Applications in Quantum Theory (Kluwer, Dordrecht, 1989)

    MATH  Google Scholar 

  24. R.I. Jibuti, K.V. Shitikova, Method of Hyperspherical Functions in Atomic and Nuclear Physics (Energoatomizdat, Moscow, 1993). (in Russian)

    Google Scholar 

  25. J. Frenkel, Phys. Rev. 37, 17 (1931)

    ADS  Google Scholar 

  26. G. Wannier, Phys. Rev. 52, 191 (1937)

    ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  28. G.R. Bhimanapati et al., ACS Nano 9, 11509 (2015)

    Google Scholar 

  29. K.S. Novoselov, A. Mishchenko, A. Carvalho, A.H. Castro Neto, Science 353, 9439 (2016)

    Google Scholar 

  30. M. Velický, P.S. Toth, Appl. Mater. Today 8, 68 (2017)

    Google Scholar 

  31. D. Jariwala, T.J. Marks, M.C. Hersam, Nat. Mater. 16, 170 (2017)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  33. A. Kormányos, G. Burkard, M. Gmitra, J. Fabian, V. Zolyomi, N.D. Drummond, V. Fal’ko, 2D Mater. 2, 022001 (2015)

    Google Scholar 

  34. J.O. Island et al., 2D Mater. 4, 022003 (2017)

    Google Scholar 

  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)

    ADS  Google Scholar 

  36. H. Liu, A.T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, P.D. Ye, ACS Nano 8, 4033 (2014)

    Google Scholar 

  37. A.H. Woomer, T.W. Farnsworth, J. Hu, R.A. Wells, C.L. Donley, S.C. Warren, ACS Nano 9, 8869 (2015)

    Google Scholar 

  38. C.R. Dean et al., Nat. Nanotechnol. 5, 722 (2010)

    ADS  Google Scholar 

  39. L. Matthes, P. Gori, O. Pulci, F. Bechstedt, Phys. Rev. B 87, 035438 (2013)

    ADS  Google Scholar 

  40. A. Molle, J. Goldberger, M. Houssa, Y. Xu, S.C. Zhang, D. Akinwande, Nat. Mater. 16, 163 (2017)

    ADS  Google Scholar 

  41. M.N. Brunetti, O.L. Berman, R.Ya. Kezerashvili, Phys. Rev. B 98, 125406 (2018)

    ADS  Google Scholar 

  42. N.D. Drummond, V. Zólyomi, V.I. Falko, Phys. Rev. B 85, 075423 (2012)

    ADS  Google Scholar 

  43. M.E. Dávila, L. Xian, S. Cahangirov, A. Rubio, G. Le Lay, N. J. Phys. 16, 095002 (2014)

    Google Scholar 

  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)

    ADS  Google Scholar 

  45. A.J. Mannix et al., Science 350, 1513 (2015)

    ADS  Google Scholar 

  46. A. Geim, I. Grigorieva, Nature 499, 419 (2014)

    Google Scholar 

  47. N.S. Rytova, Proc. Moscow State University, Phys. Astron. 3, 30 (1967)

  48. L.V. Keldysh, JETP Lett. 29, 658 (1979) ; [Pis’ma. Zh. Eksp. Teor. Fiz. 29, 716 (1979)]

  49. B. Scharf, D. Van Tuan, I. Žutić, H. Dery, J. Phys. Condens. Matter. 31, 203001 (2019)

    ADS  Google Scholar 

  50. Yu.E. Lozovik, V.N. Nishanov, Sov. Phys. Solid State 18, 1905 (1976)

  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)

    Google Scholar 

  52. Yu.E Lozovik, V.I. Yudson, Sov. Phys. JETP 44, 389 (1976)

  53. Yu.E. Lozovik, V.I. Yudson, Zh Eksp, Teor. Fiz. 71, 738 (1976)

  54. D. Snoke, Spontaneous Bose coherence of excitons and polaritons. Science 298, 1368 (2002)

    ADS  Google Scholar 

  55. L.V. Butov, J. Phys. Condens. Matter 16, R1577 (2004)

    ADS  Google Scholar 

  56. M. Combescot, R. Combescot, F. Dubin, Rep. Prog. Phys. 80, 066501 (2017)

    ADS  Google Scholar 

  57. M. Danovich, D.A. Ruiz-Tijerina, R.J. Hunt, M. Szyniszewski, N.D. Drummond, V.I. Fal’ko, Phys. Rev. 97, 195452 (2018)

    ADS  Google Scholar 

  58. O.L. Berman, R.Ya. Kezerashvili, Few-Body Syst. 50, 407 (2011)

    ADS  Google Scholar 

  59. O.L. Berman, R.Ya. Kezerashvili, K. Ziegler, Phys. Rev. B 85, 035418 (2012)

    ADS  Google Scholar 

  60. O.L. Berman, R.Ya. Kezerashvili, Phys. Rev. B 93, 245410 (2016)

    ADS  Google Scholar 

  61. O.L. Berman, R.Ya. Kezerashvili, Phys. Rev. B 96, 245410 (2017)

    Google Scholar 

  62. A.H. Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    ADS  Google Scholar 

  63. M.A.H. Vozmediano, M.I. Katsnelson, F. Guinea, Phys. Rep. 496, 109 (2010)

    ADS  MathSciNet  Google Scholar 

  64. D. Xiao, G.B. Liu, W. Feng, X. Xu, W. Yao, Phys. Rev. Lett. 108, 094502 (2012)

    Google Scholar 

  65. C.J. Tabert, E.J. Nicol, Phys. Rev. B 89, 195410 (2014)

    ADS  Google Scholar 

  66. L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, 3rd edn. (Elsevier, Oxford, 1977)

    MATH  Google Scholar 

  67. R.L. Liboff, Introductory Quantum Mechanics, 2nd edn. (Addison-Wesley, Reading, 1992)

    MATH  Google Scholar 

  68. D.J. Griffiths, Introduction to Quantum Mechanics, 2nd edn. (Prentice-Hall, New York, 2005)

    Google Scholar 

  69. O.L. Berman, R.Ya. Kezerashvili, K. Ziegler, Phys. Rev. A 87, 042513 (2013)

    ADS  Google Scholar 

  70. D. Alba, H.W. Crater, L. Lusanna, J. Phys. A Math. Theor. 40, 9585 (2007)

    ADS  Google Scholar 

  71. J. Sabio, F. Sols, F. Guinea, Phys. Rev. B 81, 045428 (2010)

    ADS  Google Scholar 

  72. A. Ramasubramaniam, Phys. Rev. B 86, 115409 (2012)

    ADS  Google Scholar 

  73. D.Y. Qiu, F.H. da Jornada, S.G. Louie, Phys. Rev. Lett. 111, 216805 (2013)

    ADS  Google Scholar 

  74. M.M. Fogler, L.V. Butov, K.S. Novoselov, Nat. Commun. 5, 4555 (2014)

    ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  76. M. Van der Donck, F.M. Peeters, Phys. Rev. B 98, 115104 (2018)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  80. I. Kylänpää, H.-P. Komsa, Phys. Rev. B 92, 205418 (2015)

    ADS  Google Scholar 

  81. M.N. Brunetti, O.L. Berman, R.Ya. Kezerashvili, J. Phys. Condens. Matter 30, 225001 (2018)

    ADS  Google Scholar 

  82. X. Wang et al., Nat. Nanotechnol. 10, 517 (2015)

    ADS  Google Scholar 

  83. A.S. Rodin, A. Carvalho, A.H. Neto, Phys. Rev. B 90, 075429 (2014)

    ADS  Google Scholar 

  84. E. Prada, J.V. Alvarez, K.L. Narasimha-Acharya, F.J. Bailen, J.J. Palacios, Phys. Rev. B 91, 245421 (2015)

    ADS  Google Scholar 

  85. R.J. Hunt, M. Szyniszewski, G.I. Prayogo, R. Maezono, N.D. Drummond, Phys. Rev. 98, 075122 (2018)

    Google Scholar 

  86. O.L. Berman, G. Gumbs, R.Ya. Kezerashvili, Phys. Rev. B 96, 014505 (2017)

    ADS  Google Scholar 

  87. M.N. Brunetti, O.L. Berman, R.Ya. Kezerashvili, Phys. Lett. A 383, 482 (2019)

    ADS  MathSciNet  Google Scholar 

  88. A.C. Bartnik, Al.L. Efros, W.-K. Koh, C.B. Murray, F.W. Wise, Phys. Rev. B 82, 195313 (2010)

  89. J. Giblin, F. Vietmeyer, M.P. McDonald, M. Kuno, Nano Lett. 11, 3307 (2011)

    ADS  Google Scholar 

  90. T. Ogawa, T. Takagahara, Phys. Rev. B 44, 8138 (1991)

    ADS  Google Scholar 

  91. R.Ya. Kezerashvili, Z. Machavariani, B. Beradze, T. Tchelidze, Physica E 109, 228 (2019)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  93. M.A. Semina, R.A. Sergeev, R.A. Suris, Semiconductors 42, 1427 (2008)

    ADS  Google Scholar 

  94. S. Bednarek, B. Szafran, T. Chwiej, J. Adamowski, Phys. Rev. B 68, 045328 (2003)

    ADS  Google Scholar 

  95. A.F. Slachmuylders, B. Partoens, W. Magnus, F.M. Peeters, J. Phys. Condens. Matter 18, 3951 (2006)

    ADS  Google Scholar 

  96. R. Loudon, Am. J. Phys. 27, 649 (1959)

    ADS  Google Scholar 

  97. R.J. Elliott, R. Loudon, J. Phys. Chem. Solids 8, 382 (1959)

    ADS  Google Scholar 

  98. R.J. Elliott, R. Loudon, J. Phys. Chem. Solids 15, 196 (1960)

    ADS  Google Scholar 

  99. M.A. Lampert, Phys. Rev. Lett. 1, 450 (1958)

    ADS  Google Scholar 

  100. B. Stébé, E. Feddi, G. Munschy, Phys. Rev. B 35, 4331 (1987)

    ADS  Google Scholar 

  101. B. Stébé, A. Ainane, Superlatt. Microstruct. 5, 545 (1989)

    ADS  Google Scholar 

  102. K. Kheng et al., Phys. Rev. Lett. 71, 1752 (1993)

    ADS  Google Scholar 

  103. I.N. Filikhin, A. Gal, V.M. Suslov, Phys. Rev. C 68, 024002 (2003)

    ADS  Google Scholar 

  104. R.Ya. Kezerashvili, S.M. Tsiklauri, I. Filikhin, V.M. Suslov, B. Vlahovic, J. Phys. G Nucl. Part. Phys. 43, 065104 (2016)

    ADS  Google Scholar 

  105. I. Filikhin, R.Ya. Kezerashvili, B. Vlahovic, Phys. Lett. A 382, 787 (2018)

    ADS  Google Scholar 

  106. G. Finkelstein, H. Shtrikman, I. Bar-Joseph, Phys. Rev. Lett. 74, 976 (1995)

    ADS  Google Scholar 

  107. A.J. Shields, M. Pepper, D.A. Ritchie, M.Y. Simmons, G.A.C. Jones, Phys. Rev. B 51, 18049 (1995)

    ADS  Google Scholar 

  108. H. Buhmann, L. Mansouri, J. Wang, P.H. Beton, N. Mori, L. Eaves, M. Henini, M. Potemski, Phys. Rev. B 51, 7969 (1995)

    ADS  Google Scholar 

  109. S.A. Brown, J.F. Young, J.A. Brum, P. Hawrylak, Z. Wasilewski, Phys. Rev. B 54, 11082 (1996)

    ADS  Google Scholar 

  110. R. Kaur, A.J. Shields, J.L. Osborne, M.Y. Simmons, D.A. Ritchie, M. Pepper, Phys. Stat. Sol. 178, 465 (2000)

    ADS  Google Scholar 

  111. V. Huard, R.T. Cox, K. Saminadayar, A. Arnoult, S. Tataremko, Phys. Rev. Lett. 84, 187 (2000)

    ADS  Google Scholar 

  112. A. Esser et al., Phys. Status Solidi (a) 178, 489 (2000)

    ADS  Google Scholar 

  113. A. Esser et al., Phys. Rev. B 62, 8232 (2000)

    ADS  Google Scholar 

  114. A.S. Bracker et al., Phys. Rev. B 72, 035332 (2005)

    ADS  Google Scholar 

  115. J. Usukura, Y. Suzuki, K. Varga, Phys. Rev. B 59, 5652 (1999)

    ADS  Google Scholar 

  116. C. Riva, F.M. Peeters, K. Varga, Phys. Rev. 61, 873 (2000)

    Google Scholar 

  117. T.F. RØnnow, T.G. Pedersen, B. Partoens, K.K. Berthelsen, Phys. Rev. B 184, 035316 (2011)

    ADS  Google Scholar 

  118. W.Y. Ruan, K.S. Chan, H.P. Ho, R.Q. Zhang, E.Y.B. Pun, Phys. Rev. B 60, 5714 (1999)

    ADS  Google Scholar 

  119. M. Braun, O.I. Kartavtsev, Nucl. Phys. A 698, 519c (2001)

    ADS  Google Scholar 

  120. M. Braun, O.I. Kartavtsev, Phys. Lett. A 331, 437 (2004)

    ADS  Google Scholar 

  121. K.F. Mak et al., Nat. Mater. 12, 207 (2013)

    ADS  Google Scholar 

  122. J.S. Ross et al., Nat. Commun. 4, 1474 (2013)

    ADS  Google Scholar 

  123. A.M. Jones et al., Nat. Nanotechnol. 8, 634 (2013)

    ADS  Google Scholar 

  124. G. Wang et al., Phys. Rev. B 90, 075413 (2014)

    ADS  Google Scholar 

  125. A. Singh et al., Phys. Rev. Lett. 112, 21680 (2014)

    Google Scholar 

  126. C.H. Liu et al., Phys. Rev. Lett. 113, 166801 (2014)

    ADS  Google Scholar 

  127. J. Shang et al., ACS Nano 9, 647 (2015)

    Google Scholar 

  128. G. Plechinger et al., Phys. Status Solidi RRL 9, 457 (2015)

    Google Scholar 

  129. Y. Zhang, H. Li, H. Wang, R. Liu, S. Zhang, Z. Qiu, ACS Nano 9, 8514 (2015)

    Google Scholar 

  130. J.W. Christopher, B.B. Goldberg, A.K. Swan, Sci. Rep. 7, 14062 (2017)

    ADS  Google Scholar 

  131. E. Courtade et al., Phys. Rev. B 96, 085302 (2017)

    ADS  Google Scholar 

  132. M.Z. Bellus, F. Ceballos, H.-Y. Chiu, H. Zhao, ACS Nano 9, 6459 (2015)

    Google Scholar 

  133. J. Shang, X. Shen, C. Cong, N. Peimyoo, B. Cao, M. Eginligil, T. Yu, ACS Nano 9, 647 (2015)

    Google Scholar 

  134. B. Zhu, H. Zeng, J. Dai, Z. Gong, X. Cui, Proc. Natl. Acad. Sci. USA 111, 11606 (2014)

    ADS  Google Scholar 

  135. J. Yang et al., ACS Nano 9, 6603 (2015)

    Google Scholar 

  136. T. Godde et al., Phys. Rev. B 94, 165301 (2016)

    ADS  Google Scholar 

  137. G. Plechinger et al., Nat. Commun. 7, 12715 (2016)

    ADS  Google Scholar 

  138. J. Yang, Y. Lu, Chin. Phys. B 26, 034201 (2017)

    ADS  Google Scholar 

  139. R. Xu et al., ACS Nano 10, 2046 (2016)

    Google Scholar 

  140. C. Zhang, H. Wang, W. Chan, C. Manolatou, F. Rana, Phys. Rev. B 89, 205436 (2014)

    ADS  Google Scholar 

  141. M. Szyniszewski, E. Mostaani, N.D. Drummond, V.I. Falko, Phys. Rev. B 95, 081301(R) (2017)

    ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  143. B. Ganchev, N. Drummond, I. Aleiner, V. Falko, Phys. Rev. Lett. 114, 107401 (2015)

    ADS  Google Scholar 

  144. K.A. Velizhanin, A. Saxena, Phys. Rev. B 92, 195305 (2015)

    ADS  Google Scholar 

  145. D.W. Kidd, D.K. Zhang, K. Varga, Phys. Rev. B 93, 125423 (2016)

    ADS  Google Scholar 

  146. M.Z. Mayers, T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, Phys. Rev. B 92, 161404 (2015)

    ADS  Google Scholar 

  147. A. Thilagam, Phys. Rev. B 55, 7804 (1997)

    ADS  Google Scholar 

  148. M. Van der Donck, M. Zarenia, F.M. Peeters, Phys. Rev. B 96, 035131 (2017)

    ADS  Google Scholar 

  149. R.Ya. Kezerashvili, S.M. Tsiklauri, Few-Body Syst. 58, 18 (2017)

  150. I. Filikhin, R.Ya. Kezerashvili, S.M. Tsiklauri, B. Vlahovic, Nanotechnology 29, 124002 (2018)

    ADS  Google Scholar 

  151. A. Ramirez-Torres, V. Turkowski, T.S. Rahman, Phys. Rev. B 90, 085419 (2014)

    ADS  Google Scholar 

  152. O.L. Berman, R.Ya. Kezerashvili, S.M. Tsiklauri, Int. J. Mod. Phys. B 28, 1450064 (2014)

    ADS  Google Scholar 

  153. I.V. Bondarev, M.R. Vladimirova, Phys. Rev. B 97, 165419 (2018)

    ADS  Google Scholar 

  154. L.A. Jauregui et al., arXiv:1812.08691 [cond-mat.mes-hall] (2018)

  155. O. Witham, R.J. Hunt, N.D. Drummond, Phys. Rev. B 97, 075424 (2018)

    ADS  Google Scholar 

  156. T. Baars, W. Braun, M. Bayer, A. Forchel, Phys. Rev. B 58, R1750 (1998)

    ADS  Google Scholar 

  157. A. Esser, R. Zimmermann, E. Runge, Phys. Stat. Sol. B 227, 317 (2001)

    ADS  Google Scholar 

  158. T. Tsuchiya, Int. J. Mod. Phys. B 15, 3985 (2001)

    ADS  Google Scholar 

  159. A. Crottini, J.L. Staehli, B. Deveaud, X.L. Wang, M. Ogura, Solid State Commun. 121, 401 (2002)

    ADS  Google Scholar 

  160. T. Otterburg et al., Phys. Rev. B 71, 033301 (2005)

    ADS  Google Scholar 

  161. B. Szafran, T. Chwiej, F.M. Peeters, S. Bednarek, J. Adamowski, Phys. Rev. B 71, 235305 (2005)

    ADS  Google Scholar 

  162. F.M. Peeters, B. Szafran, T. Chwiej, S. Bednarek, J. Adamowski, Few-Body Syst. 38, 121 (2006)

    ADS  Google Scholar 

  163. Y. Sidor, B. Partoens, F.M. Peeters, Phys. Rev. B 77, 205413 (2008)

    ADS  Google Scholar 

  164. M.J.A. Schuetz, M.G. Moore, C. Piermarocchi, Nat. Phys. 6, 919 (2010)

    Google Scholar 

  165. L.X. Zhai, Y. Wang, J.J. Liu, Phys. Lett. A 376, 1866 (2012)

    ADS  Google Scholar 

  166. T.G. Pedersen, Phys. Rev. B 67, 073401 (2003)

    ADS  Google Scholar 

  167. T.G. Pedersen, K. Pedersen, H.D. Cornean, P. Duclos, Nano Lett. 5, 291 (2005)

    ADS  Google Scholar 

  168. D. Kammerlander, D. Prezzi, G. Goldoni, E. Molinari, U. Hohenester, Phys. Rev. Lett. 99, 126806 (2007)

    ADS  Google Scholar 

  169. D. Kammerlander, D. Prezzi, G. Goldoni, E. Molinari, U. Hohenester, Physica E 40, 1997 (2008)

    ADS  Google Scholar 

  170. T.F. Rønnow, T.G. Pedersen, H.D. Cornean, Phys. Rev. B 81, 205446 (2010)

    ADS  Google Scholar 

  171. T.F. Rønnow, T.G. Pedersen, B. Partoens, K.K. Berthelsen, Phys. Rev. B 84, 035316 (2011)

    ADS  Google Scholar 

  172. R. Matsunaga, K. Matsuda, Y. Kanemitsu, Phys. Rev. Lett. 106, 037404 (2011)

    ADS  Google Scholar 

  173. S.M. Santos, B. Yuma, S. Berciaud, J. Shaver, M. Gallart, P. Gilliot et al., Phys. Rev. Lett. 107, 187401 (2011)

    ADS  Google Scholar 

  174. I.V. Bondarev, Phys. Rev. B 83, 153409 (2011)

    ADS  Google Scholar 

  175. K. Watanabe, K. Asano, Phys. Rev. B 83, 115406 (2011)

    ADS  Google Scholar 

  176. K. Watanabe, K. Asano, Phys. Rev. B 85, 035416 (2012)

    ADS  Google Scholar 

  177. T.F. Rønnow, T.G. Pedersen, B. Partoens, Phys. Rev. B 85, 045412 (2012)

    ADS  Google Scholar 

  178. L. Colombier, J. Selles, E. Rousseau, J.S. Lauret, F. Vialla, C. Voisin, G. Cassabois, Phys. Rev. Lett. 109, 197402 (2012)

    ADS  Google Scholar 

  179. B. Yuma, S. Berciaud, J. Besbas, J. Shaver, S. Santos, S. Ghosh et al., Phys. Rev. B 87, 205412 (2013)

    ADS  Google Scholar 

  180. I.V. Bondarev, Phys. Rev. B 90, 245430 (2014)

    ADS  Google Scholar 

  181. I.V. Bondarev, Mod. Phys. Lett. B 30, 1630006 (2016)

    ADS  Google Scholar 

  182. A.F. Slachmuylders, B. Partoens, W. Magnus, F.M. Peeters, Phys. Rev. B 76, 075405 (2007)

    ADS  Google Scholar 

  183. A.F. Slachmuylders, B. Partoens, W. Magnus, F.M. Peeters, Physica E 40, 2166 (2008)

    ADS  Google Scholar 

  184. T. Deilmann, M. Drüppel, M. Rohlfing, Phys. Rev. Lett. 116, 196804 (2016)

    ADS  Google Scholar 

  185. L.N. Ivanov, YuE Lozovik, D.R. Musin, J. Phys. C Solid State Phys. 11, 2527 (1978)

    ADS  Google Scholar 

  186. R.C. Miller et al., Phys. Rev. B 25, 6545 (1982)

    ADS  Google Scholar 

  187. D. Bressanini, M. Mella, G. Morosi, Phys. Rev. A 55, 200 (1997)

    ADS  Google Scholar 

  188. D. Bressanini, M. Mella, G. Morosi, Phys. Rev. A 57, 4956 (1998)

    ADS  Google Scholar 

  189. C. Mai et al., Nano Lett. 14, 202 (2014)

    ADS  Google Scholar 

  190. Y. You, X.-X. Zhang, T.C. Berkelbach, M.S. Hybertsen, D.R. Reichman, T.F. Heinz, Nat. Phys. 11, 477 (2015)

    Google Scholar 

  191. E.J. Sie, A.J. Frenzel, Y.-H. Lee, J. Kong, N. Gedik, Phys. Rev. B 92, 125417 (2015)

    ADS  Google Scholar 

  192. K. Hao et al., Nat. Commun. 8, 15552 (2017)

    ADS  Google Scholar 

  193. D.K. Zhang, D.W. Kidd, K. Varga, Nano Lett. 15, 7002 (2015)

    ADS  Google Scholar 

  194. A. Thilagam, J. Appl. Phys 116, 053523 (2014)

    ADS  Google Scholar 

  195. D.V. Tuan, M. Yang, H. Dery, Phys. Rev. B 98, 125308 (2018)

    ADS  Google Scholar 

  196. S.-Y. Chen, T. Goldstein, T. Taniguchi, K. Watanabe, J. Yan, Nat. Commun. 9, 3717 (2018)

    ADS  Google Scholar 

  197. Z. Ye, L. Waldecker, E.Y. Ma, D. Rhodes, A. Antony, B. Kim et al., Nat. Commun. 9, 3718 (2018)

    ADS  Google Scholar 

  198. Z. Li, T. Wang, Z. Lu, C. Jin, Y. Chen, Y. Meng et al., Nat. Commun. 9, 3719 (2018)

    ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  200. A. Steinhoff et al., Nat. Phys. 14, 1199 (2018)

    Google Scholar 

  201. A.D. Meyertholen, M.M. Fogler, Phys. Rev. B 78, 235307 (2008)

    ADS  Google Scholar 

  202. R.T. Pack, J.O. Hirschfelder, J. Chem. Phys. 52, 521 (1970)

    ADS  Google Scholar 

  203. M.Y.J. Tan, N.D. Drummond, R.J. Needs, Phys. Rev. B 71, 033303 (2005)

    ADS  Google Scholar 

  204. A. Chaves, M.Z. Mayers, F.M. Peeters, D.R. Reichman, Phys. Rev. B 93, 115314 (2016)

    ADS  Google Scholar 

  205. A. Crottinia, J.L. Staehlia, B. Deveauda, X.L. Wang, M. Ogura, Solid State Commun. 121, 401 (2002)

    ADS  Google Scholar 

  206. R. Baer, E. Rabani, J. Chem. Phys. 138, 051102 (2013)

    ADS  Google Scholar 

  207. C. Herring, M. Flicker, Phys. Rev. 134, A362 (1964)

    ADS  Google Scholar 

  208. N.K. Timofeyuk, D. Baye, Few-Body Syst. 58, 157 (2017)

    ADS  Google Scholar 

  209. P. Ajayan, P. Kim, K. Banerjee, Phys. Today 69(9), 38 (2016)

    Google Scholar 

  210. A. Kogar et al., Science 358, 1314 (2017)

    ADS  Google Scholar 

  211. O. Cotleţ, S. Zeytinoglu, M. Sigrist, E. Demler, A. Imamoglu, Phys. Rev. B 93, 054510 (2016)

    ADS  Google Scholar 

  212. K.S. Thygesen, 2D Mater. 4, 022004 (2017)

    Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Physics Department, New York City College of Technology, The City University of New York, Brooklyn, NY, 11201, USA

    Roman Ya. Kezerashvili

  2. The Graduate School and University Center, The City University of New York, New York, NY, 10016, USA

    Roman Ya. Kezerashvili

Authors
  1. Roman Ya. Kezerashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roman Ya. Kezerashvili.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article belongs to the Topical Collection “Ludwig Faddeev Memorial Issue”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kezerashvili, R.Y. Few-Body Systems in Condensed Matter Physics. Few-Body Syst 60, 52 (2019). https://doi.org/10.1007/s00601-019-1520-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-019-1520-1

Search

Navigation