Nonlinear excitations and bound states of electrons, holes and solitons in bilayers of triangular lattices

Abstract

We study the temporal and spatial nonlinear dynamical evolution of a coupled triangular lattice crystal bilayer system where in one layer one excess free electron is injected while an excess positive charge, a hole, is created in the other. The atoms of each of the backbone lattices interact with anharmonic (short range) Morse potentials whereas the charges interact via (long range) Coulomb potentials. Computer simulations are provided of the possibilities offered by varying interlayer separation, strength of the Coulomb force between the charges and the diverse dynamical role played by excited solitons supersonically moving along crystallographic axes in one of the layers. Optimal conditions are identified for the occurrence of electron–hole pairs and for the more significant case of a boson-like electron–hole–soliton coupled compound, a new form of quasiparticle moving along the coupled bilayer system with no need of applying an external electric field.

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References

  1. 1.

    S.H. Strogatz, Nature 410, 268 (2001)

    ADS  Article  Google Scholar 

  2. 2.

    R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    ADS  MathSciNet  Article  Google Scholar 

  3. 3.

    M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    ADS  MathSciNet  Article  Google Scholar 

  4. 4.

    S. Boccaletti, G. Bianconi, R. Criado, C.I. del Genio, J. Gómez-Gardeñes, M. Romance, I.S. Nadal, Z. Wang, M. Zanin, Phys. Rep. 544, 1 (2014)

    ADS  MathSciNet  Article  Google Scholar 

  5. 5.

    M. Kivelä, A. Arenas, M. Barthélemy, J.P. Gleeson, Y. Moreno, M.A. Porter, J. Complex Netw. 2, 203 (2014)

    Article  Google Scholar 

  6. 6.

    M. De Domenico, V. Nicosia, A. Arenas, V. Latora, Nat. Commun. 6, 6864 (2015)

    ADS  Article  Google Scholar 

  7. 7.

    S. Boccaletti, A.N. Pisarchik, C.I. del Genio, A. Amann, Synchronization: From Coupled Systems to Complex Networks (Cambridge University Press, Cambridge, 2018)

  8. 8.

    M. Toda, Theory of Nonlinear Lattices, 2nd edn. (Springer-Verlag, New York, 1989)

  9. 9.

    A.J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988)

    ADS  Article  Google Scholar 

  10. 10.

    R.S. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994)

    ADS  MathSciNet  Article  Google Scholar 

  11. 11.

    H.R. Paneth, Phys. Rev. 80, 708 (1950)

    ADS  Article  Google Scholar 

  12. 12.

    M.G. Velarde, W. Ebeling, A.P. Chetverikov, Int. J. Bifurc. Chaos 15, 245 (2005)

    Article  Google Scholar 

  13. 13.

    L.D. Landau, Phys. Z. Sowjetunion 3, 644 (1933)

    Google Scholar 

  14. 14.

    A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 70, 217 (2009)

    ADS  Article  Google Scholar 

  15. 15.

    A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 80, 137 (2011)

    ADS  Article  Google Scholar 

  16. 16.

    A.P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Contrib. Plasma Phys. 51, 814 (2011)

    ADS  Article  Google Scholar 

  17. 17.

    A.P. Chetverikov, W. Ebeling, M.G. Velarde, Toward a theory of degenerated solectrons in doped lattices, in Without bounds a scientific canvas of nonlinearity and complex dynamics, edited by R.G. Rubio et al. (Springer, Berlin 2013)

  18. 18.

    A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 85, 291 (2012)

    ADS  Article  Google Scholar 

  19. 19.

    A.P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Eur. Phys. J. B 87, 153 (2014)

    ADS  Article  Google Scholar 

  20. 20.

    A.P. Chetverikov, W. Ebeling, M.G. Velarde, Eur. Phys. J. B 89, 196 (2016)

    ADS  Article  Google Scholar 

  21. 21.

    A.P. Chetverikov, W. Ebeling, E. Schöll, M.G. Velarde, Int. J. Dyn. Control 6, 1376 (2018)

    MathSciNet  Article  Google Scholar 

  22. 22.

    R.V. Gorbachev, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, T. Tudorovskiy, Nat. Phys. 8, 896 (2012)

    Article  Google Scholar 

  23. 23.

    Y.E. Lozovik, V.I. Yudson, JETP Lett. 22, 274 (1975)

    ADS  Google Scholar 

  24. 24.

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

    ADS  Google Scholar 

  25. 25.

    S. Shevchenko, Sov. J. Low Temp. Phys. 2, 251 (1976)

    Google Scholar 

  26. 26.

    Y.E. Lozovik, O.L. Berman, Pis’ma Zh. Eksp. Teor. Fiz. 64, 526 (1996)

    Google Scholar 

  27. 27.

    Y.E. Lozovik, O.L. Berman, JETP Lett. 64, 573 (1996)

    ADS  Article  Google Scholar 

  28. 28.

    Y.E. Lozovik, O.L. Berman, Zh. Eksp. Teor. Fiz. 111, 1879 (1997)

    Google Scholar 

  29. 29.

    Y.E. Lozovik, O.L. Berman, JETP 84, 1027 (1997)

    ADS  Article  Google Scholar 

  30. 30.

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

    ADS  Article  Google Scholar 

  31. 31.

    D.K. Efimkin, V.A. Kulbachinskii, Y.E. Lozovik, JETP Lett. 93, 219 (2011)

    ADS  Article  Google Scholar 

  32. 32.

    A. Perali, D. Neilson, A.R. Hamilton, Phys. Rev. Lett. 110, 146803 (2013)

    ADS  Article  Google Scholar 

  33. 33.

    S. Conti, A. Perali, F.M. Peeters, D. Neilson, arXiv.1706.07672 (2017)

  34. 34.

    A. Perali, S. Conti, F.M. Peeters, N. Neilson, in International Conference Strongly Coupled Coulomb Systems, Kiel, 30 July–4 August 2017

  35. 35.

    A. Filinov, M. Bonitz, Y.E. Lozovik, Phys. Rev. Lett. 86, 3851 (2001)

    ADS  Article  Google Scholar 

  36. 36.

    A. Filinov, M. Bonitz, Y.E. Lozovik, Phys. Stat. Sol. (b) 221, 231 (2000)

    ADS  Article  Google Scholar 

  37. 37.

    M. Bonitz, V. Golubnychij, A.V. Filinov, Y.E. Lozovik, Microelectron. Eng. 63, 141 (2002)

    Article  Google Scholar 

  38. 38.

    P. Ludwig, A.V. Filinov, M. Bonitz, Y.E. Lozovik, Contrib. Plasma Phys. 43, 285 (2003)

    ADS  Article  Google Scholar 

  39. 39.

    J. Schleede, A. Filinov, M. Bonitz, H. Fehske, Contr. Plasma Phys. 52, 10 (2012)

    Article  Google Scholar 

  40. 40.

    A.K. Geim, I.V. Grigorieva, Nature 499, 419 (2013)

    Article  Google Scholar 

  41. 41.

    K. Lee, J. Xue, D.C. Dillen, K. Watanabe, T. Taniguchi, E. Tutuc, Phys. Rev. Lett. 117, 046803 (2016)

    ADS  Article  Google Scholar 

  42. 42.

    J. Li, T. Taguchi, K. Watanabe, J. Hone, A. Levchenko, C. Dean, Phys. Rev. Lett. 117, 046802 (2016)

    ADS  Article  Google Scholar 

  43. 43.

    M.G. Velarde, A.P. Chetverikov, W. Ebeling, S.V. Dmitriev, V.D. Lakhno, Eur. Phys. J. B 89, 233 (2016)

    ADS  Article  Google Scholar 

  44. 44.

    S.V. Dmitriev, E.A. Korznikova, Y.A. Baimova, M.G. Velarde, Phys. Uspekhi 59, 446 (2016)

    ADS  Article  Google Scholar 

  45. 45.

    A. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Contrib. Plasma Phys. 47, 465 (2007)

    ADS  Article  Google Scholar 

  46. 46.

    W. Ebeling, V.E. Fortov, V. Filinov, Quantum Statistics of Dense Gases and Nonideal Plasmas (Springer, Berlin, Heidelberg, 2017)

  47. 47.

    A.V. Savin, Z.S. Kivshar, R. Hu, Phys. Rev. B 82, 195422 (2010)

    ADS  Article  Google Scholar 

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Correspondence to Eckehard Schöll.

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Contribution to the Topical Issue “Non-Linear and Complex Dynamics in Semiconductors and Related Materials”, edited by Kathy Lüdge.

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Chetverikov, A.P., Ebeling, W., Schöll, E. et al. Nonlinear excitations and bound states of electrons, holes and solitons in bilayers of triangular lattices. Eur. Phys. J. B 92, 122 (2019). https://doi.org/10.1140/epjb/e2019-90715-8

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