Advertisement

International Journal of Dynamics and Control

, Volume 6, Issue 3, pp 1376–1383 | Cite as

Excitation of solitons in hexagonal lattices and ways of controlling electron transport

  • A. P. Chetverikov
  • W. Ebeling
  • E. SchöllEmail author
  • M. G. Velarde
Article

Abstract

We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions. Based on the tight-binding model we investigate the possibility that electrons are trapped and guided by the electric polarization field of the compression field of one soliton or two solitons with crossing pathways. We show that electrons may jump from a bound state with the first soliton to a bound state with a second soliton and changing accordingly the direction of their path. We discuss the possibility to control by this method the path of an excess electron from a source at a boundary to a selected drain at another chosen boundary by following straight pathways on crystallographic axes.

Keywords

Hexagonal lattice Morse interactions Electron transport Solitonic excitations Controlling path of electrons 

Notes

Acknowledgements

The authors acknowledge fruitful discussions and correspondence with A. Knorr, R.P.G. McNeil, C. Ford, T. Meunier, and A. Wixforth. They also wish to thank V. I. Nayanov for his enlightening description of soliton SAW in nonlinearly elastic, piezoelectric LiNbO\(_3\) layers where wave dispersion able to balance nonlinearity of the substrate is monitored by depositing, via evaporation, SiO films of suitable thickness. This work was partially supported by the Collaborative Research Center 910: Control of self-organizing nonlinear systems: Theoretical methods and concepts of application (SFB 910) funded by Deutsche Forschungsgemeinschaft. A.P.C. acknowledges also support under project 16-12-10175 from the Russian Science Foundation.

References

  1. 1.
    Radisavljevic B, Radenovic A, Brivio J, Giacometti V, Kis A (2011) Single-layer \(MoS_2\) transistors. Nat Nanotechnol 6:147CrossRefGoogle Scholar
  2. 2.
    Ferrari AC et al (2015) Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale. 7:4598CrossRefGoogle Scholar
  3. 3.
    Hoffmann R (2013) Small but strong lessons from chemistry for nanoscience. Angew Chem Int Ed 52:93CrossRefGoogle Scholar
  4. 4.
    Tao L, Cinquanta E, Chiappe D, Grazianetti C, Fanciulli M, Dubey M, Molle A, Akinwande D (2015) Silicene field-effect transistors operating at room temperature. Nat Nanotechnol 10:227CrossRefGoogle Scholar
  5. 5.
    Zhu F-F, Chen W-J, Xu Y, Gao C-I, Guan D-D, Liu C-H, Qian D, Zhang S-C, Jia J-F (2015) Epitaxial growth of two-dimensional stanene. Nat Mater 14:1020CrossRefGoogle Scholar
  6. 6.
    Insepov Z, Emelin E, Kononenko O, Roshchupkin DV, Tryshtykbayev KB, Baigarin KA (2015) Surface acoustic wave amplification by direct current-voltage supplied to graphene film. Appl Phys Lett 106:023505CrossRefGoogle Scholar
  7. 7.
    Geim AK (2011) Random walk to graphene. Phys Usp 54:12Google Scholar
  8. 8.
    Du X, Skachko I, Barker A, Andrei EY (2008) Approaching ballistic transport in suspended graphene. Nat Nanotechnol 3:491CrossRefGoogle Scholar
  9. 9.
    Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, Geim AK (2005) Two-dimensional atomic crystals. PNAS 102:10451CrossRefGoogle Scholar
  10. 10.
    Engheta N, Ziolkowski RW (2006) Metamaterials: physics and engineering explorations. Wiley, New YorkCrossRefGoogle Scholar
  11. 11.
    Rudykh S, Boyce MC (2014) Transforming wave propagation in layered media via instability-induced interfacial wrinkling. Phys Rev Lett 112:034301CrossRefGoogle Scholar
  12. 12.
    Hoskins MJ, Morko H, Hunsinger BJ (1982) Charge transport by surface acoustic waves in GaAs. Appl Phys Lett 41:332CrossRefGoogle Scholar
  13. 13.
    Nayanov VI (1986) Surface acoustic cnoidal waves and solitons in a LiNbO\(_3\)-(SiO film) structure. JETP Phys Lett 44:314Google Scholar
  14. 14.
    Wixforth A, Kotthaus JP, Weimann G (1986) Quantum oscillations in the surface-acoustic-wave attenuation caused by a two-dimensional electron system. Phys Rev Lett 56:2104CrossRefGoogle Scholar
  15. 15.
    Tanski WJ, Merritt SW, Sacks RN, Cullen DE, Branciforte EJ, Caroll RD, Eschrich TC (1988) Heterojunction acoustic charge transport devices on GaAs. Appl Phys Lett 52:18CrossRefGoogle Scholar
  16. 16.
    Mayer AP (1995) Surface acoustic waves in nonlinear elastic media. Phys Rep 256:237CrossRefGoogle Scholar
  17. 17.
    Streibl M, Wixforth A, Kotthaus JP, Govorov AO, Kadow C, Gossard AC (1999) Imaging of acoustic charge transport in semiconductor heterostructures by surface acoustic waves. Appl Phys Lett 75:4139CrossRefGoogle Scholar
  18. 18.
    Rotter M, Kalameitsev AV, Govorov AO, Ruile W, Wixforth A (1999) Charge conveyance and nonlinear acoustoelectric phenomena for intense surface acoustic waves on a semiconductor quantum well. Phys Rev Lett 82:2171CrossRefGoogle Scholar
  19. 19.
    Hess P (2002) Surface acoustic waves in materials science. Phys Today 55:42CrossRefGoogle Scholar
  20. 20.
    Lomonosov AM, Hess P, Mayer AP (2002) Observation of solitary elastic surface pulses. Phys Rev Lett 88:076104CrossRefGoogle Scholar
  21. 21.
    Mayer AP (2008) Nonlinear surface acoustic waves: theory. Ultrasonics 48:478CrossRefGoogle Scholar
  22. 22.
    Hermelin S, Takada S, Yamamoto M, Tarucha S, Wieck AD, Saminadayar L, Bäuerle C, Meunier T (2011) Electrons surfing on a sound wave as a platform for quantum optics with flying electrons. Nature 477:435CrossRefGoogle Scholar
  23. 23.
    McNeil RPG, Kataoka M, Ford CJB, Barnes CHW, Anderson D, Jones GAC, Farrer I, Ritchie DA (2011) On-demand single-electron transfer between distant quantum dots. Nature 477:439CrossRefGoogle Scholar
  24. 24.
    Velarde MG (2010) From polaron to solectron: the addition of nonlinear elasticity to quantum mechanics and its possible effect upon electric transport. J Comput Appl Math 233:1432MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Velarde MG, Chetverikov AP, Ebeling W, Wilson EG, Donovan KJ (2014) On the electron transport in polydiacetylene crystals and derivatives. Eur Phys Lett EPL 106:27004CrossRefGoogle Scholar
  26. 26.
    Velarde MG (2016) Nonlinear dynamics and the nano-mechanical control of electrons in crystalline solids. Eur Phys J ST 225:921CrossRefGoogle Scholar
  27. 27.
    Launay J-P, Verdaguer M (2013) Electrons in molecules from basic principles to molecular electronics. Oxford University Press, OxfordCrossRefGoogle Scholar
  28. 28.
    Chetverikov AP, Ebeling W, Velarde MG (2011) Soliton-like excitations and solectrons in two-dimensional nonlinear lattices. Eur Phys J B 80:137CrossRefGoogle Scholar
  29. 29.
    Chetverikov AP, Ebeling W, Velarde MG (2016) Soliton assisted control of source to drain electron transport along natural channels–crystallographic axes—in two-dimensional triangular crystal lattices. Eur Phys J B 89:196CrossRefGoogle Scholar
  30. 30.
    Savin AV, Kivshar YS, Hu B (2010) Suppression of thermal conductivity in graphene nanoribbons with rough edges. Phys Rev B 82:195422CrossRefGoogle Scholar
  31. 31.
    Toda M (1989) Theory of nonlinear lattices, 2nd edn. Springer, New YorkCrossRefzbMATHGoogle Scholar
  32. 32.
    Iskandarov AM, Medvedev NN, Zakharov PV, Dmitriev SV (2009) Crowdion mobility and self-focusing in 3D and 2D nickel. Comput Mater Sci 47:429CrossRefGoogle Scholar
  33. 33.
    Dmitriev SV, Korznikova EA, Baimova YA, Velarde MG (2016) Discrete breathers in crystals. Phys Usp 59:446CrossRefGoogle Scholar
  34. 34.
    Velarde MG, Chetverikov AP, Ebeling W, Dmitriev SV, Lakhno VD (2016) From solitons to discrete breathers. Eur Phys J B 89:233MathSciNetCrossRefGoogle Scholar
  35. 35.
    Minzoni AA, Smyth NF (1996) Evolution of lump solutions for the KP equation. Wave Motion 24:291MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Chetverikov AP, Ebeling W, Velarde MG (2011) Localized nonlinear, soliton-like waves in two-dimensional anharmonic lattices. Wave Motion 48:753MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Davydov AS (1991) Solitons in molecular systems, 2nd edn. Reidel, DordrechtCrossRefzbMATHGoogle Scholar
  38. 38.
    Chetverikov AP, Ebeling W, Velarde MG (2012) Controlling fast electron transfer at the nano-scale by solitonic excitations along crystallographic axes. Eur Phys J B 85:1–8CrossRefGoogle Scholar
  39. 39.
    Hennig D, Neissner A, Velarde MG, Ebeling W (2006) Effect of anharmonicity on charge transport in hydrogen-bonded systems. Phys Rev E 73:024306CrossRefGoogle Scholar
  40. 40.
    Hennig D, Chetverikov AP, Velarde MG, Ebeling W (2007) Electron capture and transport mediated by lattice solitons. Phys Rev E 76:046602CrossRefGoogle Scholar
  41. 41.
    Brizhik L, Chetverikov AP, Ebeling W, Röpke G, Velarde MG (2012) Electron pairing and Coulomb repulsion in one-dimensional anharmonic lattices. Phys Rev B 85:245105CrossRefGoogle Scholar
  42. 42.
    Cantu Ros OG, Cruzeiro L, Velarde MG, Ebeling W (2011) On the possibility of electric transport mediated by long living intrinsic localized solectron modes. Eur Phys J B 80:545CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Faculty of PhysicsSaratov National Research State UniversitySaratovRussia
  2. 2.Institute of PhysicsHumboldt-University BerlinBerlinGermany
  3. 3.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany
  4. 4.Instituto PluridisciplinarUniversidad ComplutenseMadridSpain

Personalised recommendations