Skip to main content
SpringerLink
Log in

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

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

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.

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
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Radisavljevic B, Radenovic A, Brivio J, Giacometti V, Kis A (2011) Single-layer \(MoS_2\) transistors. Nat Nanotechnol 6:147

    Article  Google Scholar 

  2. Ferrari AC et al (2015) Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale. 7:4598

    Article  Google Scholar 

  3. Hoffmann R (2013) Small but strong lessons from chemistry for nanoscience. Angew Chem Int Ed 52:93

    Article  Google Scholar 

  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 10:227

    Article  Google Scholar 

  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 14:1020

    Article  Google Scholar 

  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 106:023505

    Article  Google Scholar 

  7. Geim AK (2011) Random walk to graphene. Phys Usp 54:12

    Google Scholar 

  8. Du X, Skachko I, Barker A, Andrei EY (2008) Approaching ballistic transport in suspended graphene. Nat Nanotechnol 3:491

    Article  Google Scholar 

  9. Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, Geim AK (2005) Two-dimensional atomic crystals. PNAS 102:10451

    Article  Google Scholar 

  10. Engheta N, Ziolkowski RW (2006) Metamaterials: physics and engineering explorations. Wiley, New York

    Book  Google Scholar 

  11. Rudykh S, Boyce MC (2014) Transforming wave propagation in layered media via instability-induced interfacial wrinkling. Phys Rev Lett 112:034301

    Article  Google Scholar 

  12. Hoskins MJ, Morko H, Hunsinger BJ (1982) Charge transport by surface acoustic waves in GaAs. Appl Phys Lett 41:332

    Article  Google Scholar 

  13. Nayanov VI (1986) Surface acoustic cnoidal waves and solitons in a LiNbO\(_3\)-(SiO film) structure. JETP Phys Lett 44:314

    Google Scholar 

  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 56:2104

    Article  Google Scholar 

  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 52:18

    Article  Google Scholar 

  16. Mayer AP (1995) Surface acoustic waves in nonlinear elastic media. Phys Rep 256:237

    Article  Google Scholar 

  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 75:4139

    Article  Google Scholar 

  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 82:2171

    Article  Google Scholar 

  19. Hess P (2002) Surface acoustic waves in materials science. Phys Today 55:42

    Article  Google Scholar 

  20. Lomonosov AM, Hess P, Mayer AP (2002) Observation of solitary elastic surface pulses. Phys Rev Lett 88:076104

    Article  Google Scholar 

  21. Mayer AP (2008) Nonlinear surface acoustic waves: theory. Ultrasonics 48:478

    Article  Google Scholar 

  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 477:435

    Article  Google Scholar 

  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 477:439

    Article  Google Scholar 

  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 233:1432

    Article  MathSciNet  MATH  Google Scholar 

  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 106:27004

    Article  Google Scholar 

  26. Velarde MG (2016) Nonlinear dynamics and the nano-mechanical control of electrons in crystalline solids. Eur Phys J ST 225:921

    Article  Google Scholar 

  27. Launay J-P, Verdaguer M (2013) Electrons in molecules from basic principles to molecular electronics. Oxford University Press, Oxford

    Book  Google Scholar 

  28. Chetverikov AP, Ebeling W, Velarde MG (2011) Soliton-like excitations and solectrons in two-dimensional nonlinear lattices. Eur Phys J B 80:137

    Article  Google Scholar 

  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 89:196

    Article  Google Scholar 

  30. Savin AV, Kivshar YS, Hu B (2010) Suppression of thermal conductivity in graphene nanoribbons with rough edges. Phys Rev B 82:195422

    Article  Google Scholar 

  31. Toda M (1989) Theory of nonlinear lattices, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

  32. Iskandarov AM, Medvedev NN, Zakharov PV, Dmitriev SV (2009) Crowdion mobility and self-focusing in 3D and 2D nickel. Comput Mater Sci 47:429

    Article  Google Scholar 

  33. Dmitriev SV, Korznikova EA, Baimova YA, Velarde MG (2016) Discrete breathers in crystals. Phys Usp 59:446

    Article  Google Scholar 

  34. Velarde MG, Chetverikov AP, Ebeling W, Dmitriev SV, Lakhno VD (2016) From solitons to discrete breathers. Eur Phys J B 89:233

    Article  MathSciNet  Google Scholar 

  35. Minzoni AA, Smyth NF (1996) Evolution of lump solutions for the KP equation. Wave Motion 24:291

    Article  MathSciNet  MATH  Google Scholar 

  36. Chetverikov AP, Ebeling W, Velarde MG (2011) Localized nonlinear, soliton-like waves in two-dimensional anharmonic lattices. Wave Motion 48:753

    Article  MathSciNet  MATH  Google Scholar 

  37. Davydov AS (1991) Solitons in molecular systems, 2nd edn. Reidel, Dordrecht

    Book  MATH  Google Scholar 

  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 85:1–8

    Article  Google Scholar 

  39. Hennig D, Neissner A, Velarde MG, Ebeling W (2006) Effect of anharmonicity on charge transport in hydrogen-bonded systems. Phys Rev E 73:024306

    Article  Google Scholar 

  40. Hennig D, Chetverikov AP, Velarde MG, Ebeling W (2007) Electron capture and transport mediated by lattice solitons. Phys Rev E 76:046602

    Article  Google Scholar 

  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 85:245105

    Article  Google Scholar 

  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 80:545

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Faculty of Physics, Saratov National Research State University, Astrakhanskaya 83, Saratov, Russia, 410012

    A. P. Chetverikov

  2. Institute of Physics, Humboldt-University Berlin, Newtonstraße 15, 12489, Berlin, Germany

    W. Ebeling

  3. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergestraße 36, 10623, Berlin, Germany

    E. Schöll

  4. Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, 28040, Madrid, Spain

    M. G. Velarde

Authors
  1. A. P. Chetverikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Ebeling
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Schöll
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. G. Velarde
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Schöll.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chetverikov, A.P., Ebeling, W., Schöll, E. et al. Excitation of solitons in hexagonal lattices and ways of controlling electron transport. Int. J. Dynam. Control 6, 1376–1383 (2018). https://doi.org/10.1007/s40435-017-0383-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-017-0383-x

Keywords

Search

Navigation