Skip to main content
SpringerLink
Log in

Self-Consistent Approach to Solving the Problem of Crystal Lattice Formation in an Electron-Hole Plasma

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We transform the Hubbard Hamiltonian for electrons of ns bands of crystal atoms into the electron-hole Hamiltonian using Shiba operators. We use this Hamiltonian to study the behavior of the electron-hole system as a function of its internal and external parameters and show that in contrast to a one-component electron system, there are no conditions for the appearance of structural phase transitions in this two-component system.

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

Similar content being viewed by others

References

  1. V. E. Fortov, Equations of State of Matter from an Ideal Gas to Quark-Gluon Plasma [in Russian], Fizmatlit, Moscow (2013).

    MATH  Google Scholar 

  2. P. Abbamonte, G. Blumberg, A. Rusydi, A. Gozar, P. G. Evans, T. Siegrist, L. Venema, H. Eisaki, E. D. Isaacs, and G. A. Sawatzky, “Crystallization of charge holes in the spin ladder of Sr14Cu24O41,” Nature, 431, 1078–1081 (2004).

    Article  ADS  Google Scholar 

  3. S. K. Sarker, H. R. Krishnamurthy, C. Jayaprakash, and W. Wenzel, “Mean-field theories of Hubbard and t-J models,” Phys. B, 163, 541–543 (1990).

    Article  ADS  Google Scholar 

  4. E. P. Wigner, “On the interaction of electrons in metals,” Phys. Rev., 46, 1002–1011 (1934).

    Article  ADS  MATH  Google Scholar 

  5. S. Raimes, Many-Electron Theory, North-Holland, Amsterdam (1972).

    Google Scholar 

  6. J. Hubbard, “Electron correlations in narrow energy bands,” Proc. Roy. Soc. London Ser. A, 236, 238 (1963).

    ADS  Google Scholar 

  7. H. Shiba, “Thermodynamic properties of the one-dimensional half-filled-band Hubbard model: II. Application of the grand canonical method,” Prog. Theor. Phys., 48, 2171–2186 (1972).

    Article  ADS  Google Scholar 

  8. M. F. Sarry, “Analytical methods of calculating correlation functions in quantum statistical physics,” Sov. Phys. Usp., 34, 958–979 (1991).

    Article  ADS  Google Scholar 

  9. D. Pines, The Many-Body Problem, W. A. Benjamin, New York (1962).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Russian Federal Nuclear Center — Russian Scientific Research Institute of Experimental Physics, Sarov, Nizhny Novgorod Oblast, Russia

    T. O. Voronkova, A. M. Sarry, M. F. Sarry & S. G. Skidan

  2. Yaroslav-the-Wise Novgorod State University, Veliky Novgorod, Novgorod Oblast, Russia

    A. M. Sarry

Authors
  1. T. O. Voronkova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Sarry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. F. Sarry
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. G. Skidan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. M. Sarry.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 1, pp. 158–170, July, 2019.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Voronkova, T.O., Sarry, A.M., Sarry, M.F. et al. Self-Consistent Approach to Solving the Problem of Crystal Lattice Formation in an Electron-Hole Plasma. Theor Math Phys 200, 1063–1073 (2019). https://doi.org/10.1134/S0040577919070109

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0040577919070109

Keywords

Search

Navigation