Skip to main content

Absorption of Microwave Radiation by Bernstein Magnetoplasmon Modes in Inhomogeneous Two-Dimensional Electronic Systems


A study is performed of microwave absorption in inhomogeneous two-dimensional electron systems characterized by a finite size or by a modulation of parameters. Experiments and calculations are compared to show that resonance maxima in absorption are observed at the frequencies of Bernstein modes corresponding to the characteristic wave vector of inhomogeneity k. At low k, the absorption maxima at the second harmonic of the cyclotron resonance are observed in addition to the main resonance at the frequency of cyclotron magnetoplasmon with wave vector k. At high k corresponding to condition \(k{{R}_{{\text{c}}}} > 1,\) the position of the resonant absorption are parameterized in coordinates (\(k{{R}_{{\text{c}}}},~\,\,{{{\omega }} \mathord{\left/ {\vphantom {{{\omega }} {{{{{\omega }}}_{{\text{c}}}}}}} \right. \kern-0em} {{{{{\omega }}}_{{\text{c}}}}}}\)), where \({{{{\omega }}}_{{\text{c}}}}\) is the cyclotron frequency, \({{R}_{{\text{c}}}}\) is the cyclotron radius of an electron, and ω is the circular frequency of radiation.

This is a preview of subscription content, access via your institution.

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


  1. Kukushkin, I.V., Muravev, V.M., Smet, J.H., et al., Phys. Rev. B, 2006, vol. 73, no. 11, 113310.

    ADS  Article  Google Scholar 

  2. Khisameeva, A.R., Shchepetilnikov, A.V., Muravev, V.M., et al., J. Exp. Theor. Phys., 2020, vol. 130, no. 4, p. 594.

    ADS  Article  Google Scholar 

  3. Volkov V.A. and Takhtamirov E.E., J. Exp. Theor. Phys., 2007, vol. 104, no. 4, p. 602.

    ADS  Article  Google Scholar 

  4. Dorozhkin, S.I. and Kapustin, A.A., JETP Lett., 2015, vol. 101, no. 2, p. 97.

    ADS  Article  Google Scholar 

  5. Bernstein, I.B., Phys. Rev., 1958, vol. 109, no. 1, p. 10.

    ADS  MathSciNet  Article  Google Scholar 

  6. Batke, E., Heitmann, D., and Tu, C.W., Phys. Rev. B, 1986, vol. 34, no. 10, p. 6951.

    ADS  Article  Google Scholar 

  7. Kukushkin, I.V. and Volkov, V.A., Dvumernaya elektronnaya zhidkost’ v sil’nom magnitnom pole: magnitoplazmony, magnitorotony, kompozitnye fermiony (Two-Dimensional Electron Fluid in a Strong Magnetic Field: Magnetoplasmons, Magnetorotons, Composite Fermions), Moscow: Fizmatkniga, 2016.

  8. Dorozhkin, S.I., Kapustin, A.A., Umansky, V., and Smet, J.H., JETP Lett., 2021, vol. 113, no. 10, p. 670.

    ADS  Article  Google Scholar 

  9. Pechenezhskii, I.V., Dorozhkin, S.I., and Dmitriev, I.A., JETP Lett., 2007, vol. 85, no. 1, p. 86.

    ADS  Article  Google Scholar 

  10. Chaplik, A.V. and Heitmann, D., J. Phys. C, 1985, vol. 18, no. 17, p. 3357.

    ADS  Article  Google Scholar 

  11. Zudov, M.A., Du, R.R., Simmons, J.A., and Reno, J.L., Phys. Rev. B, 2001, vol. 64, no. 20, 201311(R).

    ADS  Article  Google Scholar 

  12. Dmitriev, I.A., Mirlin, A.D., Polyakov, D.G., and Zudov, M.A., Rev. Mod. Phys., 2012, vol. 84, no. 4, p. 1709.

    ADS  Article  Google Scholar 

  13. Dorozhkin, S.I., JETP Lett., 2003, vol. 77, no. 10, p. 681.

    Article  Google Scholar 

  14. Mikhailov, S.A. and Savostianova, N.A., Phys. Rev. B, 2005, vol. 71, no. 3, 035320.

    ADS  Article  Google Scholar 

  15. Kapustin, A.A., Dorozhkin, S.I., and Kukushkin, I.V., J. Surf. Invest.: X-ray, Synchrotron Neutron Tech., 2021, vol. 15, no. 6, p. 1133.

    Article  Google Scholar 

Download references


This work was performed as part of a State Task for the Institute of Solid State Physics, Russian Academy of Sciences.

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. A. Kapustin.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by N. Petrov

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kapustin, A.A., Dorozhkin, S.I. & Kukushkin, I.V. Absorption of Microwave Radiation by Bernstein Magnetoplasmon Modes in Inhomogeneous Two-Dimensional Electronic Systems. Bull. Russ. Acad. Sci. Phys. 86, 394–399 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: