Electron Distribution on a Deformed Liquid-Helium Surface

  • B. I. Lev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • V. P. Ostroukh Taras Shevchenko National University of Kyiv
  • V. B. Tymchyshyn Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • A. G. Zagorodny Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
Keywords: liquid helium, electrons, bubblon, two-dimensional electron systems

Abstract

A simple quasiclassical statistical model for the description of electrons on a liquid-helium surface in an external electric field is proposed. The model involves the electrostatic interaction energy with due regards to the medium polarization and electron interactions associated with the surface deformation. The explanation of some phenomena observed in the experiments is given. In particular, a method for numerical calculation of inhomogeneities of the charge distribution in an external electric field is introduced. The obtained results can be used to explain the peculiarities of the electron distribution function measured in experiments.

References

M.W. Cole, Phys. Rev. B 2, 4239 (1970).

http://dx.doi.org/10.1103/PhysRevB.2.4239

M.W. Cole and M.H. Cohen, Phys. Rev. Lett. 23, 1238 (1969).

http://dx.doi.org/10.1103/PhysRevLett.23.1238

E. Wigner, Phys. Rev. 46, 1002 (1934).

http://dx.doi.org/10.1103/PhysRev.46.1002

C.C. Grimes, and G. Adams, Phys. Rev. Lett. 42, 795 (1979).

http://dx.doi.org/10.1103/PhysRevLett.42.795

P.M. Platzman and M.I. Dykman, Science 284, 1967 (1999).

http://dx.doi.org/10.1126/science.284.5422.1967

V.B. Shikin, Sov. Phys. JETP 31, 936 (1970).

F.I.B. Williams, R.S. Crandall, and A.H. Willis, Phys. Rev. Lett. 26, 7 (1971).

http://dx.doi.org/10.1103/PhysRevLett.26.7

V.S. Edel'man, Usp. Fiz. Nauk 23, 227 (1980).

T. Ando, A. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982).

http://dx.doi.org/10.1103/RevModPhys.54.437

P.M. Platzman and H. Fukuyama, Phys. Rev. B 10, 3150 (1974).

http://dx.doi.org/10.1103/PhysRevB.10.3150

M. Haque, I. Paul, and S. Pankov, Phys. Rev. B 68, 045427 (2003).

http://dx.doi.org/10.1103/PhysRevB.68.045427

P. Leiderer and M. Wanner, Phys. Lett. A 73, 189 (1979).

http://dx.doi.org/10.1016/0375-9601(79)90704-7

W. Ebner and P. Leiderer, Phys. Lett. A 80, 277 (1980).

http://dx.doi.org/10.1016/0375-9601(80)90021-3

J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon Press, Oxford, 1996).

D.J. Thouless, Phys. Rep. 13, 93 (1974).

http://dx.doi.org/10.1016/0370-1573(74)90029-5

S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge Univ. Press, Cambridge, 1995).

http://dx.doi.org/10.1017/CBO9780511805776

Yu.P. Monarkha and K. Kono, Two-Dimensional Coulomb Liquids and Solids (Springer, Berlin, 2004).

http://dx.doi.org/10.1007/978-3-662-10639-6

B.I. Lev and A.G. Zagorodny, Phys. Rev. E 84, 061115 (2011).

http://dx.doi.org/10.1103/PhysRevE.84.061115

B.I. Lev and A.Y. Zhugaevych, Phys. Rev. E 57, 6460 (1998).

http://dx.doi.org/10.1103/PhysRevE.57.6460

L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, New York, 1984).

I. Skachko, Phase Diagram of a 2-Dimensional Electron System on the Surface of liquid helium, Ph.D. thesis, Rutgers, The State Univ. of New Jersey (2006).

S. Koutsoumpos, Surface State Electron Dynamics on Deformed Liquid Helium Films, Ph.D. thesis, Konstanz (2010).

D.K. Lambert, Electrons on the Surface of Liquid Helium, Ph.D. thesis, Lawrence Berkeley Laboratory (1979).

B.I. Lev and A.G. Zagorodny, Phys. Lett. A, 373, 1101 (2009).

http://dx.doi.org/10.1016/j.physleta.2009.01.044

B.I. Lev, V.B. Tymchyshyn, and A.G. Zagorodny, Cond. Matter Phys. 12, 1 (2009).

http://dx.doi.org/10.5488/CMP.12.4.593

B.I. Lev, V.B. Tymchyshyn, and A.G. Zagorodny, Phys. Lett. A 375, 593 (2011).

http://dx.doi.org/10.1016/j.physleta.2010.12.020

A.J. Archer, Phys. Rev. E 78, 031402 (2008).

http://dx.doi.org/10.1103/PhysRevE.78.031402

A. Imperio and L. Reatto, J. Chem. Phys. 124, 164712 (2006).

http://dx.doi.org/10.1063/1.2185618

A. Imperio and L. Reatto, Phys. Rev. E 76, 040402 (2007).

http://dx.doi.org/10.1103/PhysRevE.76.040402

B.I. Lev, V.P. Ostroukh, V.B. Tymchyshyn, and A.G. Zagorodny, arXiv:1308.3852 (2013).

Yu. Nesterov, Introductory Lectures on Convex Optimization. A Basic Course (Kluwer, Dordrecht, 2004).

http://dx.doi.org/10.1007/978-1-4419-8853-9

Published
2019-01-21
How to Cite
Lev, B., Ostroukh, V., Tymchyshyn, V., & Zagorodny, A. (2019). Electron Distribution on a Deformed Liquid-Helium Surface. Ukrainian Journal of Physics, 60(3), 247. https://doi.org/10.15407/ujpe60.03.0247
Section
Soft matter