Journal of Experimental and Theoretical Physics

, Volume 123, Issue 2, pp 322–347 | Cite as

Electron in the field of flexural vibrations of a membrane: Quantum time, magnetic oscillations, and coherence breaking

  • I. V. Gornyi
  • A. P. Dmitriev
  • A. D. Mirlin
  • I. V. Protopopov
Electronic Properties of Solid

Abstract

We have studied the motion of an electron in a membrane under the influence of flexural vibrations with a correlator that decreases upon an increase in the distance in accordance with the law r. We have conducted a detailed consideration of the case with η < 1/2, in which the perturbation theory is inapplicable, even for an arbitrarily weak interaction. It is shown that, in this case, reciprocal quantum time 1/τq is proportional to g1/(1–η)T(2–η)/(2–2η), where g is the electron–phonon interaction constant and T is the temperature. The method developed here is applied for calculating the electron density of states in a magnetic field perpendicular to the membrane. In particular, it is shown that the Landau levels in the regime with ωcτq » 1 have a Gaussian shape with a width that depends on the magnetic field as Bη. In addition, we calculate the time τφ of dephasing of the electron wave function that emerges due to the interaction with flexural phonons for η < 1/2. It has been shown that, in several temperature intervals, quantity 1/τφ can be expressed by various power functions of the electron–phonon interaction constant, temperature, and electron energy.

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Copyright information

© Pleiades Publishing, Inc. 2016

Authors and Affiliations

  • I. V. Gornyi
    • 1
    • 2
    • 3
    • 4
  • A. P. Dmitriev
    • 2
  • A. D. Mirlin
    • 1
    • 3
    • 4
    • 5
  • I. V. Protopopov
    • 1
    • 3
    • 4
  1. 1.Institut für NanotechnologieKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Ioffe Physicotechnical InstituteRussian Academy of SciencesSt. PetersburgRussia
  3. 3.Institut für Theorie der kondensierten MaterieKarlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.Landau Institute for Theoretical PhysicsRussian Academy of Sciences, ChernogolovkaMoscow oblastRussia
  5. 5.Konstantinov St. Petersburg Institute of Nuclear PhysicsGatchina, Leningradskaya oblastRussia

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