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

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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–2η. 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/τ q is proportional to g 1/(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 ω c τ q » 1 have a Gaussian shape with a width that depends on the magnetic field as B η. 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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Author information

Authors and Affiliations

  1. Institut für Nanotechnologie, Karlsruhe Institute of Technology, Karlsruhe, 76021, Germany

    I. V. Gornyi, A. D. Mirlin & I. V. Protopopov

  2. Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, 194021, Russia

    I. V. Gornyi & A. P. Dmitriev

  3. Institut für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, Karlsruhe, 76128, Germany

    I. V. Gornyi, A. D. Mirlin & I. V. Protopopov

  4. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia

    I. V. Gornyi, A. D. Mirlin & I. V. Protopopov

  5. Konstantinov St. Petersburg Institute of Nuclear Physics, Gatchina, Leningradskaya oblast, 188300, Russia

    A. D. Mirlin

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  1. I. V. Gornyi
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  2. A. P. Dmitriev
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  3. A. D. Mirlin
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  4. I. V. Protopopov
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Correspondence to A. P. Dmitriev.

Additional information

Original Russian Text © I.V. Gornyi, A.P. Dmitriev, A.D. Mirlin, I.V. Protopopov, 2016, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2016, Vol. 150, No. 2, pp. 372–400.

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Gornyi, I.V., Dmitriev, A.P., Mirlin, A.D. et al. Electron in the field of flexural vibrations of a membrane: Quantum time, magnetic oscillations, and coherence breaking. J. Exp. Theor. Phys. 123, 322–347 (2016). https://doi.org/10.1134/S1063776116060030

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  • DOI: https://doi.org/10.1134/S1063776116060030

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