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

Journal of Experimental and Theoretical Physics, ISSN: 1063-7761, Vol: 123, Issue: 2, Page: 322-347
2016
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  • Citations
    2
    • Citation Indexes
      2

Article Description

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/τ is proportional to gT, 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 ωτ » 1 have a Gaussian shape with a width that depends on the magnetic field as B. In addition, we calculate the time τ 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/τ can be expressed by various power functions of the electron–phonon interaction constant, temperature, and electron energy.

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