Electron in the field of flexural vibrations of a membrane: Quantum time, magnetic oscillations, and coherence breaking
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/(1η)} T ^{(2η)/(22η)}, where g is the electronphonon 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 τ_{φ} 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_{φ} can be expressed by various power functions of the electronphonon interaction constant, temperature, and electron energy.
 Publication:

Soviet Journal of Experimental and Theoretical Physics
 Pub Date:
 August 2016
 DOI:
 10.1134/S1063776116060030
 Bibcode:
 2016JETP..123..322G