Theory of Triple Magnetopolarons in Quantum-Dimensional Nanostructures

Barat Eshpulatov,Eshkuvat Arzikulov

doi:10.4236/ajac.2013.49058

Abstract

A theory of triple magnetopolarons in an isolated quantum well in a strong magnetic field was developed. We study the behavior of the magnetooptical absorption peaks corresponding to the transitions of an electron at the Landau level with quantum numbers n ≥ 2. For n = 2 at the point of equality of cyclotron frequency and the frequency of optical phonon (LO), there is a cross of three terms of the electron-phonon system (the electron at the Landau level n = 2, the electron at n = 1, and the optical phonon and electron at n = 0 and two phonons), considered as a function of the cyclotron frequency. Interaction with phonons takes off the degeneracy of the terms and leads to three disjoint branches of the electron-phonon spectrum. The theory predicts that in the resonant magnetic field, the peak of magnetooptical absorption splits into three peaks, the intensity and position of which are dependent in a complex way on the magnitude of the magnetic field and the constant of the electron-phonon coupling.

Highlights

When the following condition is valid: c 0 (1)(where 0 is maxima frequency of longitudinal optical phonon (OP), c eН сmc is the cyclotron frequency, е is the electron’s charge, Н is the magnetic field tension, с is the velocity of light in the vacuum, тс is the effective mass of electron), the magnetopolaron states are formed in semiconductors
We study the behavior of the magnetooptical absorption peaks corresponding to the transitions of an electron at the Landau level with quantum numbers n ≥ 2
For n = 2 at the point of equality of cyclotron frequency and the frequency of optical phonon (LO), there is a cross of three terms of the electron-phonon system, considered as a function of the cyclotron frequency

Summary

Introduction

In many semi-conductors the following condition is valid: mc mv 1 (where mv is the effective mass of the hole) We consider in this case the interband optical transitions, which creates an electron in a potential well of the conduction band and a hole near the peak of the Landau band or in a potential well in the valence band in the case of GaAs heterojunction (possibility of formation of exciton states is neglected). The problem of calculation of the spectrum is complicated by the fact that emission of phonons is connected with transitions of electrons between Landau levels, where the density of states is high It means the impropriety of usual series expansion of the mass operator with respect to coupling constant, and necessity of selective summation of the series

Cq 2 J 1 q 2 0 c 1 i 1 q 1

Evaluation of the Spectrum of Electron-Phonon System

Splitting of Magnetooptical Absorption and Results Discussion