Theoretical Study of the Influence of Confined Phonons and a Strong Electromagnetic Wave on the Hall Effect in an One–Dimensional Cylindrical Quantum Wire GaAs/GaAsAl

抄録

The Hall effect in an one-dimensional cylindrical quantum wire (CQW) with an infinite potential is studied by using the quantum kinetic equation under the influence a strong electromagnetic wave within the mechanising of scattering on confined acoustic phonons. We consider a case where an one-dimensional CQW is placed in a magnetic field , a constant–electric field and a strong electromagnetic wave (where E₀ and Ω are the amplitude and the frequency of the strong electromagnetic wave, respectively). Analytical expressions for the Hall conductivity tensors and the Hall coefficient (HC) are obtained. It is found that the Hall conductivity tensors and the Hall coefficient depend on the frequency Ω and the amplitude E₀ of the strong electromagnetic wave, the magnetic field B, the temperature T the system, the radius of CQW, and the quantum indies m₁ and m₂ characterizing the phonon confinement. These are different from the case of normal bulk semiconductor and from the case of cylindrical quantum wire with electron–unconfined acoustic phonons scattering mechanism. Numerical calculations are performed using parameters of a GaAs/GaAsAl one-dimensional cylindrical quantum wire. The phonon confinement increase of Hall coefficient by 2.3 times in comparition with the case of unconfined acoustic phonons. When the quantum numbers m₁ and m₂ go to zero, the result is the same as in the case of unconfined phonons. The Hall conductivity tensors (The Shubnikov–de Haas magnetoresistance oscillations) in the case of confined acoustic phonon scattering mechanism and in the presence of a strong electromagnetic wave have more resonance peaks.

The dependence of the conductivity tensor σ_xx on the magnetic field B for the case of scattering mechanism electron-confined acoustic phonons (m₁ = m₂ = 0; 1) and bulk phonons in the GaAs/GaAsAl CQW.