The Hall Effect in bulk semiconductors under the influence of the Electromagnetic wave (EMW) has been studied in much details. The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a MF perpendicular to the current. It was discovered by Edwin Hall in 1879. | VNU Journal of Science: Mathematics – Physics, Vol. 32, No. 2 (2016) 69-75 Shubnikov-De Haas Effect in Cylindrical Quantum Wires under the Influence of a Laser Radiation Nguyen Thu Huong1,*, Nguyen Vu Nhan2, Dang Thi Thanh Thuy1 1 Faculty of Physics, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam 2 Academy of Air Defense and Air Force, Kim Son, Son Tay, Hanoi, Vietnam Received 25 March 2016 Revised 20 May 2016; Accepted 27 June 2016 Abstract: Considering an infinite potential Cylindrical Quantum Wire (CQW) subjected to a dc electric field E1 = (0,0, E1 ) , a Magnetic Field (MF) B = ( B,0,0) and a laser radiation E0 = E sin Ωt (where E0 and Ω are the amplitude and the frequency of the laser radiation, respectively), the quantum kinetic equation for electron distribution function is obtained. Assuming the electron gas is non-degenerate and considering the Electron - Acoustic Phonon (AP) interaction, we achieve analytical expressions for the conductivity tensor and the Hall Coefficient (HC), which are different from those for the case of the Electron - AP interaction in a Rectangular Quantum Wire (RQW) or in Two-Dimensional Electron Gas (2DEG). The Shubnikov-de Haas (SdH) oscillations will appear. The amplitudes of SdH oscillations in the dependence of Magnetoresistance (MR) decrease with increasing MF. Numerical calculations are applied for GaAs/GaAsAl CQW to show the nonlinear dependence of the HC on the frequency of the laser radiation Ω , and Magnetic Field (MF) B . Wave function and energy spectrum in a CQW are dissiminar to those in other Quantum Wires (QWs). Therefore, all numerical results are different from those in the case of QWs. The most important result is that the HC reaches saturation as the magnetic field or the EMW frequency increases. Keywords: Hall coefficient; cylindrical quantum wires; electron - optical phonon interaction; Shubnikov-de Haas oscillations. 1. Introduction∗ The Hall Effect in bulk .
