Dependence of the Hall Coefficient on a length of rectangular quantum wires with infinitely high potential under the influence of a Laser Radiation

The Hall coefficient (HC) of a strong electromagnetic wave (EMW) caused by confined electrons in a rectangular quantum wire (RQW) is theoretically studied by using the quantum kinetic equation for electrons. The problem is considered in the case of electrons - acoustic phonons scattering. Wave function and energy spectrum in a RQW are different from those in a cylindrical quantum wire (CQW) or two dimensional systems (2D). Therefore analytical expressions for the HC in a RQW is obtained, different from CQW or 2D. Numerical calculations are carried out with a specific GaAs/GaAsAl RQW to show clearly the dependence of HC on a length Lx (Ly) RQW with different low temperature values. We can see that the length Lx (Ly) increases in value within the domain that HC increases. The HC reaches a peak before slightly decreases when the length Lx (Ly) continues going up. However, the HC depends on the radius and the length of CQW and wire size of RQW Lx and Ly at different values of temperatures; this is the fundamental difference between CQW and RQW. If the length Lx (Ly) continues to increase, the HC remains constant. It means that HC is no longer dependent on the length of quantum wires (This behavior is similar to the case of the independence of the HC on the length in bulk semiconductor). (paper)