Comparison of magnetotransport in two-dimensional arrays of quantum dots and antidots

The longitudinal and Hall conductivities and resistivities are compared for two-dimensional (2D) square arrays of quantum dots and antidots in 2D electronic systems (ES’s). The effects on the magnetotransport from the bound and coherent collimated states are explained. The energy eigenvalue spectra are obtained as a function of the magnetic field. The wave-vector dispersion of the energy eigenvalues is also calculated for the two systems. For antidots, there is a threshold magnetic field above which the system behaves like a homogeneous 2D ES. This threshold and the quenching of the Hall effect for antidots and the insulating behavior and Aharonov-Bohm quantum oscillations in a quantum-dot array are the main findings in this paper.