Phase modulation of charge density wave around a short-range potential by the Aharonov-Bohm effect

The analytic result of the Aharonov-Bohm effect for its influence on the oscillation of a two-dimensional charge density around a short range potential is given. Without losing generality, the cases of δ-function and hard disc potentials were examined. Numerical calculations show that the interferences among quantum particles are greatly influenced by the nonlocal effect, which leads to the modulation of phase and amplitude of the oscillation of charge density. Since the presence of a nonlocal influence of the Aharonov-Bohm effect on charged particles is universal, the results in the specific potentials examined are expected to appear also in other general systems which may be beneficial to the study of nanotechnology.