  We investigate the efficiency of electrical manipulation on two-dimensional
topological insulators by considering a lateral potential superlattice on the
system. The electronic states under various conditions are examined carefully.
It is found that the dispersion of the mini-band and the electron distribution
in the potential well region display an oscillatory behavior as the potential
strength of the lateral superlattice increases. The probability of finding an
electron in the potential well region can be larger or smaller than the average
as the potential strength varies. This indicates that the electric manipulation
efficiency on two-dimensional topological insulators is not as high as
expected, which should be carefully considered in designing a device
application that bases on two-dimensional topological insulators. These
features can be attributed to the coupled multiple-band nature of the
topological insulator model. In addition, it is also found that these behaviors
are not sensitive to the gap parameter of the two-dimensional topological
insulator model.
