  We study the effect of perpendicular electric fields on the band structures
of ABA and ABC graphene multilayers, and find that the electronic screening
effect is significantly different between them. In ABA multilayers, the field
produces a band overlap and gives a linear screening, while in ABC multilayers,
in contrast, it opens an energy gap in the surface-state band at low energy,
leading to a strong screening effect essentially non-linear to the field
amplitude. The energy gap of a large ABC stack sharply rises when the external
field exceeds a certain critical value.
