  Stability and electronic properties of atomic layers of GaN are investigated
in the framework of the van der Waals-density functional theory. We find that
the ground state of the layered GaN is a planar graphene-like configuration
rather than a buckled bulk-like configuration. Application of an external
perpendicular electric field to the layered GaN induces distinct
stacking-dependent features of the tunability of the band gap; the band gap of
the monolayer does not change whereas that of the trilayer GaN is significantly
reduced for the applied field of 0.4 V/ {\AA}. It is suggested that such a
stacking-dependent tunability of the band gap in the presence of an applied
field may lead to novel applications of the devices based on the layered GaN.
