  We study the effect of vertical electric-field (E-field) on the electronic
properties of the multilayer armchair graphene nanoribbon (aGNR). Under
E-field, the band structure of a bilayer aGNR undergoes interesting
transformations such as change in the electron velocity, sign of the electron
effective mass, band gap, the position of the band gap in the momentum space.
Depending on the width of the aGNR and the applied E-field, the band gap of the
aGNR may either be increased or decreased. When the applied E-field is above a
critical value, the band gap of the bilayer aGNR is identical to that of the
bilayer graphene, independent of the width. We also show that, for
semiconducting multilayer aGNR with more than two layers, the band gap
decreases with increasing E-field, resulting in a semiconductor-to-metallic
transition. This can be utilized to enhance the performance of a graphene based
transistor devices.
