Biased voltage boundary condition to operate Bilayer Graphene in the insulating region

Graphene has received significant attention due to its excellent transport properties. Bilayer Graphene Nanoribbon (BGN), double Bernal stacked honeycomb sheets of carbon which have quadratic dispersion relations instead of single layer Graphene Nanoribbon (GNR) by linear dispersion, provides an interesting area of research activity. In this paper, we show that isolating properties appears in the limit of external applied voltage in BGNs. The gap between conduction and valance band which is opened by an applied electric field is strongly varied by the value of the external voltage. The band gap is opened for V_ext = 0 V_ext^max to where the conduction and valance band meet each other and overlap through the conduction and valance band. In this boundary condition, BGNs are expected to behave as an insulator. In contrast, beyond this boundary condition it is estimated to be semi-metallic. Also we showed changing the value of interlayer hopping strongly affected the maximum band gap and it creates a wider possible external electric field which opens the band gap in BGNs.