Gate-controlled carrier injection into hexagonal boron nitride

First-principle calculations show that free-electron carriers are induced in few-layer hexagonal boron nitride ($h$-BN) by applying an external electric field. The electric field substantially shifts the particular states downward, and they finally cross the Fermi level under an electric field of a few volts per nanometer. In the metallic phase of $h$-BN, the carriers are distributed not only at atomic sites but also in the spacious regions in $h$-BN. It is found that the threshold voltage resulting in metal--insulator transition decreases as the number of layers increases. This indicates the possibility of realizing a two-dimensional metallic layered material without the chemical doping of atoms or molecules.