Scaling law of the giant Stark effect in boron nitride nanoribbons and nanotubes

Ab initio calculations reveal a universal scaling law on how the electronic structure of boron nitride (BN) nanoribbons and nanotubes is modified by a transverse electric field. Due to the structural symmetry difference, the energy gap of zigzag BN ribbons can be reduced or increased by the electric field depending on the sign of the field, while that of the armchair ones is always reduced. However, the linear giant Stark effect coefficients of zigzag and armchair BN nanoribbons, as well as those of BN nanotubes, are found to obey a unified scaling law where the coefficient increases linearly with the ribbon width or the tube diameter with a slope of 1.0. The mechanism of the scaling law is identified using a general model, which may be applicable to other semiconducting nanostructures.