Bandgap engineering of carbon allotropes

Abstract

Starting from the graphene layer, the bandgap engineering of carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) is described by applying an appropriate boundary condition. Linear E-k relationship of graphene transforms to a parabolic one as momentum vector in the tube direction is reduced to dimensions smaller than inverse of the tube diameter of a CNT. Similar transition is noticeable for narrow width of a GNR. In this regime, effective mass and bandgap expressions are obtained. A CNT or GNR displays a distinctly 1D character suitable for applications in quantum transport.