first-principles tight-binding study of band gaps in graphene ribbons

Graphene has recently received much attention for the many interesting physical properties that it exhibits, including light Dirac fermion characteristics of its charge carriers and some experimental evidence of a minimum conductivity, even as the carrier concentration goes to zero. From a practical standpoint, the potential for large carrier mobility in graphene provides an attractive alternative to silicon-based devices, e.g. for field-effect transistors. Theoretical efforts towards designing these devices are focused on determining the geometry and chemistry needed to open up a semiconducting gap in the otherwise semi-metal band structure of a perfect, infinite graphene sheet. Such effects may allow gate control of the electronic conductance as found in semiconducting carbon nanotube devices. Here we use the NRL tight-binding method, which is fit to first-principles calculated data, to study the possibility of opening a gap in graphene by varying strip-width, edge shape with and without termination, and by allowing Peierl's distortion of the edges for narrow ribbons. We compare the tight-binding results with calculations based on the density functional theory.