A theory of electron states for graphene nanoribbons with a smoothly varying width is developed. It is demonstrated that the standard adiabatic approximation allowing to neglect the mixing of different standing waves is more restrictive for the massless Dirac fermions in graphene than for the...

It has been recently demonstrated experimentally that graphene, or single-layer carbon, is a gapless semiconductor with massless Dirac energy spectrum. A finite conductivity per channel of order of e<Superscript>2</Superscript>/h in the limit of zero temperature and zero charge carrier density is one of the striking...</superscript>