Eur. Phys. J. B 57, 225-228 (2007)
https://doi.org/10.1140/epjb/e2007-00168-5

Conductance quantization in graphene nanoribbons: adiabatic approximation

Institute for Molecules and Materials, Radboud University Nijmegen, 6525 ED Nijmegen, The Netherlands

Corresponding author: ^a M.Katsnelson@science.ru.nl

Received: 5 March 2007
Revised: 14 May 2007
Published online: 15 June 2007

Abstract

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 conventional electron gas. For the case of zigzag boundary conditions, one can expect a well-pronounced conductance quantization only for highly excited states. This difference is related to the relativistic Zitterbewegung effect in graphene.