Conductance quantization in graphene nanoribbons: Adiabatic approximation

TL;DR

This paper develops a theory for electron states in graphene nanoribbons with varying width, revealing that conductance quantization is limited to highly excited states due to relativistic effects unique to graphene.

Contribution

It introduces a modified adiabatic approximation for massless Dirac fermions in graphene nanoribbons, highlighting differences from conventional electron gases.

Findings

Adiabatic approximation is more restrictive for graphene's Dirac fermions.

Conductance quantization occurs mainly in highly excited states.

Relativistic Zitterbewegung affects electron behavior in graphene nanoribbons.

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.