Robustness of the optical-conductivity sum rule in Bilayer Graphene

TL;DR

This paper investigates the optical conductivity sum rule in bilayer graphene, showing it remains robust despite the opening of a tunable bandgap, contrasting with other correlated systems.

Contribution

It demonstrates that the optical sum rule in bilayer graphene is protected against gap opening, unlike in strongly correlated materials.

Findings

Sum rule remains unchanged with gap opening

Bandgap tunability does not affect optical sum rule

Contrast with correlated systems where sum rule varies

Abstract

We calculate the optical sum associated with the in-plane conductivity of a graphene bilayer. A bilayer asymmetry gap generated in a field-effect device can split apart valence and conduction bands, which otherwise would meet at two K points in the Brillouin zone. In this way one can go from a compensated semimetal to a semiconductor with a tunable gap. However, the sum rule turns out to be 'protected' against the opening of this semiconducting gap, in contrast to the large variations observed in other systems where the gap is induced by strong correlation effects.