Sign reversal of Hall conductivity and quantum confinement in graphene ribbons

TL;DR

This paper investigates how quantum confinement and edge structures in narrow graphene ribbons cause sign reversals in Hall conductivity, revealing new behaviors linked to ribbon width and boundary type.

Contribution

It introduces a theoretical analysis of Hall conductivity sign reversal in narrow graphene ribbons, highlighting the role of multi-band crossings and a new classification based on flat bands.

Findings

Hall conductivities exhibit sign reversals in narrow ribbons.

Multi-band crossings depend on ribbon width and boundary type.

A new classification of armchair ribbons based on flat bands.

Abstract

Characterized by zigzag and armchair boundaries, the narrow ribbons display the very different characteristics in Hall conductivities. It is shown that the multi-band-crossings occur in the energy spectrum for armchair ribbons, and the number of them depends on the width of ribbons. Theoretically, it is predicated that the conductivities exhibit drastic sign reversals for narrow ribbons as the Fermi energy sweep over the band-crossings. A new classification of armchair ribbons is suggested based on the emergence of a flat band in the energy spectrum only for odd armchair ribbons. The evolution of jumped Hall conductivities to step-like plateaus and the restore of density of states at the van Hove singularity in the limitation to graphene sheet have been analyzed.