Fast and slow edges in bilayer graphene nanoribbons: Tuning the transition from band- to Mott-insulator

TL;DR

This paper investigates how edge states in gated bilayer graphene nanoribbons exhibit different velocities and how interactions can induce a tunable gap, enabling control over the transition from band- to Mott-insulator phases.

Contribution

It reveals the existence of fast and slow edges with distinct velocities and demonstrates how interactions induce a tunable gap on the slow edge using bosonization and renormalization group techniques.

Findings

Edge states have different velocities due to next-nearest-neighbor hopping.

Interaction-induced gap on the slow edge can be tuned by gate voltage.

The gap's dependence on on-site potential is non-monotonous.

Abstract

We show that gated bilayer graphene zigzag ribbons possess a fast and a slow edge, characterized by edge state velocities that differ due to non-negligible next-nearest-neighbor hopping elements. By applying bosonization and renormalization group methods, we find that the slow edge can acquire a sizable interaction-induced gap, which is tunable via an external gate voltage V_{g}. In contrast to the gate-induced gap in the bulk, the interaction-induced gap depends non-monotonously on the on-site potential V.