Chiral symmetry breaking and topological charge of graphene nanoribbons

TL;DR

This paper investigates the topological properties and chiral symmetry breaking in graphene nanoribbons, revealing their status as symmetry-protected topological insulators with unique edge states influenced by doping and magnetic order.

Contribution

It demonstrates that graphene nanoribbons are short-range entangled symmetry-protected topological insulators with novel edge states, despite chiral symmetry breaking.

Findings

Edge ferromagnetism induces topological charge on zigzag edges.

Low-doped ribbons exhibit nearly zero-energy edge modes.

System falls outside conventional topological insulator classification.

Abstract

We explore the edge properties of rectangular graphene nanoribbons featuring two zigzag edges and two armchair edges. Although the self-consistent Hartree-Fock fields break chiral symmetry, our work demonstrates that graphene nanoribbons maintain their status as short-range entangled symmetry-protected topological insulators. The relevant symmetry involves combined mirror and time-reversal operations. In undoped ribbons displaying edge ferromagnetism, the band gap edge states with a topological charge form on the zigzag edges. An analysis of the anomalous continuity equation elucidates that this topological charge is induced by the gap term. In low-doped zigzag ribbons, where the ground state exhibits edge spin density waves, this topological charge appears as a nearly zero-energy edge mode. Our system is outside the conventional calssification for topological insulators.