Chiral symmetry breaking and topological charge of graphene nanoribbons
arxiv(2023)
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.
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