Non-Abelian Chern band in rhombohedral graphene multilayers

TL;DR

This paper demonstrates the spontaneous emergence of a non-Abelian Chern band with SU(2) symmetry in rhombohedral multilayer graphene, driven by interactions and characterized by non-Abelian Berry curvature.

Contribution

It reveals a new class of interaction-driven non-Abelian topological phases in multilayer graphene, previously only realized in highly engineered systems.

Findings

Non-Abelian Chern bands emerge spontaneously at filling ν=2 in rhombohedral multilayer graphene.

Fock term induces spontaneous symmetry breaking and generates non-Abelian Berry curvature.

The non-Abelian topology involves SU(2) gauge flux and global non-Abelian holonomy.

Abstract

Moir\'e flat bands in rhombohedral multilayer graphene provide a platform for exploring interaction-driven topological phases, where a single isolated band often forms a Chern band. However, non-Abelian degenerate Chern bands with internal symmetries such as $\mathrm{SU}(N)$ have so far been realized only in highly engineered systems. Here, we show that a doubly degenerate non-Abelian Chern band with Chern number $|C|=1$ emerges spontaneously at filling $\nu=2$ in rhombohedral 3-, 4-, and 5-layer graphene, regardless of the presence of an hBN substrate. Using self-consistent Hartree-Fock calculations, we map out phase diagrams as functions of displacement field and electronic periodicity, and analytically demonstrate that the Fock term drives spontaneous symmetry breaking and generates non-Abelian Berry curvature. We further show that this non-Abelian topology is characterized by $\mathrm{SU}(2)$ gauge flux threading the noncontractible cycles of the Brillouin zone, leading to a global non-Abelian holonomy. Our findings unveil a new class of interaction-driven non-Abelian topological phases, distinct from quantum anomalous Hall and fractional Chern phases.