Non-Abelian Chern Band in Rhombohedral Graphene Multilayers

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Moiré flat bands in rhombohedral multilayer graphene are known platforms for interaction-driven topological phases.
• Chern bands are often observed, but non-Abelian degenerate Chern bands with internal symmetries (SU(N)) are rare and require engineered systems.

Purpose of the Study:

• To investigate the spontaneous emergence of non-Abelian degenerate Chern bands in rhombohedral multilayer graphene.
• To characterize the topological properties and underlying mechanisms of these emergent bands.

Main Methods:

• Utilized self-consistent Hartree-Fock calculations.
• Mapped phase diagrams based on displacement field and electronic periodicity.
• Employed analytical methods to demonstrate symmetry breaking and Berry curvature generation.

Main Results:

• A doubly degenerate non-Abelian Chern band with a Chern number of |C|=1 was observed spontaneously at filling ν=2 in 3-, 4-, and 5-layer graphene.
• The Fock term was identified as the driver for spontaneous symmetry breaking and the generation of non-Abelian Berry curvature.
• The non-Abelian topology was characterized by SU(2) gauge flux and global non-Abelian holonomy.

Conclusions:

• This study reveals a new class of interaction-driven non-Abelian topological phases in multilayer graphene.
• These phases are distinct from previously known quantum anomalous Hall and fractional Chern phases.
• The findings suggest rhombohedral multilayer graphene as a natural platform for realizing complex topological phenomena without external engineering.