Gate-Tunable Topological Flat Bands in Trilayer Graphene-Boron Nitride Moir\'e Superlattices

TL;DR

This paper explores how moiré superlattices and electric fields in trilayer graphene-boron nitride interfaces create tunable flat bands with topological properties, enabling potential quantum Hall phases driven by Coulomb interactions.

Contribution

It demonstrates the emergence of valley-spin resolved topological flat bands with Chern number 3 in TLG/BN systems under specific electric fields and twist angles, revealing new tunable quantum phases.

Findings

Flat bands with Chern number 3 near charge neutrality.

Narrow bandwidths (~10 meV) for twist angles less than 0.6°.

Electric-field controlled Coulomb-driven spontaneous Hall phases.

Abstract

We investigate the electronic structure of the flat bands induced by moir\'e superlattices and electric fields in nearly aligned ABC trilayer graphene-boron nitride interfaces where Coulomb effects can lead to correlated gapped phases. Our calculations indicate that valley-spin resolved isolated superlattice flat bands that carry a finite Chern number $C = 3$ proportional to layer number can appear near charge neutrality for appropriate perpendicular electric fields and twist angles. When the degeneracy of the bands is lifted by Coulomb interactions these topological bands can lead to anomalous quantum Hall phases that embody orbital and spin magnetism. Narrow bandwidths of $\sim10$ meV achievable for a continuous range of twist angles $\theta \lesssim 0.6^{\circ}$ with moderate interlayer potential differences of $\sim$50 meV make the TLG/BN systems a promising platform for the study of electric-field tunable Coulomb interaction driven spontaneous Hall phases.