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

Understand

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.