Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models

TL;DR

This paper introduces models of twisted multilayer graphene with exactly flat bands of arbitrary Chern numbers and ideal geometries, enabling potential realization of exotic fractional Chern insulators.

Contribution

The authors construct analytically solvable models of twisted multilayer graphene with flat bands of arbitrary Chern numbers and demonstrate their ideal band geometries and topological properties.

Findings

Flat bands with arbitrary Chern numbers are realized in the models.

Wavefunction exchange mechanism explains high Chern numbers.

Numerical evidence shows potential for exotic fractional Chern insulators.

Abstract

We propose models of twisted multilayer graphene that exhibit exactly flat Bloch bands with arbitrary Chern numbers and ideal band geometries. The models are constructed by twisting two sheets of Bernal-stacked multiple graphene layers with only inter-sublattice couplings. Analytically we show that flatband wavefunctions in these models exhibit a momentum space holomorphic character, leading to ideal band geometries. We also explicitly demonstrate a generic "wavefunction exchange" mechanism that generates the high Chern numbers of these ideal flatbands. The ideal band geometries and high Chern numbers of the flatbands imply the possibility of hosting exotic fractional Chern insulators which do not have analogues in continuum Landau levels. We numerically verify that these exotic fractional Chern insulators are model states for short-range interactions, characterized by exact ground-state degeneracies at zero energy and infinite particle-cut entanglement gaps.