Quantum mechanics

Theoretical physics

Philosophy

Pure mathematics

Physics

Ideal (ethics)

Mathematics

Epistemology

Chern class

Holomorphic function

Mathematical analysis

Geometry

Wave function

Twist

Physical Review Letters

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 intersublattice couplings. Analytically we show that flatband wave functions in these models exhibit a momentum space holomorphic character, leading to ideal band geometries. We also explicitly demonstrate a generic "wave function 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.

Hierarchy of Ideal Flatbands in Chiral Twisted Multilayer Graphene Models