Moir\'e Landau fans and magic zeros

Abstract

We study the energy spectrum of moir\'e systems under a uniform magnetic field. The superlattice potential generally broadens Landau levels into Chern bands with finite bandwidth. However, we find that these Chern bands become flat at a discrete set of magnetic fields which we dub "magic zeros". The flat band subspace is generally different from the Landau level subspace in the absence of the moir\'e superlattice. By developing a semiclassical quantization method and taking account of superlattice induced Bragg reflection, we prove that magic zeros arise from the simultaneous quantization of two distinct $k$-space orbits. The flat bands at magic zeros provide a new setting for exploring crystalline fractional quantum Hall physics.