Moir\'e Landau fans and magic zeros

TL;DR

This paper investigates how moiré superlattices in magnetic fields create flat Chern bands at specific 'magic zero' magnetic fields, offering new avenues for fractional quantum Hall physics exploration.

Contribution

It introduces the concept of 'magic zeros' where moiré systems exhibit flat Chern bands, and develops a semiclassical method to explain their origin.

Findings

Flat Chern bands occur at discrete 'magic zero' magnetic fields.

Magic zeros result from simultaneous quantization of two distinct k-space orbits.

These flat bands enable new studies of fractional quantum Hall effects in moiré systems.

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.