Dirac electron under periodic magnetic field: Platform for fractional Chern insulator and generalized Wigner crystal

TL;DR

This paper proposes a platform using 2D Dirac materials under periodic magnetic fields to realize flat topological bands, enabling fractional Chern insulators and Wigner crystals with potential applications in quantum materials.

Contribution

It introduces a method to create flat, topologically protected bands in Dirac materials via periodic magnetic fields, leading to new fractional and crystalline phases.

Findings

Fractional Chern insulators emerge at specific fillings with generalized Laughlin states.

Flat bands remain at zero energy, dispersionless and topologically protected.

Potential formation of generalized Wigner crystals under nonuniform magnetic fields.

Abstract

We propose a platform for flat Chern band by subjecting two-dimensional Dirac materials -- such as graphene and topological insulator thin films -- to a periodic magnetic field, which can be created by the vortex lattice of a type-II superconductor. As a generalization of the $n=0$ Landau level, the flat band of Dirac fermion under a nonuniform magnetic field remains at zero energy, exactly dispersionless and topologically protected, while its local density of states is spatially modulated due to the magnetic field variation. In the presence of short-range repulsion, we find fractional Chern insulators emerge at filling factors $\nu=1/m$, whose ground states are generalized Laughlin wavefunctions. We further argue that generalized Wigner crystals may emerge at certain commensurate fillings under a highly nonuniform magnetic field in the form of a flux line lattice.