Fractional quantum Hall effect in the absence of Landau levels

TLDR

Topological phenomena with fractional excitations, such as the fractional quantum Hall effect, traditionally arise when electrons occupy Landau levels. This work reports the discovery of the FQHE in a system lacking Landau levels, specifically in an interacting fermion model. The study employs a topologically nontrivial flat‑band Hamiltonian on a checkerboard lattice as the non‑interacting part, adding nearest‑ and next‑nearest‑neighbor repulsions to drive interactions. At 1/3 filling the Fermi‑liquid state becomes unstable to the FQHE under nearest‑neighbor repulsion, while at 1/5 filling a next‑nearest‑neighbor repulsion is required when the nearest‑neighbor interaction is not too strong, and the authors map the resulting phase diagram and confirm characteristic signatures of these novel states.

Abstract

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the FQHE in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically nontrivial flat band model on the checkerboard lattice \cite{sun}. In the presence of nearest-neighboring repulsion ($U$), we find that at 1/3 filling, the Fermi-liquid state is unstable towards FQHE. At 1/5 filling, however, a next-nearest-neighboring repulsion is needed for the occurrence of the 1/5 FQHE when $U$ is not too strong. We demonstrate the characteristic features of these novel states and determine the phase diagram correspondingly.