Nearly flat band with Chern number C=2 on the dice lattice

TL;DR

This paper demonstrates the theoretical possibility of nearly flat bands with Chern number C=2 on the dice lattice, which could lead to quantum anomalous Hall effects and exotic fractional quantum Hall states in certain heterostructures.

Contribution

It introduces a simple tight-binding model on the dice lattice showing nearly flat bands with C=2, and discusses their potential realization and topological properties.

Findings

Nearly flat bands with C=2 can exist on the dice lattice.

Rashba spin-orbit coupling preserves flatness while separating bands.

Interactions can induce ferromagnetism and split bands into C=±2 states.

Abstract

We point out the possibility of nearly flat band with Chern number C=2 on the dice lattice in a simple nearest-neighbor tightbinding model. This lattice can be naturally formed by three adjacent $(111)$ layers of cubic lattice, which may be realized in certain thin films or artificial heterostructures, such as SrTiO$_3$/SrIrO$_3$/SrTiO$_3$ trilayer heterostructure grown along $(111)$ direction. The flatness of two bands is protected by the bipartite nature of the lattice. Including the Rashba spin-orbit coupling on nearest-neighbor bonds separate the flat bands with others but maintains their flatness. Repulsive interaction will drive spontaneous ferromagnetism on the Kramer pair of flat bands and split them into two nearly flat bands with Chern number $C=\pm 2$. We thus propose that this may be a route to quantum anomalous Hall effect and further conjecture that partial filling of the C=2 band may realize exotic fractional quantum Hall effects.