Flat bands with non-trivial topology in three dimensions

TL;DR

This paper presents a model for 3D electrons with nearly flat bands exhibiting non-trivial topology, suggesting potential for a 3D fractional topological insulator driven by electron interactions.

Contribution

It introduces a simple 3D model combining hopping and spin-orbit coupling to realize flat bands with non-trivial Z2 topology, a novel theoretical development.

Findings

Flat bands are separated by a large bandgap from other bands.

The model indicates possible formation of a 3D fractional topological insulator.

Potential for interaction-driven topological phases in 3D materials.

Abstract

We construct a simple model for electrons in a three-dimensional crystal where a combination of short-range hopping and spin-orbit coupling results in nearly flat bands characterized by a non-trivial Z2 topological index. The flat band is separated from other bands by a bandgap much larger than the bandwidth. We discuss the fate of the many-body ground state of electrons in the flat band in the presence of repulsive interactions at partial filling and conjecture that it may become a three-dimensional fractional topological insulator if conventional magnetic instabilities can be avoided.