Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices

TL;DR

This paper presents a universal method to generate topological quasi-flat bands in 2D materials using line and split graphs of bipartite lattices, highlighting the role of spin-orbit coupling in inducing nontrivial topology.

Contribution

The authors introduce a generic approach to create topological quasi-flat bands from line and split graphs of bipartite lattices, emphasizing the impact of spin-orbit coupling.

Findings

Spin-orbit coupling turns flat bands into topologically nontrivial quasi-flat bands.

Non-degenerate flat bands with certain symmetries lead to topological quasi-flat bands.

Degenerate flat bands can be made topologically nontrivial with appropriate SOC potential.

Abstract

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to construct two-dimensional (2D) topological quasi-flat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasi-flat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or $C_2$ symmetry and is non-degenerate, then the resulting quasi-flat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists an SOC potential such that the resulting quasi-flat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasi-flat bands in 2D crystalline materials and meta-materials.