Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
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 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.
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Cite
@article{arxiv.2008.08231,
title = {Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices},
author = {Da-Shuai Ma and Yuanfeng Xu and Christie S. Chiu and Nicolas Regnault and Andrew A. Houck and Zhida Song and B. Andrei Bernevig},
journal= {arXiv preprint arXiv:2008.08231},
year = {2021}
}