Orbital Design of Flat Bands in Non-Line-Graph Lattices via Line-Graph Wavefunctions

TL;DR

This paper introduces a universal orbital design principle to create flat bands with specific symmetries and topological properties in non-line-graph lattices, broadening the scope of flat band material design.

Contribution

It develops a linear-combination-of-atomic-orbital theory to systematically design flat bands in non-line-graph lattices with desired symmetries and topological features.

Findings

Designed flat bands in square, trigonal, and hexagonal lattices matching specific lattice symmetries.

Achieved systematic design of high Chern number flat bands.

Expanded the scope of flat band materials beyond simple single-orbital models.

Abstract

Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive interference of Bloch wavefunctions encoded in pure lattice symmetry. Here, we develop a generic atomic/molecular orbital design principle for FBs in non-LG lattices. Based on linear-combination-of-atomic-orbital (LCAO) theory, we demonstrate that the underlying wavefunction symmetry of FBs in a LG lattice can be transformed into the atomic/molecular orbital symmetry in a non-LG lattice. We illustrate such orbital-designed topological FBs in three 2D non-LG, square, trigonal, and hexagonal lattices, where the designed orbitals faithfully reproduce the corresponding lattice symmetries of checkerboard, Kagome, and diatomic-Kagome lattices, respectively. Interestingly, systematic design of FBs with a high Chern number is also achieved based on the same principle. Fundamentally our theory enriches the FB physics; practically it significantly expands the scope of FB materials, since most materials have multiple atomic/molecular orbitals at each lattice site, rather than a single s orbital mandated in graph theory and generic lattice models.