Orbital design of flat bands in non-line-graph lattices via line-graph wave functions

Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive interference of Bloch wave functions encoded in only 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 theory, we demonstrate that the underlying wave-function 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 singles orbital mandated in graph theory and generic lattice models.

Automated summary

This article introduces a generic atomic/molecular orbital design principle for flat bands (FBs) in non-LG lattices, demonstrating the transformation of wave-function symmetry of FBs in a LG lattice into atomic/molecular orbital symmetry in a non-LG lattice. The designed orbitals faithfully reproduce the corresponding lattice symmetries in three different 2D non-LG lattices, and systematic design of FBs with a high Chern number is also achieved based on the same principle.