Journal
PHYSICAL REVIEW B
Volume 105, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.105.085128
Keywords
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Funding
- National Natural Science Foundation of China [12025407, 11934003, 12147136]
- Chinese Academy of Sciences [XDB330301]
- China Post-doctoral Science Foundation [2021M700163]
- Guangdong Basic and Applied Basic Research Foundation [2021A1515110466]
- U.S. DOE-BES [DE-FG02-04ER46148]
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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.
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.
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