Revisiting Flat bands and localization

TL;DR

This paper explores the properties of flat band systems using molecular orbital models, demonstrating their robustness under randomness and providing numerical examples across various lattice structures.

Contribution

It introduces random molecular orbital models for flat band systems, preserving degeneracy under randomness and extending flat band constructions to higher-dimensional lattices.

Findings

Flat bands can be modeled with molecular orbitals that remain degenerate despite randomness.

Numerical demonstrations show flat band features in sawtooth and hyper-Pyrochlore lattices.

The approach extends flat band concepts to arbitrary dimensions.

Abstract

Flat bands imply lack of itinerancy due to some constraints that, in principle, results in anomalous behaviors with randomness. By a molecular orbital (MO) representation of the flat band systems, random MO models are introduced where the degeneracy due to the flat bands is preserved even with randomness. The zero modes of the chiral symmetric system with sublattice imbalance belong to the class. After explaining the generic flat band construction by MOs, several examples are discussed with numerical demonstration as sawtooth lattice in one dimension and hyper-Pyrochlore lattice in any $d$-dimensions that extends the Kagome ($d=2$) and Pyrochlore ($d=3$) lattices to general dimensions.