# Molecular-orbital representation of generic flat-band models

## TL;DR

This paper introduces a molecular-orbital framework to analyze flat-band models, revealing how band touchings occur due to orbital collapse and providing a method to open gaps by modulating orbitals.

## Contribution

It presents a novel molecular-orbital approach to understand and control flat-band models, applicable with or without translational symmetry.

## Key findings

- Band touching linked to molecular orbital collapse
- Method to gap out flat bands by orbital modulation
- Framework applicable to a wide class of models

## Abstract

We develop a framework to describe a wide class of flat-band models, with and without a translational symmetry, by using "molecular orbitals" introduced in the prior work (HATSUGAI Y. and MARUYAMA I., \textit{EPL}, \textbf{95}, (2011) 20003). Using the molecular-orbital representation, we shed new light on the band-touching problem between flat and dispersive bands. We show that the band touching occurs as a result of collapse, or the linearly dependent nature, of molecular orbitals. Conversely, we can gap out the flat bands by modulating the molecular orbitals so that they do not collapse, which provides a simple prescription to construct models having a finite energy gap between flat bands and dispersive bands.