Robust Flat Bands with Tunable Energies in Honeycomb Superlattices

TL;DR

This paper analytically demonstrates that flat bands in honeycomb superlattices can have their energies tuned by longer-range hopping perturbations, with wave functions constructed from standing waves ensuring robustness.

Contribution

It provides an analytical derivation showing how flat band energies in honeycomb superlattices are tunable via longer-range hoppings, highlighting the robustness of these flat bands.

Findings

Flat band energies are tunable by longer-range hopping.

Wave functions are constructed from standing waves on honeycomb edges.

Flat bands are robust against long-range perturbations.

Abstract

Flat bands in lattice models have provided useful platforms for studying strong correlation and topological physics. Recently, honeycomb superlattices have been shown to host flat bands that persist in the presence of local perturbations respecting lattice symmetries. We analytically derive the flat band energies in the presence of longer range hopping and find that the energies of flat bands are tunable by these perturbations. In real space, the wave function is constructed from standing waves on each honeycomb edge, allowing the construction of plaquette and loop eigenstates due to destructive interference in real space that give rise to the flat bands robust against long range hoppings.