Designing single and degenerate flat bands in the kagome lattice with long-range hopping

TL;DR

This paper explores how tuning long-range hopping in the kagome lattice can create and control flat bands, with implications for electronic structure design and optical properties.

Contribution

It demonstrates the creation of single and degenerate flat bands through specific long-range hopping parameters in the kagome lattice.

Findings

Degenerate flat bands can be engineered on the b3 - M line.

Flat bands lead to sharp peaks in optical conductivity.

Conditions for flat band realization are detailed.

Abstract

We investigate the electronic structure of the kagome lattice model with first, second, and two kinds of third nearest-neighbor hoppings. We reveal that by tuning the third nearest-neighbor hoppings, not only single flat band but also degenerate flat band can be created on the \Gamma - M line. We provide the detailed conditions to realize them. The coexistence of these bands can be almost realized near the fundamental band gap in graphene with triangular defects in a superhoneycomb arrangement. Furthermore, due to these flat bands, several sharp peaks appear in the optical conductivity. Our results strongly indicate that long-range electron hopping has a new possibility for designing electronic structures.