Tight-binding approach to penta-graphene

TL;DR

This paper develops an effective tight-binding model for penta-graphene, capturing its electronic bands and optical properties, including anisotropic absorption, with analytical solutions and energy-dependent hopping terms.

Contribution

It introduces a novel tight-binding model focusing on $\pi$-orbitals and incorporates energy-dependent hopping and interactions to accurately describe penta-graphene's electronic structure.

Findings

Reproduces the two highest valence bands accurately.

Approximates the two lowest conduction bands with additional interactions.

Predicts large isotropic optical absorption up to 24% at the $\Gamma$-point.

Abstract

We introduce an effective tight-binding model to discuss penta-graphene and present an analytical solution. This model only involves the $\pi$-orbitals of the sp$^2$-hybridized carbon atoms and reproduces the two highest valence bands. By introducing energy-dependent hopping elements, originating from the elimination of the sp$^3$-hybridized carbon atoms, also the two lowest conduction bands can be well approximated - but only after the inclusion of a Hubbard onsite interaction as well as of assisted hopping terms. The eigenfunctions can be approximated analytically for the effective model without energy-dependent hopping elements and the optical absorption is discussed. We find large isotropic absorption of up to 24\% for transitions at the $\Gamma$-point, but the general absorption will show a strongly anisotropic behaviour depending on the linear polarization of the incident light.