Multiple gaps in the tight-binding band of a pentagonal lattice

TL;DR

This paper analytically investigates the electronic band structure of a pentagonal lattice with irregular pentagons, revealing multiple band-gaps that could lead to novel electronic properties.

Contribution

It provides exact solutions for the tight-binding Hamiltonian of an irregular pentagonal lattice, identifying multiple band-gaps and their potential implications.

Findings

Four distinct band-gaps identified

Two indirect band-gaps at Harrison point

Analytic expressions for dispersion relations

Abstract

Multiple gaps in the tight-binding band of a pentagonal lattice are found. Unlike the Cairo pentagonal lattice this lattice is made of irregular pentagons with arms of different lengths. The tight-binding Hamiltonian is exactly solved to obtain analytic expressions of dispersion relations and eigenvectors. Four different band-gaps are identified along with two distinct indirect band-gaps at the Harrison point. Multiple band-gaps in this model may give rise to exotic electronic properties.