Tight-binding dispersion of the prismatic pentagonal lattice

TL;DR

This paper analytically solves the tight-binding Hamiltonian for the prismatic pentagonal lattice, revealing its unique dispersion relations, density of states, and the absence of a band gap or Dirac cones, with notable van Hove singularities.

Contribution

It provides the first exact analytical dispersion relations and eigenvectors for the prismatic pentagonal lattice, distinguishing it from Cairo pentagon structures.

Findings

Six dispersion relations derived analytically.

No band gap or Dirac cone observed.

Presence of two van Hove singularities.

Abstract

Tight-binding Hamiltonian on the prismatic pentagonal lattice is exactly solved to obtain the analytic expressions of dispersion relations and eigenvectors. This lattice is made of prismatic pentagon which is different from Cairo pentagon. Six different dispersion relations and total density of states are obtained. Dispersion relations are symmetric about the zero energy at a particular point in the parameter space. Although a large gap is found for the Cairo pentagonal lattice, no gap as well as no Dirac cone is found to appear in the tight-binding band structure for this prismatic pentagonal lattice. Instead, a pair of van Hove singularities has been identified at two different energy values in the band structure.