2017/08/11 by Susobhan Paul, Asim Kumar Ghosh
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #2D Materials and Applications #Band gap #Chemistry #Condensed matter physics #Crystal structure #Crystallography #Dispersion relation #Electronic band structure #Electronic structure #Empty lattice approximation #Geometry #Graphene research and applications #Hamiltonian (control theory) #Lattice (music) #Mathematics #Particle in a one-dimensional lattice #Pentagon #Physics #Quantum mechanics #Quantum optics and atomic interactions #Reciprocal lattice #Tight binding #cond-mat.mes-hall
paper · pdf · doi:10.1142/s0217979217502733
published as International Journal of Modern Physics B Vol. 31 (2017) 1750273 (10 pages) · 11 pages, single column, 3 figures. arXiv admin note: substantial text overlap with arXiv:1611.06029
openalex publication_date 2017/08/11 · arxiv created 2017/09/12 · arxiv updated 2017/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.