On the graphene Hamiltonian operator

Conca, C.; Orive, R.; Martín, J. San; Solano, V.

Abstract

We solve a second-order elliptic equation with quasi-periodic boundary conditions defined on a honeycomb lattice that represents the arrangement of carbon atoms in graphene. Our results generalize those found by Kuchment and Post (Commun Math Phys 275(3):805-826, 2007) to characterize not only the stability but also the instability intervals of the solutions. This characterization is obtained from the solutions of the energy eigenvalue problem given by the lattice Hamiltonian. We employ tools of the one-dimensional Floquet theory and specify under which conditions the one-dimensional theory is applicable to the structure of graphene. The systematic study of such stability and instability regions provides a tool to understand the propagation properties and behavior of the electrons wavefunction in a hexagonal lattice, a key problem in graphene-based technologies.

Más información

Título según WOS: On the graphene Hamiltonian operator
Título según SCOPUS: On the graphene Hamiltonian operator
Título de la Revista: COMPUTATIONAL & APPLIED MATHEMATICS
Volumen: 39
Número: 1
Editorial: SPRINGER HEIDELBERG
Fecha de publicación: 2020
Idioma: English
DOI:

10.1007/s40314-019-0986-2

Notas: ISI, SCOPUS