Specific features of the $\pi$-electron spectrum of narrow achiral $(2m,m)$ nanoribbons

Abstract

On the basis of the Su-Schrieffer-Heeger-H\"uckel-type Hamiltonian, we consider the tight-binding eigenvalue problem for a sequence of pyrene molecules forming a narrow $(2m,m)$ graphene nanoribbon. Specific features of the corresponding dispersion relation are analyzed and illustrated with several examples. It is shown that the $\pi$-electron spectrum of the pyrene oligomer includes local states, in contrast to the spectrum of linear acene, which consists only of extended states. We analyze and illustrate the difference in the behavior of the electron density distribution for extended and local electronic states. Explicit analytic expressions for the Green's function coefficients of the pyrene molecule are also presented.