Excitonic and vibronic spectra of Frenkel excitons in a two-dimensional simple latice

Abstract

Excitonic and vibronic spectra of Frenkel excitons (FEs) in a two-dimensional (2D) lattice with one molecule per unit cell have been studied and their manifestation in the linear absorption is simulated. We use the Green function formalism, the vibronic approach (see Lalov and Zhelyazkov [Phys. Rev. B \textbf{75}, 245435 (2007)]), and the nearest-neighbor approximation to find expressions of the linear absorption lineshape in closed form (in terms of the elliptic integrals) for the following 2D models: (a) vibronic spectra of polyacenes (naphthalene, anthracene, tetracene); (b) vibronic spectra of a simple hexagonal lattice. The two 2D models include both linear and quadratic FE--phonon coupling. Our simulations concern the excitonic density of state (DOS), and also the position and lineshape of vibronic spectra (FE plus one phonon, FE plus two phonons). The positions of many-particle (MP-unbound) FE--phonon states, as well as the impact of the Van Hove singularities on the linear absorption have been established by using typical values of the excitonic and vibrational parameters. In the case of a simple hexagonal lattice the following types of FEs have been considered: (i) non-degenerate FEs whose transition dipole moment is perpendicular to the plane of the lattice, and (ii) degenerate FEs with transition dipole moments parallel to the layer. We found a cumulative impact of the linear and quadratic FE--phonon coupling on the positions of vibronic maxima in the case (ii), and a compensating impact in the case (i).