Excitonic and Vibronic Spectra of a Two-Dimensional Graphene-like Molecular Lattice

Abstract

Recently, graphene has shown interesting physical properties with promising applications. In this paper, we study the excitonic and vibronic spectra of Frenkel excitons (FEs) in a two-dimensional hexagonal graphene-like lattice with two identical and nonequivalently positioned molecules per unit cell. The excitonic Hamiltonian and the excitonic levels with transition dipole moments perpendicular to the layer or parallel to it represent the electronic excitations of this hexagonal lattice. The vibronic spectra consist of both types of dipole active FEs plus one or several quanta of intramolecular vibrations coupled with FEs via linear and quadratic coupling. The expressions and numerical simulations of the absorption spectra manifest excitonic, one-particle (bound), and many-particle unbound exciton–phonon states depending on the strength of the linear exciton–phonon coupling as well as Davydov splitting of the vibronic spectra.

Haldane Model and Molecular Excitons’ Spectra

“…In the present communication we connect this model and our previous investigations on excitonic spectra of 2D hexagonal lattices [3][4][5]. Using Haldane model we treat more complicated excitonic problems.…”

“…Practically we treat the problem of FEs spectra with two molecules in unit cell [6,7]. Two types of dipole active FEs exist, notably [5], a) z-excitons with transition dipole perpendicular to the plane; b) xy-excitons with in-plane transition dipole moment.…”

“…Let B Z1 (n) and B Z2 (n) denote the operators of annihilations of FEs on molecule 1(2) of site 𝑛 ⃗⃗⃗ . Hamiltonian of z-excitons in momentum space can be represented as follows [5]: (2) a being the length of hexagonal lattice vectors (𝑎 1 , ⃗⃗⃗⃗⃗ 𝑎 2 ⃗⃗⃗⃗ ) , and…”