Theory of Two-Photon Absorptions in Graphene Fragments

Electron-electron correlations in graphene is currently an active field of research [1-3]. The carbon atoms in graphene have the same sp$^2$ hybridization as in strongly correlated $\pi$-conjugated polymer systems. The low energy behavior in graphene however appears to be reasonably described within the one-electron Dirac massless fermions model. Historically, the occurrence of the lowest two-photon state {\it below} the optical one-photon state provided the strongest proof for strong electron correlations in linear polyenes [4]. We systematically study the Coulomb interaction effects on the ground state and nonlinear absorptions in graphene fragments as a function of system size, beginning from the smallest stable fragment coronene. We report high order calculations of one- vs two-photon spin singlet and triplet states, in coronene, hexabenzocoronene and other molecular fragments that clearly indicate the strong role of electron-electron interactions. We will discuss the implications of our work on molecular systems for the thermodynamic limit of graphene. \\[4pt] [1] Siegel David A.; et al., PNAS, v108, 28, 11365-11369 (2011)\\[0pt] [2] Gr\"onqvist J. H.; et al., arXiv: 1107.5653v1\\[0pt] [3] Uchoa B.; et al., arXiv: 1109.1577v1\\[0pt] [4] Ramasesha S.; et al., J. Chem. Phys. 80, 3278 (1984)