Abstract
We report on excitonic spectra of armchair graphene nanoribbons (AGNRs) obtained from a full many-body exact diagonalization of the Hubbard model within low and intermediate correlation regimes and with a complete characterization of the spin multiplicity of the calculated eigenstates. Our results allow us to group these systems into three different families according to the sequence of the one- and two-photon allowed states and the magnitude of the respective optical oscillator strengths within the investigated correlation regime. The oscillator strengths for the one-photon allowed transitions are found to be lower than those obtained previously for zigzag semiconducting single-walled carbon nanotubes, pointing out a qualitatively different photophysical behaviour of AGNRs.
Highlights
GW–Bethe–Salpeter-based methods [26, 27], Pariser–Parr–Pople effective model Hamiltonians for π -electrons incorporating longer-range Coulomb interactions [28, 29] and Hubbard modelbased approaches, either within the mean-field approximation applied to investigate the edgestate in zigzag ribbons [17] or with configuration interaction calculations applied to both armchair and zigzag edge geometry [30]
For semiconducting armchair graphene nanoribbons (AGNRs) belonging to the N = 3p + 1 family, namely 4- and 7-AGNRs, in the very low correlation regime U/t 1, both one-photon active states ES11 and ES22 occur at lower energies than the two-photon active states, whereas for the semiconducting N = 3p (6-AGNR) the ES22 transition is found above the first twophoton active transition energy
We have investigated the excitonic structure of pristine AGNRs of width less than 10 nm by exact diagonalization (ED) of the Hubbard model for several two-leg ladder models mimicking ribbons with 4 N 7 dimer lines and with light polarized along the ribbon edges
Summary
GW–Bethe–Salpeter-based methods [26, 27], Pariser–Parr–Pople effective model Hamiltonians for π -electrons incorporating longer-range Coulomb interactions [28, 29] and Hubbard modelbased approaches, either within the mean-field approximation applied to investigate the edgestate in zigzag ribbons [17] or with configuration interaction calculations applied to both armchair and zigzag edge geometry [30]. We choose two-leg ladder models mimicking AGNRs of different widths and consider optical transitions with light polarization along the nanoribbon edges In this way, we sample a set of k-points equivalent to those considered for the van Hove singularities in the electronic DOS and longitudinal optical matrix elements of zigzag SWNTs. By performing ED calculations in the low–intermediate correlation regime for different values of the total spin Sz, we are able to provide a detailed description of the lowest-energy optically active (bright) and inactive (dark) excitons within a full many-body picture, which has not been presented so far in the GNR literature. Our results for the allowed transitions and related optical oscillator strength versus U/t point out a qualitatively different behaviour than that found for semiconducting SWCNTs and allow us to group AGNRs into three different families according to the sequence of oneand two-photon transitions in the electronic spectrum and the magnitude of the corresponding optical matrix elements within the considered correlation regime
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