Excitonic states of single-walled carbon nanotubes (SWNTs) have usually been calculated using many-body perturbation theories or mean field approaches because a large number of sites cannot be considered within an exact diagonalization (ED) calculation based on the Hubbard model. We use a small crystal approach and show that, for the π structure of nanotubes, an ED calculation is possible. We apply this approach to small-diameter SWNTs and the results show that a crossing of the first bright state with the second excited states occurs when U, the correlation parameter of the Hubbard model, equals 4t, where t is the hopping integral. Two or three strong two-photon absorption (TPA) states are found at energies above the first bright state for U/t≤3. Beyond this value, these states become relevant for TPA below the first bright state. A number of dark states are always calculated below the first bright state at energies that, in the intermediate coupling regime, are of the order of tens to hundreds of meV. This result seems to be consistent with recent experiments.
Exact diagonalization of Hubbard models for the optical properties of single-wall carbon nanotubes
ALFONSI, JESSICA;MENEGHETTI, MORENO
2010
Abstract
Excitonic states of single-walled carbon nanotubes (SWNTs) have usually been calculated using many-body perturbation theories or mean field approaches because a large number of sites cannot be considered within an exact diagonalization (ED) calculation based on the Hubbard model. We use a small crystal approach and show that, for the π structure of nanotubes, an ED calculation is possible. We apply this approach to small-diameter SWNTs and the results show that a crossing of the first bright state with the second excited states occurs when U, the correlation parameter of the Hubbard model, equals 4t, where t is the hopping integral. Two or three strong two-photon absorption (TPA) states are found at energies above the first bright state for U/t≤3. Beyond this value, these states become relevant for TPA below the first bright state. A number of dark states are always calculated below the first bright state at energies that, in the intermediate coupling regime, are of the order of tens to hundreds of meV. This result seems to be consistent with recent experiments.Pubblicazioni consigliate
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