The Mott-Hubbard Interaction and Exciton Binding Energies in
Semiconducting and Metallic Single-Walled Carbon Nanotubes
S. Mazumdar, D. Psiachos and Z. Wang
Department of Physics, University of Arizona, Tucson, AZ 85721, USA
DFT-based ab initio calculations, and the quantum chemical configuration interaction
method as applied to the molecular Pariser-Parr-Pople (PPP) model, have both been
used to estimate exciton binding energies in semiconducting and metallic single-walled
carbon nanotubes (S-SWCNTs and M-SWCNTs.) Ab initio exciton binding energies for
S-SWCNTs with diameters of 1 nm are 1 eV or even larger. In contrast the PPP exciton
binding energies are 0.3 - 0.4 eV [1], close to what have been estimated from the
experimentally determined energy location of the two-photon exciton above the optical
exciton [2,3]. It has been claimed that the ab initio exciton binding energies are for
single nanotubes, and the experimental quantities reflect screening of Coulomb
interactions in bulk materials. It has also been claimed that in one-dimension the true
exciton binding energies are much larger than the energy difference between the lowest
two-photon state and the optical exciton. We examine both these issues critically, and
conclude that screening affects nonlinear
absorption measurements weakly, and that
the two-photon exciton is indeed close to the
continuum threshold, in agreement with PPP
calculations [3]. We ascribe the discrepancy
between the experimental binding energies
and the ab initio predictions to the difficulty
of treating the Mott-Hubbard interaction
within DFT-based theories.
We discuss M-SWCNTs also within the PPP Fig. 1 Calculated absorption spectrum
model [5]. Standard theories of screening do (red curve) in the E22 region of the (21,21)
not apply to systems with strong short-range M- SWCNT, superimposed on the
Coulomb interactions. As with the experimental data (black dots) [4].
semiconductors, theoretical fits to the experimental absorption spectra in M-SWCNTs
are excellent (see Fig. 1). Our calculated exciton binding energies for M-SWCNTs are
only slightly smaller than in the S-SWCNTs. For the (21,21) NT, we calculate a binding
energy of 0.12 eV for the E22 exciton [4]. We make verifiable predictions about optical
absorptions in M-SWCNTs [5].
References:
[1] Z. Wang, H. Zhao and S. Mazumdar, Phys. Rev. B 75, 195406 (2006).
[2] G. Dukovic et al., Nano Lett. 5, 2314 (2005).
[3] H. Zhao et al., Phys. Rev B 73, 075403 (2006).
[4] F. Wang et al., Phys. Rev. Lett. 99, 227401 (2007).
[5]. Z. Wang, D. Psiachos, R. F. Badilla and S. Mazumdar, J. Phys.: Condens. Matter 21,
095009 (2009)
Corresponding Author: Sumit Mazumdar
Email: sumit@physics.arizona.edu