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Previous transport studies have also shown devices without gaps in the range of gate voltage studied. Observing a gap requires reaching a well-defined charge neutrality point, which may not occur in all devices within the gate voltage range studied because of, for example, doping or disorder.
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Our known-chirality nanotubes require a fabrication procedure (21) which in a number of trials did not produce the clean data seen in our as-grown nanotubes.
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Because of the sensitivity of the exponent on the model used and the general difficulty of accurately estimating it, the agreement to theory may be somewhat fortuitous. For example, a recent study gives an alternative scaling exponent of a, 2 for the gap (26, Nevertheless, our data are described both quantitatively and qualitatively by the theoretical calculations of (10, and the exponent of 1.3 is within the range a, 1 2 of theoretically predicted values for all the theoretical works cited that include long-ranged Coulomb interactions 10-12, 26
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Because of the sensitivity of the exponent on the model used and the general difficulty of accurately estimating it, the agreement to theory may be somewhat fortuitous. For example, a recent study gives an alternative scaling exponent of a = 2 for the gap (26). Nevertheless, our data are described both quantitatively and qualitatively by the theoretical calculations of (10), and the exponent of 1.3 is within the range a = 1 2 of theoretically predicted values for all the theoretical works cited that include long-ranged Coulomb interactions (10-12, 26).
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We acknowledge Micro Nano Laboratory at Caltech and Nanotech at the University of California, Santa Barbara where fabrication was performed. We thank A. Andreev, D. Cobden, M. Garst, L. Glazman, S. Ilani, P. King, K. Le Hur, L. Levitov, G. Refael, and G. Steele for helpful discussions. M.B. and V.V.D. acknowledge the support of the Office of Naval Research, the Sloan Foundation, and the Ross Brown. D.N. was supported by NSF grants DMR-0749220 and DMR-0754613
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We acknowledge Micro Nano Laboratory at Caltech and Nanotech at the University of California, Santa Barbara where fabrication was performed. We thank A. Andreev, D. Cobden, M. Garst, L. Glazman, S. Ilani, P. King, K. Le Hur, L. Levitov, G. Refael, and G. Steele for helpful discussions. M.B. and V.V.D. acknowledge the support of the Office of Naval Research, the Sloan Foundation, and the Ross Brown. D.N. was supported by NSF grants DMR-0749220 and DMR-0754613.
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