By Slava V. Rotkin, Shekhar Subramoney
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Extra resources for Applied Physics of Carbon Nanotubes: Fundamentals of Theory, Optics and Transport Devices
4. Phaedon Avouris, Marko Radosavljevi´c and Shalom J. Wind: “Carbon Nanotube Electronics and Optoelectronics”, Chapter 9, in this volume. 5. R. Bruce Weisman: “Fluorescence Spectroscopy of Single-Walled Carbon Nanotubes”, Chapter 8, in this volume. 6. Anand Jagota, Bruce A. Diner, Salah Boussaad, and Ming Zheng: “Carbon Nanotube – Biomolecule Interactions: Applications in Carbon Nanotube Separation and Biosensing”, Chapter 10, in this volume. 7. S. L. W. A. Heller and S. Baik: “The Selective Chemistry of Single Walled Carbon Nanotubes”, Chapter 6, in this volume.
Here we study an extra component of the polarization which is due to the induced charge density. Thus, we need to consider only transitions from the levels above the charge neutrality level, E = 0, and below the Fermi level, E = EF (the shaded area in Fig. 4). Hence, the dipole polarization is proportional to the net charge density σ, and the dipole charge density of the armchair SWNT is given by the following expression: √ 2 3CQ (2πRσA )2 R 2h 2 δσ1 = . 35) log ∝ Ext e h R 32π We single out the term 2πRσA , which is the speciﬁc one–dimensional charge density of the SWNT, ρ, proportional to the external potential and thus to the external ﬁeld, Ext .
Subbands of orbital quantization m = 0, 1 . . 9 are shown from top to bottom in an conduction band (from bottom to top in the valence band). The two closest massless subbands, A and B, have the same m = 10. The upper right inset shows a zoom view of the Fermi point with the opening of a gap in the M–SWNT due to perturbation as described in the text. The lower left inset shows how the gap grows linearly with applied potential. The upper left inset shows IVC for METFET with gate width 15 nm long–range potential [57,58].