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Dispersion in Single-Wall Carbon Nanotube Film: An Application of Bogoliubov–Valatin Transformation for Hamiltonian Diagonalization
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  • Chandra Mani Adhikari,
  • Da’Shawn Morris,
  • Thomas Noonan,
  • Tikaram Neupane,
  • Basu Ram Lamichhane,
  • Bhoj Raj Gautam
Chandra Mani Adhikari
Fayetteville State University

Corresponding Author:[email protected]

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Da’Shawn Morris
Fayetteville State University
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Thomas Noonan
Fayetteville State University
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Tikaram Neupane
UNC Pembroke
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Basu Ram Lamichhane
Eckerd College
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Bhoj Raj Gautam
Fayetteville State University
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Abstract

We present a theoretical study on the energy dispersion of an ultrathin film of periodically aligned single-walled carbon nanotubes (SWCNTs) with the help of the Bogoliubov–Valatin transformation. The Hamiltonian of the film is derived using the many-particle green function technique in the Matsubara frequency formalism. The periodic array of SWCNTs is embedded in a dielectric with comparatively higher permittivity than the substrate and the superstrate such that the SWCNT film becomes independent with the axis of quantization but keeps the thickness as the variable parameter making the film neither two-dimensional nor three-dimensional, but transdimensional. It is revealed that the energy dispersion of the SWCNT film is thickness dependent.