Journal
JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
Volume 77, Issue 1, Pages -Publisher
PHYSICAL SOC JAPAN
DOI: 10.1143/JPSJ.77.014707
Keywords
carbon nanotube; graphene; graphite; optical phonon; softening; hardening; effective-mass theory; Aharonov-Bohm effect
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The dependence of the frequency and broadening of optical phonons on carrier concentration is studied in carbon nanotubes within an effective-mass approximation. In metallic nanotubes, the frequency shift exhibits a logarithmic divergence and the broadening vanishes discontinuously when the Fermi level reaches the half of the optical-phonon frequency for the longitudinal mode with displacement in the axis direction, while the transverse mode is not affected. In semiconducting nanotubes, the frequency is raised for both transverse and longitudinal modes, exhibiting a behavior similar to level crossing.
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