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Temperature Dependence of the Band Gap of Semiconducting Carbon Nanotubes
The temperature dependence of the band gap of semiconducting single-wall
carbon nanotubes (SWNTs) is calculated by direct evaluation of electron-phonon
couplings within a ``frozen-phonon'' scheme. An interesting diameter and
chirality dependence of is obtained, including non-monotonic behavior
for certain tubes and distinct ``family'' behavior. These results are traced to
a strong and complex coupling between band-edge states and the lowest-energy
optical phonon modes in SWNTs. The curves are modeled by an analytic
function with diameter and chirality dependent parameters; these provide a
valuable guide for systematic estimates of for any given SWNT.
Magnitudes of the temperature shifts at 300 K are smaller than 12 meV and
should not affect assignments based on optical measurements.Comment: To appear in Phys. Rev. Let