Temperature Dependence of the Band Gap of Semiconducting Carbon Nanotubes

TL;DR

This paper calculates how the band gap of semiconducting carbon nanotubes changes with temperature, revealing diameter and chirality effects, and provides models for estimating these shifts.

Contribution

It introduces a direct evaluation method for temperature-dependent band gaps in SWNTs, highlighting complex coupling effects and providing analytic models for practical estimates.

Findings

Temperature shifts at 300 K are smaller than 12 meV.

Band gap dependence on temperature shows non-monotonic and family behaviors.

Strong coupling between band-edge states and optical phonons influences $E_g(T)$.

Abstract

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 $E_g(T)$ 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 $E_g(T)$ curves are modeled by an analytic function with diameter and chirality dependent parameters; these provide a valuable guide for systematic estimates of $E_g(T)$ for any given SWNT. Magnitudes of the temperature shifts at 300 K are smaller than 12 meV and should not affect $(n,m)$ assignments based on optical measurements.