Abstract Submitted to the    NANOTUBE'06 Conference:

Excitons in Carbon Nanotubes

Rodrigo B. Capaz ¹, Catalin D. Spataru ², Sohrab Ismail-Beigi ³, Steven G. Louie ⁴

¹ Physics Institute, Universidade Federal do Rio de Janeiro
² Columbia University
³ Yale University
⁴ U. C. Berkeley and Lawrence Berkeley National Laboratory

capaz@if.ufrj.br

XVI. Optical Properties and Optoelectronics

We calculate several properties of excitons in single-wall carbon nanotubes (SWNTs) (binding energies, sizes, optical activities and radiative lifetimes) using a combination of {\it ab initio} and empirical methods. First, we present a theoretical analysis and first-principles calculation of the radiative lifetime of excitons in semiconducting SWNTs. Assuming a thermal occupation of bright and dark exciton bands, we find an effective lifetime of the order of 10 ns at room temperature, in good accord with recent experiments [1]. Second, employing insights and results from the first-principles calculations, we develop an empirical method consisting of a symmetry-based, effective-mass, variational approach with tight-binding wavefuntions. This approach provides exciton binding energies in good agreement with available first-principles results and its simplicity allows calculations for a variety of diameters ($d$) and chiralities. The exciton binding energies present an overall decrease with $1/d$, with strong chirality dependence and family behavior. The exciton sizes scale with $d$, also showing family behavior. We also address the important issue of bright-dark exciton splittings, which are found to decrease as $1/d^2$. Dependence of these properties on the dielectric screening will also be addressed, in the light of recent experimental measurements.\\

[1] C. D. Spataru, S. Ismail-Beigi, R. B. Capaz, and S. G. Louie, Phys. Rev. Lett. 95, 247402 (2005).

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