Many body corrections for higher optical transitions in semiconducting SWCNTs

In this work, Coulomb effect on determining optical transition energies of semiconducting single wall carbon nanotubes is discussed. Due to their quasi-one-dimensional structure, electron-electron and electron-hole interaction and corresponding self energy and exciton binding energy are important in SWCNTs and the difference between these two energies gives many body effect. Here, at first, a brief review of nature of correction in the conventional single particle electronic picture of SWCNTs to include many body effect in first four optical transitions is presented. Then, many body corrections needed for next three higher optical transitions i.e. 5th, 6th and 7th transitions of semiconducting SWCNTs are investigated. Experimental values of these higher transitions are collected from recent experimental reports so as to explain those data by extending single-particle picture corrected for nanotube curvature and chirality effect along with many body corrections. Our result shows that these three transitions excellently follow the proposed corrected picture with less than 0.5% average absolute error which proves that excitonic behaviour is strong in 5th, 6th and 7th optical transitions of semiconducting SWCNTs unlike 3rd and 4th transitions as reported in some recent works.