Abstract
Firstly, the multi-band semiconductor Bloch equations (MB-SBE) for the quantum optical properties are reformulated in momentum space to investigate the influence of spin-orbit couplings (SOCs) on the linear optical response of semiconducting carbon nanotubes (SCNTs). One remarkable feature in numerical results is that a new low-strength peak appears at the lower-excited energy position than the peak E11. Comparing the data with/without SOCs, obviously, this new lowest-excited peak originates from the brightened spin-triplet exciton E11T, which has higher binding energy than the spin-singlet exciton E11S. For eight SCNTs with small radius, further comparison shows that the appearance and strength of this new peak E11T is dependent on the chiral of SCNTs. For (n, 1) tubes belonging to the family ν = +1 the effect of SOCs on this new brightened peak E11T is stronger relative to other SCNTs having the approximative strength of SOCs.
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