Sorting single-chirality enantiomers is the ultimate goal for single-wall carbon nanotube (SWCNT) separation. In this work, aqueous two-phase extraction (ATPE) is used to obtain highly purified (>80%) left- and right-handed (6,5) SWCNTs with limited experimental steps. The optimized surfactant conditions are presented, and analytical ultracentrifugation (AUC) and near-infrared photoluminescence (PL) measurements are used to examine the surfactant wrapping and partition coefficient change conditions (PCCCs) required for separation. Our study provides valuable insights into the underlying mechanisms behind surfactant-assisted SWCNT separations and facilitates the use of SWCNT enantiomers in fundamental studies and applications in the future. [Display omitted] • Single-wall carbon nanotube enantiomers are prepared using a simple aqueous two-phase extraction method. • Different co-surfactant systems are examined to optimize the separation results. • Surfactant wrapping on both right- and left-handed (6,5) SWCNTs are investigated by analytical ultracentrifugation. • The partition coefficient change conditions are measured for handedness sorting. [ABSTRACT FROM AUTHOR]