  Auger-ionized carriers in a one-dimensional semiconductor are predicted to
result in a strong band-gap renormalization. Isolated single-walled carbon
nanotubes (SWCNT) under high-intensity laser irradiation exhibit strong
nonlinear photoluminescence (PL) due to exciton-exciton annihilation (EEA). The
presence of exciton disassociation during the rapid Auger-ionization caused by
EEA would lead to a strong nonlinear absorption. By simultaneously measuring
SWCNT PL and optical absorption of isolated SWCNT clusters in the PL saturation
regime, we give evidence that Auger-ionized excitons do not disassociate but
remain bound.
