The trion, a three-body charge-exciton bound state, offers unique opportunities to simultaneously manipulate charge, spin, and excitation in one-dimensional single-walled carbon nanotubes (SWNTs) at room temperature. Effective exploitation of trion quasi-particles requires fundamental insight into their creation and decay dynamics. Such knowledge, however, remains elusive for SWNT trion states, due to the electronic and morphological heterogeneity of commonly interrogated SWNT samples, and the fact that transient spectroscopic signals uniquely associated with the trion state have not been identified. Here, we prepare length-sorted SWNTs and precisely control charge-carrier-doping densities to determine trion dynamics using femtosecond pump–probe spectroscopy. Identification of the trion transient absorptive hallmark enables us to demonstrate that trions (i) derive from a precursor excitonic state, (ii) are produced via migration of excitons to stationary hole-polaron sites, and (iii) decay in a first-order manner. Importantly, under appropriate carrier-doping densities, exciton-to-trion conversion in SWNTs can approach 100% at ambient temperature. Our findings open up possibilities for exploiting trions in SWNT optoelectronics, ranging from photovoltaics and photodetectors to spintronics.
An Approximation in the Quantum-Mechanical Treatment of the Nonrelativistic Three-Body Bound-State Problem
