Diffusion-limited exciton-exciton annihilation in single-walled carbon nanotubes: A time-dependent analysis

TL;DR

This paper presents a time-dependent theoretical and simulation study of diffusion-limited exciton-exciton annihilation in single-walled carbon nanotubes, explaining photoluminescence saturation at high exciton densities.

Contribution

It introduces an exact analytical model including radiative decay and validates it with Monte Carlo simulations, providing new insights into exciton dynamics in SWNTs.

Findings

Reproduces photoluminescence saturation behavior at high exciton densities.

Validates analytical model with Monte Carlo simulations.

Suggests low temperature and magnetic field conditions to achieve high excitonic densities.

Abstract

To provide physical insight into the recently observed photoluminescence saturation behaviors in single-walled carbon nanotubes implying the existence of an upper limit of exciton densities, we have performed a time-dependent theoretical study of diffusion-limited exciton-exciton annihilation in the general context of reaction-diffusion processes, for which exact treatments exist. By including the radiative recombination decay as a Poissonian process in the exactly-solvable problem of one-dimensional diffusion-driven two-particle annihilation, we were able to correctly model the dynamics of excitons as a function of time with different initial densities, which in turn allowed us to reproduce the experimentally observed photoluminescence saturation behavior at high exciton densities. We also performed Monte Carlo simulations of the purely stochastic, Brownian diffusive motion of one-dimensional excitons, which validated our analytical results. Finally, we consider the temperature-dependence of this diffusion-limited exciton-exciton annihilation and point out that high excitonic densities in SWNTs could be achieved at low temperature in an external magnetic field.