Exciton Lifetime Paradoxically Enhanced by Dissipation and Decoherence: Toward Efficient Energy Conversion of a Solar Cell

Energy dissipation and decoherence are at first glance harmful to acquiring the long exciton lifetime desired for efficient photovoltaics. In the presence of both optically forbidden (namely, dark) and allowed (bright) excitons, however, they can be instrumental, as suggested in photosynthesis. By simulating the quantum dynamics of exciton relaxations, we show that the optimized decoherence that imposes a quantum-to-classical crossover with the dissipation realizes a dramatically longer lifetime. In an example of a carbon nanotube, the exciton lifetime increases by nearly 2 orders of magnitude when the crossover triggers a stable high population in the dark excitons.

Figure 1

Dissipative quantum model of excitons in a semiconducting single-walled carbon nanotube with (6,5) chirality. Both the bright exciton generation and the charge recombination result from the dipole coupling with photons with the same strength $g$. The photons are dissipated to the environment with the rate $\kappa$. The bright exciton is coupled with two dark excitons via a phonon continuum.

Figure 2

(a) Time-resolved photoluminescence $L(t)$ and quantum yield $Y(t)$. The parameter for radiative dissipation to the environment is fixed at ${\kappa }^{-1}=10\mathrm{ns}$. The solid red line indicates the triexponential fitting of the numerical result $L_{\text{fit}}(t)$. The time-dependent energy $E(t)\equiv \mathrm{Tr}[\widehat{\rho }(t){\widehat{H}}_S]$ is also plotted in the same figure. (b) Population dynamics of the exciton-photon system with $n_{\mathrm{ph}}(t)\equiv \mathrm{Tr}[\widehat{\rho }(t){\widehat{a}}^{†}\widehat{a}]$ and $n_{r=\mathrm{br},d1,d2}(t)\equiv \mathrm{Tr}[\widehat{\rho }(t){\widehat{b}}_r^{†}{\widehat{b}}_r]$. The shadow region indicates the dwell time ${\tau }_{\text{dwell}}\approx 630\mathrm{ns}$. (c) Time evolution of the von Neumann entropy $S(t)$ and the quantum mutual information $I(t)$.

Figure 3

(a) Time-resolved photoluminescence with several choices of ${\kappa }^{-1}$. The solid red lines indicate the triexponential fitting functions on the numerical results. (b) $\kappa$ dependence of decay constants in the triexponential fitting function. (c) Correlation between ${\tau }_1$ and ${\tau }_2$ for several choices of ${\kappa }^{-1}$ ranging from 10 ps to $1\mu \mathrm{s}$ (black filled circles). The filled square (red) symbols indicate the experimentally measured decay constants for the (6,5) SWCNT reproduced from Ref. [23].

Figure 4

(a),(b) Normalized energy $E/{ϵ}_{\mathrm{br}}$ as a function of time and $\kappa$ for the (6,5) SWCNT model (dissipative system), and for the hypothetical model with the same parameters as those in the dissipative system except for the energy levels, $\hslash {\omega }_{\mathrm{ph}}={ϵ}_{\mathrm{br}}={ϵ}_{d1}={ϵ}_{d2}=1.27\mathrm{eV}$ (nondissipative system). Solid lines indicate the contours of the normalized energy. (c) Energy lifetime ${\tau }_{\mathrm{LT}}$ as a function of $\kappa$ in the dissipative and nondissipative systems. The lifetime is normalized by ${\tau }_{\mathrm{TL}}^{\text{nodark}}=2{\kappa }^{-1}$, which is the lifetime in the system with no dark exciton. The inset shows the normalized lifetime in the dissipative system as a function of $\mathrm{Im}[ϵ({\omega }_{\mathrm{ph}})]=\kappa /{\omega }_{\mathrm{ph}}$.