Non-Markovian Quantum-Classical Ratchet for Ultrafast Long-Range Electron-Hole Separation in Condensed Phases

In organic photovoltaic systems, a photogenerated molecular exciton in the donor domain dissociates into a hole and an electron at the donor-acceptor heterojunction, and subsequently separates into free charge carriers that can be extracted as photocurrents. The recombination of the once-separated electron and hole is a major loss mechanism in photovoltaic systems, which controls their performance. Hence, efficient photovoltaic systems need built-in ratchet mechanisms, namely, ultrafast charge separation and retarded charge recombination. In order to obtain insight into the internal working of the experimentally observed ultrafast long-range charge separation and protection against charge recombination, we theoretically investigate a potential ratchet mechanism arising from the combination of quantum delocalization and its destruction by performing numerically accurate quantum-dynamics calculations on a model system. We demonstrate that the non-Markovian effect originating from the slow polaron formation strongly suppresses the electron-transfer reaction back to the interfacial charge-transfer state stabilized at the donor-accepter interface and that it plays a critical role in maintaining the long-range electron-hole separation.

Figure 1

Schematics of the charge separation dynamics. (a) The electron located at the donor-acceptor interface is transferred via quantum delocalization, and long-range charge separation is achieved as a fast process. The backward propagation of the electron is described by the incoherent hopping motion, which is a slow process. Therefore, the recombination is suppressed by the dynamical coherent-incoherent transition. (b) The dynamical transition is caused by the small polaron formation, which is induced by the coupling with the surrounding phonon environment. The timescale of the polaron formation significantly affects the timescale of both the coherent-incoherent transition and the recombination.

Figure 2

Time evolution of the mean electron-hole (e.-h.) distance $⟨L_n{⟩}_t=\sum _{n=1}^{N}n\ell {\rho }_{nn}(t)$ for various values of the small polaron formation time $\tau$.

Figure 3

Time evolution of the statistically averaged collective phonon coordinate associated with the terminal CT site $⟨{\widehat{X}}_{N=10}(t)⟩$ and the time evolution of the electron population at the terminal CT site. The polaron formation time $\tau$ is set to be (a) 10 and (b) 200 fs.