Drift of charge carriers in crystalline organic semiconductors

A reciprocal-space formulation of mixed quantum-classical dynamics

We derive a formulation of mixed quantum-classical dynamics for modeling electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. Taking these variables as a Fourier series then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfest's theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum-derivative contributions in addition to the position-derivative terms commonly seen in real space. To illustrate the advantage of the reciprocal-space formulation, we present a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons using a truncated reciprocal-space basis, which is not possible within a real-space formulation.

Bloch Oscillations in Fibonacci lattices: polaron formation

We investigated the dynamics of an electron subjected to a uniform electric field in the scope of a tight-binding electron-phonon interacting approach. We aimed at describing the transport in a one-dimensional lattice in which the on-site energies are distributed according to a Fibonacci sequence. Within this physical picture, we obtained a novel dynamical process with no counterpart in ordered lattices. Our findings showed that in low-disorder limit, the electron performs spatial Bloch oscillations, generating, in the turning points of its trajectory, composite quasi-particles-namely, polarons. When it comes to highly disordered systems, two strongly localized polarons are formed in the region where the oscillating charge is confined, thus propagating excitations that are present in the lattice.

Stationary polaron properties in organic crystalline semiconductors

Polarons play a crucial role in the charge transport mechanism when it comes to organic molecular crystals. The features of their underlying properties - mostly the ones that directly impact the yield of the net charge mobility - are still not completely understood. Here, a two-dimensional Holstein-Peierls model is employed to numerically describe the stationary polaron properties in organic semiconductors at a molecular scale. Our computational protocol yields model parameters that accurately characterize the formation and stability of polarons in ordered and disordered oligoacene-like crystals. The results show that the interplay between the intramolecular (Holstein) and intermolecular (Peierls) electron-lattice interactions critically impacts the polaron stability. Such an interplay can produce four distinct quasi-particle solutions: free-like electrons, metastable polarons, and small and large polarons. The latter governs the charge transport in organic crystalline semiconductors. Regarding disordered lattices, the model takes into account two modes of static disorder. Interestingly, the results show that intramolecular disorder is always unfavorable to the formation of polarons whereas intermolecular disorder may favor the polaron generation in regimes below a threshold for the electronic transfer integral strength.

Crossover from hopping to band-like transport in crystalline organic semiconductors: The effect of shallow traps

We show a crossover from coherent to incoherent behavior of charge transport in crystalline organic semiconductors by considering the effect of shallow traps within the dynamical disorder model. The mixed quantum-classical system is treated by the Ehrenfest dynamics method complementing with instantaneous decoherence corrections and energy relaxation, which has been shown to properly make the system close to equilibrium. The shallow traps, which are incorporated by a static diagonal disorder, are shown to play a central role in the crossover. Temperature dependence of charge-carrier mobility is shown to be changed from being negative to positive with the strength of shallow traps increasing, which implies that there is a crossover from hopping to band-like transport. A higher electric field helps to recover the charge-carrier band-like transport behavior from the traps-caused hopping transport. In this way, a unified physical picture of the charge transport in crystalline organic semiconductors is proposed.

Polaron dynamics with off-diagonal coupling: beyond the Ehrenfest approximation

Treated traditionally by the Ehrenfest approximation, the dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling is investigated in this work using the Dirac-Frenkel time-dependent variational principle with the multi-D₂Ansatz. It is shown that the Ehrenfest method is equivalent to our variational method with the single D₂Ansatz, and with the multi-D₂Ansatz, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-D₂Ansatz is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation. The results demonstrate that the exciton momentum distributions in the steady state are determined by a combination of the transfer integral and the off-diagonal coupling strength, independent of the excitonic initial conditions. We also probe the effect of the transfer integral and the off-diagonal coupling on exciton transport in both real and reciprocal space representations. Finally, the variational method with importance sampling is employed to investigate temperature effects on exciton transport using the multi-D₂Ansatz, and it is demonstrated that the variational approach is valid in both low and high temperature regimes.

A map of high-mobility molecular semiconductors

The charge mobility of molecular semiconductors is limited by the large fluctuation of intermolecular transfer integrals, often referred to as off-diagonal dynamic disorder, which causes transient localization of the carriers' eigenstates. Using a recently developed theoretical framework, we show here that the electronic structure of the molecular crystals determines its sensitivity to intermolecular fluctuations. We build a map of the transient localization lengths of high-mobility molecular semiconductors to identify what patterns of nearest-neighbour transfer integrals in the two-dimensional (2D) high-mobility plane protect the semiconductor from the effect of dynamic disorder and yield larger mobility. Such a map helps rationalizing the transport properties of the whole family of molecular semiconductors and is also used to demonstrate why common textbook approaches fail in describing this important class of materials. These results can be used to rapidly screen many compounds and design new ones with optimal transport characteristics.