Quantum-Classical Study of Charge Transport in Organic Semiconductors with Multiple Low-Frequency Vibrational Modes

Abstract

Building on the recent success of a quantum-classical method for computing transport properties in the Holstein model with a single phonon mode [Phys. Rev. B ${\bf 111}$, L161105 (2025)], we now assess its reliability in more realistic scenarios involving multiple phonon modes in the Holstein model, as well as single- and multi-mode Peierls models. For parameters relevant to the prototypical organic semiconductor rubrene, we compute the frequency-dependent charge mobility and find excellent agreement with results from the state-of-the-art hierarchical equations of motion method. These results show that the method, previously validated only for the single-mode Holstein model, preserves quantitative accuracy in substantially more complex and material-relevant regimes. Our microscopic approach complements the phenomenological transient-localization theory and is readily applicable to realistic electron-phonon Hamiltonians.

Figures (3)

• Figure 1: (a) Time-dependent diffusion constant and (b) frequency-dependent mobility for (c) several distributions of coupling constants for the Holstein model. (d) The corresponding mode-dependent dynamic disorder standard deviation. Here $T=1$, $\omega_0 = 1/3$ and $\lambda^{\mathrm{H}}=0.5$.
• Figure 2: Comparison of the QC (dashed line) and HEOM (solid lines) time-dependent diffusion constant for the Peierls model at $T=0.175$, $\omega_0 = 0.044$, $\lambda^{\mathrm{P}}=0.336$. The inset shows the relative increase of the electron kinetic energy with the propagation time in QC equations.
• Figure 3: (a) Time-dependent diffusion constant and (b) frequency-dependent mobility for (c) several distributions of coupling constants for the Peierls model. (d) The corresponding mode-dependent dynamic disorder standard deviation. Here $T=0.175$, $\omega_0 = 0.044$ and $\lambda^{\mathrm{P}}=0.336$.