[Paper Review] Incoherent charge transport in an organic polariton condensate

M. Ahsan Zeb, Peter Kirton+1 more|arXiv (Cornell University)|Apr 21, 2020

Strong Light-Matter Interactions4 citations

TL;DR

This paper investigates how strong matter-light coupling and polariton condensation in organic materials modify incoherent charge hopping transport. Using a model of Frenkel excitons with vibrational dressing, it shows that hopping rates can be exponentially sensitive to cavity detuning and condensate density—enabling up to two orders of magnitude enhancement or suppression of transport—due to changes in vibrational overlap with charged states.

ABSTRACT

We study how polariton condensation modifies charge transport in organic materials. In typical organic materials, charge transport proceeds via incoherent hopping. We therefore provide an approach to determine how the rate and final state of this hopping process is affected by strong matter-light coupling and polariton condensation. We show how the hopping process may create excitations when starting from a state with a finite excitation density. That is, how hopping can change the state of a lower polariton condensate by creating upper polaritons, optically inactive excitonic dark states, or by exciting vibrational sidebands. While the matrix elements for these processes can be large, for typical materials at room temperature, such excitations are suppressed by thermal factors, and ground state processes dominate. We thus study how the ground state hopping rate depends on condensate density, matter-light coupling, and cavity photon detuning. All these factors change the vibrational configuration associated with the optically active molecules, which can enhance or suppress hopping by increasing or decreasing the vibrational overlap with the state of a charged molecule. We show that hopping rates can be exponentially sensitive to detuning and condensate density, allowing an increase or decrease of hopping rate by two orders of magnitude.

Motivation & Objective

• To understand how polariton condensation and strong light-matter coupling affect incoherent charge transport in organic semiconductors.
• To determine how hopping processes are modified when starting from a lower polariton condensate, including transitions to upper polaritons, dark excitons, or vibrational sidebands.
• To quantify the dependence of hopping rates on condensate density, matter-light coupling strength, and cavity photon detuning.
• To assess the role of thermal factors in suppressing non-ground-state transitions despite large matrix elements.
• To provide a theoretical framework for designing electrically driven organic polariton condensates with tunable charge transport.

Proposed method

• Models organic molecules using a Frenkel exciton picture with strong vibrational dressing, incorporating phonon modes via a Holstein-type coupling.
• Introduces a hopping operator that couples charged states to polariton and vibrational states, derived from the Hamiltonian of the hybridized system.
• Uses the HTC (Holstein-Tavis-Cummings) model to describe the coupled system of excitons, photons, and phonons, with eigenstates and energies computed numerically.
• Calculates transition matrix elements between initial and final states, including upper polaritons, dark excitons, and vibrational sidebands, using density matrix formalism.
• Evaluates spectral weights and transition probabilities via trace operations on density matrices, with fitting parameters for the reduced density matrix of the ground state.
• Analyzes the dependence of hopping rates on detuning and excitation density by computing the conditional displacement, frequency, and electronic state probability from Gaussian fits to the density matrix.

Experimental results

Research questions

• RQ1 How does the presence of a lower polariton condensate modify the rate and final state of incoherent charge hopping in organic materials?
• RQ2 What are the dominant final states accessible via hopping from a condensate, and how do their matrix elements compare?
• RQ3 To what extent are non-ground-state transitions (e.g., to upper polaritons or vibrational sidebands) suppressed at room temperature?
• RQ4 How do the hopping rates depend on the matter-light coupling strength, cavity detuning, and condensate density?
• RQ5 Can the hopping rate be tuned significantly via external control of detuning or excitation density, and by how much?

Key findings

• Hopping from a lower polariton condensate can create upper polaritons, dark excitonic states, or vibrational sidebands, though matrix elements for these are often suppressed in the thermodynamic limit.
• At room temperature, thermal factors strongly suppress non-ground-state transitions, making ground state hopping the dominant process.
• The hopping rate exhibits exponential sensitivity to cavity detuning and condensate density, allowing for up to a two-order-of-magnitude increase or decrease in rate.
• Condensate density and detuning alter the vibrational configuration of optically active molecules, thereby modifying the vibrational overlap with charged states and tuning the hopping rate.
• The conditional displacement parameter $\lambda_{\sigma}$ and electronic state probability $p_{\sigma}$ evolve non-trivially with excitation density and detuning, with $p_{\uparrow} \to 1/2$ in the high-density limit.
• The vibrational frequency $\omega_{v,\sigma}$ shows only weak dependence on detuning and excitation density, indicating minimal broadening of the probability distribution.