Theory of exciton transport in molecular crystals strongly coupled to a cavity: A temperature-dependent variational approach

We present a semianalytical theory for the exciton transport in organic molecular crystals interacting strongly with a single cavity mode. Based on the Holstein-Tavis-Cummings model and the Kubo formula, we derive an exciton mobility expression in the framework of a temperature-dependent variational canonical transformation, which can cover a wide range of exciton-vibration coupling, exciton-cavity coupling, and temperatures. A closed-form expression for the coherent part of the total mobility is obtained in the zeroth order of the exciton-vibration coupling, which demonstrates the significance of vibrationally dressed dark excitons in the determination of the transport mechanism. By performing numerical simulations on both the H- and J-aggregates, we find that the exciton-cavity coupling has significant effects on the total mobility: (1) At low temperatures, there exists an optimal exciton-cavity coupling strength for the H-aggregate at which a maximal mobility is reached, while the mobility in the J-aggregate decreases monotonically with an increase in the exciton-cavity coupling and (2) at high temperatures, the mobility in both types of aggregates get enhanced by the cavity. We illustrate the above-mentioned low-temperature optimal mobility observed in the H-aggregate by using realistic parameters at room temperature.