Predicting polaron mobility in organic semiconductors with the Feynman variational approach

We extend the Feynman variational method applied to the parabolic-band Fr\"ohlich (continuum) large polaron~\cite{Feynman1955} to a Holstein (lattice) small polaron, with a parabolic-band. This new theory shows a discrete localisation as a function of coupling strength. Having build the theory with the same quasi-particle Lagrangian as the 1955 work, we can directly use the FHIP~\cite{Feynman1962} response theory to calculate DC mobility and complex conductivity. We show that we can take matrix elements from electronic structure calculations on real materials, by modelling charge-carrier mobility in crystalline Rubrene. Good agreement is found to measurement, with a predicted mobility of $\mu = 47.72$~\si{cm^2 V^{-1} s^{-1}} at $300$~\si{K}.