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Spectral and transport properties of the quasi two-dimensional adiabaticSu-Schrieffer-Heeger model are studied adjusting the parameters in order tomodel rubrene single-crystal field effect transistors with small but finitedensity of injected charge carriers. We show that, with increasing temperature$T$, the chemical potential moves into the tail of the density of statescorresponding to localized states, but this is not enough to drive the systeminto an insulating state. The mobility along different crystallographicdirections is calculated including vertex corrections which give rise to atransport lifetime one order of magnitude smaller than spectral lifetime of thestates involved in the transport mechanism. With increasing temperature, thetransport properties reach the Ioffe-Regel limit which is ascribed to less andless appreciable contribution of itinerant states to the conduction process.The model provides features of the mobility in close agreement withexperiments: right order of magnitude, scaling as a power law $T^{-\gamma}$,with $\gamma$ close or larger than two, and correct anisotropy ratio betweendifferent in-plane directions. Due to a realistic high dimensional model, theresults are not biased by uncontrolled approximations.

Electronic transport within a quasi two-dimensional model for rubrene single-crystal field effect transistors