Charge carrier mobility in highly ordered smectic and discotic mesophases

The recently published data on phototransit signals in smectic and discotic liquid crystals, have led us to reconsider the old problem of the weak temperature dependence of the mobility in ordered narrow band systems and in the liquid crystalline phases. We argue that one has to distinguish between currents which are due to light-generated carriers and currents due to band conduction in equilibrium and which can be described using the Kubo-Greenwood formula. We use a first principle band model in an electric field and show how a T-independent mobility can be derived for a single particle which obeys band transport, includes joule energy relaxation, elastic disorder, and agrees with the few carrier limit of the Kubo formula. The result is essentially a generalised Drude velocity applicable to describe ``single particle currents''. We also discuss alternative explanations for the observed temperature independent mobilities which are based on hopping with weak disorder and polaron theories.