Unified thermopower in the variable range hopping regime

Since nearly 4 decades, various theoretical behaviours have been found for the thermopower in the variable range hopping regime. In 1969, Cutler and Mott have predicted a linear variation with temperature T of the thermopower: S = const.T. In the seventies, it has beenfound by Zvyagin, Overhof and Mott that S = const.T(1/2). In 1986, Triberis and Friedman have found S = const.T^(-1/4) . But there is up to now no theoretical formulation of the thermopower when this one is T-independent. By choosing a specific distribution for the density of states, we show in this paper that all behaviours above can be unified in a unique thermopower formula. We find in addition with this formula, a T-independent expression given by: S=(L/xi)(k/e), in which xi is the wave function decay length and L is a characteristic length, depending on the form of the density of states.