I suppose there are several ways to do it, but the most standard one involves the thermopower. Either type of hopping conduction shows thermally activated temperature dependence, with an activation energy we'll call ER
. The thermopower is also thermally activated in each case. For simple electron hopping, it has that same activation energy as the conductance. For small polarons, the thermopower activation energy is different, ER
-W, where W is half the formation energy of the small polaron. So that difference between the two activation energies seen in the temperature dependencies of the conductivity and the thermopower is the signature of small polaron conductivity.
Since any trapped electron will inevitably create at least some small distortion of the nearby lattice, you might even say that all of these cases are to some degree polaron hopping. The distinction is quantitative- in some cases W is significant compared to ER
and in other cases it isn't.
(published on 01/31/2012)