Reappraisal of variable-range hopping in quantum-dot solids

The temperature dependence of the electrical conductivity of assemblies of ZnO nanocrystals, studied with an electrochemically gated transistor is very accurately described by the relation ln σ = ln σ0 − (T0/T)x with x = 2/3 over the entire temperature range from 7 to 200 K, independent of charge concentration and dielectric environment. These results cannot be explained by existing models but are supported by results on Au nanocrystals where an identical temperature dependence was observed (Zabet-Khosousi et al., Phys. Rev. Lett. 2006, 96 (15), 156403). We propose an adaptation of the Efros−Shklovskii variable-range hopping model by introducing an expression for nonresonant tunneling based on local energy fluctuations, which yields exactly the temperature dependence that is observed experimentally.