• Coulomb glasses;
  • hopping transport.


A long-standing debate in the theory of hopping insulators concerns the role of multi-electron transitions in the dynamics of the system. The natural assumption is that as temperature is lowered, two-electron transitions will play an increasingly important role since they provide a way of tunneling through additional energy barriers which would be energetically unfavorable as successive one-electron transitions. This was disputed in [1], but later it was seen in [2]. The reason for this discrepancy is not clear and deserves further attention. One point where the two approaches diverged was in the selection and weighting of the two-electron transitions relative to one-electron transitions. We present calculations of the transition rates to second order in the tunneling matrix element, which will be used in improved numerical studies. We compare results for only one-electron jumps with results including also two-electron jumps.