Stick-breaking model for variable-range hopping

Abstract

We consider the optimal conduction path of the one-dimensional variable-range hopping problem. We describe a hierarchical procedure for constructing the path which is in excellent agreement with numerical results obtained from a percolation approach. The advantage of the hierarchical construction is that it is easier to analyse. We show that the distribution of hopping lengths is well-approximated by a model for the repeated breaking of a stick at its weakest point, until the fragments are too strong to be broken.

Keywords:

• disordered materials
• electrical transport
• hopping conduction
• localised states

Acknowledgements

Support from Vetenskapsrådet is gratefully acknowledged.