Frontiers of Physics

, 13:137205 | Cite as

A critical path approach for elucidating the temperature dependence of granular hopping conduction

  • Tsz Chun Wu
  • Juhn-Jong Lin
  • Ping ShengEmail author
Research article


We revisit the classical problem of granular hopping conduction’s σ ∝ exp[-(To/T)1/2] temperature dependence, where σ denotes conductivity, T is temperature, and To is a sample-dependent constant. By using the hopping conduction formulation in conjunction with the incorporation of the random potential that has been shown to exist in insulator-conductor composites, it is demonstrated that the widely observed temperature dependence of granular hopping conduction emerges very naturally through the immediate-neighbor critical-path argument. Here, immediate-neighbor pairs are defined to be those where a line connecting two grains does not cross or by-pass other grains, and the critical-path argument denotes the derivation of sample conductance based on the geometric percolation condition that is marked by the critical conduction path in a random granular composite. Simulations based on the exact electrical network evaluation of finite-sample conductance show that the configurationaveraged results agree well with those obtained using the immediate-neighbor critical-path method. Furthermore, the results obtained using both these methods show good agreement with experimental data on hopping conduction in a sputtered metal-insulator composite Agx(SnO2)1-x, where x denotes the metal volume fraction. The present approach offers a relatively straightforward and simple explanation for the temperature behavior that has been widely observed over diverse material systems, but which has remained a puzzle in spite of the various efforts made to explain this phenomenon.


granular hopping conduction insulator-conductor composites critical path method immediate-neighbor hopping 


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsHong Kong University of Science and TechnologyKowloon, Hong KongChina
  2. 2.Institute of Physics and Department of ElectrophysicsChiao Tung UniversityHsinchuChina
  3. 3.Center for Emergent Functional Matter ScienceChiao Tung UniversityHsinchuChina

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