## Abstract

We revisit the classical problem of granular hopping conduction’s σ ∝ exp[-(T
_{o}
/T)
^{1/2}
] temperature dependence, where σ denotes conductivity, T is temperature, and T
_{o}
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 Ag
_{x}
(SnO
_{2}
)
_{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.

Original language | English |
---|---|

Article number | 137205 |

Number of pages | 10 |

Journal | Frontiers of Physics |

Volume | 13 |

Issue number | 5 |

DOIs | |

State | Published - 1 Oct 2018 |

## Keywords

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