Explosive metallic breakdown

TL;DR

This paper models metallic breakdown as a percolation process influenced by electric fields, revealing a transition from continuous to explosive breakdown depending on particle adsorption probabilities.

Contribution

It introduces a model linking electric field-dependent particle adsorption to percolation, demonstrating a transition from continuous to discontinuous breakdown, including an exact mapping to the Potts model.

Findings

Breakdown transition can be continuous or explosive depending on parameters.

Exact mapping to the q-state Potts model at q=4.

Model provides a potential experimental realization of discontinuous percolation.

Abstract

We investigate the metallic breakdown of a substrate on which highly conducting particles are adsorbed and desorbed with a probability that depends on the local electric field. We find that, by tuning the relative strength $q$ of this dependence, the breakdown can change from continuous to explosive. Precisely, in the limit in which the adsorption probability is the same for any finite voltage drop, we can map our model exactly onto the $q$-state Potts model and thus the transition to a jump occurs at $q=4$. In another limit, where the adsorption probability becomes independent of the local field strength, the traditional bond percolation model is recovered. Our model is thus an example of a possible experimental realization exhibiting a truly discontinuous percolation transition.