Classical and quantum breakdown in disordered materials

TL;DR

This paper explores classical and quantum breakdown phenomena in disordered materials, analyzing statistical distributions, disorder effects, and extensions of breakdown concepts from band to Anderson insulators.

Contribution

It provides a comprehensive analysis of breakdown mechanisms in disordered systems, highlighting the role of extreme value statistics and disorder concentration effects.

Findings

Gumbel distribution describes failure processes at low disorder.

Transition from extreme value to percolation statistics near the threshold.

System size influences failure current distribution in low disorder regimes.

Abstract

We have discussed the classical failure of the fuse system, the dielectric breakdown and the quantum breakdown in the Anderson insulators. We have discussed how the extreme value statistics and the resulting Gumbel distribution arises in breakdown and failure processes, especially when the disorder concentration is low. At high concentration of disorder near the percolation threshold, we have discussed how the cross-over might take place from extreme value to percolation statistics. We have discussed the system size dependence that arises at the distribution of the failure current at low disordered regime. Finally, the extension of Zener breakdown phenomenon for band insulators to the disordered-induced Anderson insulators has been discussed.