# A novel conductivity mechanism of highly disordered carbon systems based on an investigation of graph zeta function

## TL;DR

This paper proposes a new understanding of electrical conductivity in highly disordered carbon systems, linking quantum chaos and graph zeta functions to explain experimental observations of metal-insulator transitions.

## Contribution

It introduces a novel conductivity mechanism based on graph zeta functions, revising previous assumptions about level statistics and quantum chaos in disordered carbon materials.

## Key findings

- Revised the origin of Wigner surmise in carbon systems
- Linked quantum chaos behavior to graph theory concepts
- Provided a new theoretical framework for conductivity mechanisms

## Abstract

In the previous report [Phys. Rev. B {\bf{62}} 13812 (2000)], by proposing the mechanism under which electric conductivity is caused by the activational hopping conduction with the Wigner surmise of the level statistics, the temperature-dependent of electronic conductivity of a highly disordered carbon system was evaluated including apparent metal-insulator transition. Since the system consists of small pieces of graphite, it was assumed that the reason why the level statistics appears is due to the behavior of the quantum chaos in each granular graphite. In this article, we revise the assumption and show another origin of the Wigner surmise, which is more natural for the carbon system based on a recent investigation of graph zeta function in graph theory.