Absence of the diffusion pole in the Anderson insulator

TL;DR

This paper argues that the diffusion pole, associated with electron diffusion, cannot exist in the Anderson insulator phase, challenging previous assumptions and providing a new understanding of localization transition.

Contribution

It presents a nonperturbative analysis showing the diffusion pole's absence in the Anderson insulator, clarifying the nature of the localization transition.

Findings

Diffusion pole exists only in the metallic regime.

Diffusion pole's absence in the Anderson insulator avoids physical inconsistencies.

Provides a consistent framework for understanding Anderson localization transition.

Abstract

We discuss conditions for the existence of the diffusion pole and its consequences in disordered noninteracting electron systems. Using only nonperturbative and exact arguments we find against expectations that the diffusion pole can exist only in the diffusive (metallic) regime. We demonstrate that the diffusion pole in the Anderson localization phase would lead to nonexistence of the self-energy and hence to a physically inconsistent picture. The way how to consistently treat and understand the Anderson localization transition with vanishing of the diffusion pole is presented.