Breakup of a Dimer: a New Approach to Localization Transition

TL;DR

This paper introduces a new approach to understanding localization transitions in aperiodic systems by analyzing a dimer defect within a renormalized lattice, unifying Anderson and resonance transitions.

Contribution

It presents a novel framework that links dimer defects to localization phenomena, offering a unified view of metal-insulator transitions in aperiodic systems.

Findings

Dimer acts as a resonant cavity influencing transport properties

Localization correlates with the vanishing coupling in the dimer

Unifies Anderson and resonance transition mechanisms

Abstract

Within the framework of tight binding models, aperiodic systems are mapped to a renormalized lattice with a dimer defect. In models exhibiting metal-insulator transition, the dimer acts like a resonant cavity and explains the existence of the ballistic transport in the system. The localization in the model can be attributed to the vanishing of the coupling between the two sites of the dimer. Our approach unifies Anderson transition and resonance transition and provides a new formulation to understand localization and its absence in aperiodic systems.