Metal-insulator transition in one-dimensional lattices with chaotic energy sequences

TL;DR

This paper investigates how chaotic energy sequences influence electronic transport in one-dimensional lattices, revealing a metal-insulator transition driven by the degree of chaos in the system.

Contribution

It introduces a model with site energies from chaotic sequences and demonstrates a transition from metallic to insulating behavior based on chaos degree.

Findings

Localization length varies with chaos degree

Conductance distribution shifts from non-Gaussian to Gaussian at transition

Wave functions show localization or delocalization depending on chaos

Abstract

We study electronic transport through a one-dimensional array of sites by using a tight binding Hamiltonian, whose site-energies are drawn from a chaotic sequence. The correlation degree between these energies is controlled by a parameter regulating the dynamic Lyapunov exponent measuring the degree of chaos. We observe the effect of chaotic sequences on the localization length, conductance, conductance distribution and wave function, finding evidence of a Metal-Insulator Transition (MIT) at a critical degree of chaos. The one-dimensional metallic phase is characterized by a Gaussian conductance distribution and exhibits a peculiar non-selfaveraging.