Extended electronic states in disordered 1-d lattices: an example

TL;DR

This paper presents a simple 1-d disordered lattice model where all electronic eigenstates are extended, challenging the typical localization expectation, and explores their unique properties and origins.

Contribution

It introduces a new type of correlation leading to extended states in a disordered 1-d lattice, distinct from known dimer correlations.

Findings

All eigenstates are extended despite disorder.

Eigenfunctions are not Bloch functions but extend throughout the chain.

Extended states arise from a novel correlation mechanism.

Abstract

We discuss a very simple model of a 1-d disordered lattice, in which {\em all} the electronic eigenstates are extended. The nature of these states is examined from several viewpoints, and it is found that the eigenfunctions are not Bloch functions although they extend throughout the chain. Some typical wavefunctions are plotted. This problem originated in our earlier study of extended states in the quasiperiodic copper-mean lattice [ Sil, Karmakar, Moitra and Chakrabarti, Phys. Rev. B (1993) ]. In the present investigation extended states are found to arise from a different kind of correlation than that of the well-known dimer-type.