Extended states in 1D lattices: application to quasiperiodic copper-mean chain

TL;DR

This paper investigates the conditions for extended electronic states in 1D systems, providing analytical criteria and demonstrating the existence of infinitely many extended states in the quasiperiodic copper-mean chain.

Contribution

It introduces a general real space renormalisation group approach to identify extended states and analytically proves the existence of infinitely many extended eigenstates in the copper-mean chain.

Findings

Infinite number of extended eigenstates in the copper-mean chain

Extended states form fragmented minibands

Criteria for extended states in disordered and quasiperiodic systems

Abstract

The question of the conditions under which 1D systems support extended electronic eigenstates is addressed in a very general context. Using real space renormalisation group arguments we discuss the precise criteria for determining the entire spertrum of extended eigenstates and the corresponding eigenfunctions in disordered as well as quasiperiodic systems. For purposes of illustration we calculate a few selected eigenvalues and the corresponding extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for the infinite copper-mean chain, only a single energy has been numerically shown to support an extended eigenstate [ You et al. (1991)] : we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.