Complete absence of localization in a family of disordered lattices

TL;DR

This paper analytically demonstrates that certain disordered quasi-one-dimensional lattices can exhibit extended states with absolutely continuous energy spectra when specific correlations and magnetic fluxes are introduced, leading to enhanced electronic transport.

Contribution

It provides exact analytical results showing how correlations and magnetic flux can induce delocalization in disordered lattices, a novel insight into controlling electronic states.

Findings

Presence of absolutely continuous spectrum in correlated disordered lattices

Magnetic flux enables spectrum transition to extended states

Flux-controlled enhancement of electronic transport

Abstract

We present analytically exact results to show that, certain quasi one-dimensional lattices where the building blocks are arranged in a random fashion, can have an absolutely continuous part in the energy spectrum when special correlations are introduced among some of the parameters describing the corresponding Hamiltonians. We explicitly work out two prototype cases, one being a disordered array of a simple diamond network and isolated dots, and the other an array of triangular plaquettes and dots. In the latter case, a magnetic flux threading each plaquette plays a crucial role in converting the energy spectrum into an absolutely continuous one. A flux controlled enhancement in the electronic transport is an interesting observation in the triangle-dot system that may be useful while considering prospective devices. The analytical findings are comprehensively supported by extensive numerical calculations of the density of states and transmission coefficient in each case.