Islands in the Gap: Intertwined Transport and Localization in Structurally Complex Materials

TL;DR

This paper introduces a new class of structurally complex materials called chaotic crystals, which interpolate between periodic and disordered structures, revealing novel transport and localization phenomena including islands of transport within band gaps.

Contribution

It systematically explores the transition between order and disorder in materials, uncovering new localization behaviors and transport phenomena not seen in purely ordered or disordered systems.

Findings

Strong localization occurs even with low disorder levels.

Coexistence of enhanced localization and delocalization at specific energies.

Emergence of transport islands within band gaps.

Abstract

Localized waves in disordered one-dimensional materials have been studied for decades, including white-noise and correlated disorder, as well as quasi-periodic disorder. How these wave phenomena relate to those in crystalline (periodic ordered) materials---arguably the better understood setting---has been a mystery ever since Anderson discovered disorder-induced localization. Nonetheless, together these revolutionized materials science and technology and led to new physics far beyond the solid state. We introduce a broad family of structurally complex materials---chaotic crystals---that interpolate between these organizational extremes---systematically spanning periodic structures and random disorder. Within the family one can tune the degree of disorder to sweep through an intermediate structurally disordered region between two periodic lattices. This reveals new transport and localization phenomena reflected in a rich array of energy-dependent localization degree and density of states. In particular, strong localization is observed even with a very low degree of disorder. Moreover, markedly enhanced localization and delocalization coexist in a very narrow range of energies. Most notably, beyond the simply smoothed bands found in previous disorder studies, islands of transport emerge in band gaps and sharp band boundaries persist in the presence of substantial disorder. Finally, the family of materials comes with rather direct specifications of how to assemble the requisite material organizations.