Emergence of criticality through a cascade of delocalization transitions in quasiperiodic chains

TL;DR

This paper investigates how quasiperiodic chains transition from extended to localized states through a cascade of band-specific localization/delocalization events, combining theory and experiments to reveal new critical phenomena.

Contribution

It introduces a continuous interpolation between two key quasiperiodic models, uncovering a cascade of localization transitions that shape self-similar critical wavefunctions, supported by experimental validation.

Findings

Discovery of a cascade of band-selective localization/delocalization transitions.

Experimental demonstration using cavity-polariton devices.

Insight into engineering band-pass filters and studying many-body effects.

Abstract

Conduction through materials crucially depends on how ordered they are. Periodically ordered systems exhibit extended Bloch waves that generate metallic bands, whereas disorder is known to limit conduction and localize the motion of particles in a medium. In this context, quasiperiodic systems, which are neither periodic nor disordered, reveal exotic conduction properties, self-similar wavefunctions, and critical phenomena. Here, we explore the localization properties of waves in a novel family of quasiperiodic chains obtained when continuously interpolating between two paradigmatic limits: the Aubry-Andr\'e model, famous for its metal-to-insulator transition, and the Fibonacci chain, known for its critical nature. Using both theoretical analysis and experiments on cavity-polariton devices, we discover that the Aubry-Andr\'e model evolves into criticality through a cascade of band-selective localization/delocalization transitions that iteratively shape the self-similar critical wavefunctions of the Fibonacci chain. Our findings offer (i) a unique new insight into understanding the criticality of quasiperiodic chains, (ii) a controllable knob by which to engineer band-selective pass filters, and (iii) a versatile experimental platform with which to further study the interplay of many-body interactions and dissipation in a wide range of quasiperiodic models.