Energy landscape in two-dimensional Penrose-tiled quasicrystal

TL;DR

This paper investigates the energy landscape and eigenstates of a two-dimensional microwave Penrose-tiled quasicrystal, providing experimental measurements and analysis that enhance understanding of spectral properties in higher-dimensional quasicrystals.

Contribution

It presents the first detailed experimental measurements and energy-scaling analysis of gap labelling and eigenstate distributions in 2D Penrose-tiled quasicrystals, extending theoretical understanding.

Findings

Observed gap labelling in 2D quasicrystal eigenstates

Analyzed spatial intensity distribution of eigenstates

Results applicable to broader classes of systems

Abstract

Since their spectacular experimental realisation in the early 80's, quasicrystals have been the subject of very active research, whose domains extend far beyond the scope of solid state physics. In optics, for instance, photonic quasicrystals have attracted strong interest for their specific behaviour, induced by the particular spectral properties, in light transport, plasmonic and laser action. Very recently, one of the most salient spectral feature of quasicrystals, namely the gap labelling, has been observed for a polariton gas confined in a one dimensional quasi-periodic cavity. This experimental result confirms a theory which is now very complete in dimension one. In dimension greater than one, the theory is very far from being complete. Furthermore, some intriguing phenomena, like the existence of self-similar eigenmodes can occur. All this makes two dimensional experimental realisations and numerical simulations pertinent and attractive. Here, we report on measurements and energy-scaling analysis of the gap labelling and the spatial intensity distribution of the eigenstates for a microwave Penrose-tiled quasicrystal. Far from being restricted to the microwave system under consideration, our results apply to a more general class of systems.