Localization and spectral structure in two-dimensional quasicrystal potentials

TL;DR

This paper explores the localization and spectral properties of quantum particles in two-dimensional quasicrystalline optical potentials, revealing complex energy gaps and state behaviors that deepen understanding of quantum quasicrystals.

Contribution

It provides the first detailed analysis of localization and spectral structures in 2D quantum quasicrystals, highlighting the role of ring states and energy gaps across different symmetries.

Findings

States are localized at low energy and extended at high energy.

Alternating localized and critical states occur at intermediate energies.

Energy gaps are primarily due to localized ring states and are stable across various conditions.

Abstract

Quasicrystals, a fascinating class of materials with long-range but nonperiodic order, have revolutionized our understanding of solid-state physics due to their unique properties at the crossroads of long-range-ordered and disordered systems. Since their discovery, they continue to spark broad interest for their structural and electronic properties. The quantum simulation of quasicrystals in synthetic quantum matter systems offers a unique playground to investigate these systems with unprecedented control parameters. Here, we investigate the localization properties and spectral structure of quantum particles in 2D quasicrystalline optical potentials. While states are generally localized at low energy and extended at high energy, we find alternating localized and critical states at intermediate energies. Moreover, we identify a complex succession of gaps in the energy spectrum. We show that the most prominent gap arises from strongly localized ring states, with the gap width determined by the energy splitting between states with different quantized winding numbers. In addition, we find that these gaps are stable for quasicrystals with different rotational symmetries and potential depths, provided that other localized states do not enter the gap generated by the ring states. Our findings shed light on the unique properties of quantum quasicrystals and have implications for their many-body counterparts.