Non-factorizable 4D quantum Hall state from photonic crystal defects

TL;DR

This paper proposes a method to realize 4D topological phases with non-factorizable properties in photonic crystals using defect resonators and quasiperiodic modulations, enabling experimental exploration of higher-dimensional topological phenomena.

Contribution

It introduces a novel approach to create 4D non-factorizable topological states in photonic crystals using defect resonators with quasiperiodic modulations, distinct from traditional models.

Findings

Demonstrates a photonic system with non-abelian Berry curvature in 4D synthetic space.

Shows the system cannot be factorized into two 1st Chern models, indicating non-factorizability.

Proposes an experimentally feasible setup with dielectric rods in air.

Abstract

In the recent years, there has been a drive towards the realization of topological phases beyond conventional electronic materials, including phases defined in more than three dimensions. We propose a way to realize 2nd Chern number topological phases with photonic crystals simply made up of defect resonators embedded within a regular lattice of resonators. In particular, through a novel quasiperiodic spatial modulations in the defect radii, a defect lattice possessing topologically nontrivial Chern bands with non-abelian berry curvature living in four-dimensional synthetic space is proposed. This system cannot be factorized by a direct product of two 1st Chern number models, distinguishing itself from the Hofstadter model. Such photonic systems can be easily experimentally realized with regular photonic crystals consisting of dielectric rods in air.