Entangled multi-component 4D quantum Hall states from photonic crystal defects

Abstract

Recently, 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 versatile and experimentally realistic approach of realizing a large variety of multi-component topological phases in 2D photonic crystals with quasi-periodically modulated defects. With a length scale introduced by a background resonator lattice, the defects are found to host various effective orbitals of $s$, $p$ and $d$-type symmetries, thus providing a monolithic platform for realizing multi-component topological states without requiring separate internal degrees of freedom in the physical setup. Notably, by coupling the defect modulations diagonally, we report the novel realization of an ``entangled'' 4D QH phase which cannot be factorized into two copies of 2D QH phases, each described by the 1st Chern number. The structure of this non-factorizability can be quantified by a classical entanglement entropy inspired by quantum information theory. In another embodiment, we present 4D p-orbital nodal lines in a nonsymmorphic photonic lattice, hosting boundary states with an exotic manifold. Our simple and versatile approach holds the promise of novel topological optoelectronic and photonic applications such as one-way optical fibers.

arXiv comment22 pages, 14 figures

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• Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$
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• Emergent Weyl-like points in periodically modulated systems
• Gapless hinge states from adiabatic pumping of axion coupling