Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice

TL;DR

This paper explores topological phenomena in a photonic Kagome lattice, demonstrating chiral edge modes, anomalous Hall effects, and methods to measure Berry phases, with potential for experimental realization and robustness against disorder.

Contribution

It introduces a theoretical framework for realizing and probing topological photonic states in Kagome lattices with artificial gauge fields and disorder resilience.

Findings

Chiral edge modes coexist with flat bands in the Kagome lattice.

Photonic systems exhibit quantum Hall and anomalous Hall effects without Landau levels.

Proposed wavepacket interference method measures Berry's phases and Chern numbers.

Abstract

We theoretically investigate a photonic Kagome lattice which can be realized in microwave cavity arrays using current technology. The Kagome lattice exhibits an exotic band structure with three bands one of which can be made completely flat. The presence of artificial gauge fields allows to emulate topological phases and induce chiral edge modes which can coexist inside the energy gap with the flat band that is topologically trivial. By tuning the artificial fluxes or in the presence of disorder, the flat band can also acquire a bandwidth in energy allowing the coexistence between chiral edge modes and bulk extended states; in this case the chiral modes become fragile towards scattering into the bulk. The photonic system then exhibits equivalents of both a quantum Hall effect without Landau levels, and an anomalous Hall effect characterized by a non-quantized Chern number. We discuss experimental observables such as local density of states and edge currents. We show how synthetic uniform magnetic fields can be engineered, which allows an experimental probe of Landau levels in the photonic Kagome lattice. We then draw on semiclassical Boltzmann equations for transport to devise a method to measure Berry's phases around loops in the Brillouin zone. The method is based solely on wavepacket interference and can be used to determine band Chern numbers or the photonic equivalent of the anomalous Hall response. We demonstrate the robustness of these measurements towards on-site and gauge-field disorder. We also show the stability of the anomalous quantum Hall phase for nonlinear cavities and for (artificial) atom-photon interactions.