First Principles Calculation of the Topological Phases of the Photonic Haldane Model

TL;DR

This paper uses first principles calculations to analyze the topological phases of a photonic Haldane model implemented with a Tellegen photonic crystal, revealing how the structure controls topological phase transitions.

Contribution

It introduces a Greens function method to determine band diagrams and topological invariants of the photonic Haldane model from first principles, including the phase diagram.

Findings

Identified topological phase diagram of the photonic Haldane model.

Demonstrated control of topological phases via the pseudo Tellegen parameter.

Showed nontrivial phase transitions depend on the crystal's granular structure.

Abstract

Photonic topological materials with a broken time reversal symmetry are characterized by nontrivial topological phases, such that they do not support propagation in the bulk region but forcibly support a nontrivial net number of unidirectional edge states when enclosed by an opaque type boundary, e.g., an electric wall. The Haldane model played a central role in the development of topological methods in condensed matter systems, as it unveiled that a broken time reversal is the essential ingredient to have a quantized electronic Hall phase. Recently, it was proved that the magnetic field of the Haldane model can be imitated in photonics with a spatially varying pseudo Tellegen coupling. Here, we use a Greens function method to determine from first principles the band diagram and the topological invariants of the photonic Haldane model, implemented as a Tellegen photonic crystal. Furthermore, the topological phase diagram of the system is found, and it is shown with first principles calculations that the granular structure of the photonic crystal can create nontrivial phase transitions controlled by the amplitude of the pseudo Tellegen parameter.