Annihilation of Dirac points and its topological obstruction in a photonic Kagome lattice

TL;DR

This paper investigates how Dirac points in a photonic Kagome lattice can be manipulated and shows a topological obstruction to their annihilation, revealing complex topological transitions governed by non-Abelian symmetries.

Contribution

It demonstrates the control of Dirac point dynamics and topological invariants in a photonic lattice, highlighting a novel topological obstruction to Dirac point annihilation.

Findings

Dirac points can be moved in reciprocal space via optical engineering.

An obstruction prevents Dirac points from annihilating during collision.

A topological transition involves a change in the Euler number linked to non-Abelian eigenstate rotations.

Abstract

Dirac points (DPs) are topological singularities that determine the extraordinary properties of two-dimensional materials. They are generally classified by discrete topological invariants, which determine the possibility of DPs' annihilation upon their collision. Here, we study the behaviors of DPs within a photonic Kagome lattice created in atomic vapor. With optically engineering the potential difference among three sites constituting the Kagome unit cell while preserving time-reversal symmetry and the stability of an isolated DP, the DPs move in reciprocal space. By employing conical diffraction to measure their position and the topological invariant (Euler number), we demonstrate an obstruction to DPs' annihilation during collision and a transition to a case where the Euler number changes and annihilation occurs. Such topological transition is induced by a non-Abelian frame rotation of the eigenstates around the Brillouin zone torus. The associated conversion of the DP quaternionic charges during their motion explains the change of Euler number.