# Observation of topological Bloch-state defects and their merging transition

## TL;DR

This study measures topological Bloch-state defects in a hexagonal optical lattice, revealing their merging transition and advancing understanding of geometric properties in systems with spin-orbit coupling.

## Contribution

It introduces a versatile method to measure azimuthal phase in optical lattices and maps the merging transition of Dirac points.

## Key findings

- Complete measurement of azimuthal phase in a hexagonal optical lattice
- Observation of the merging transition of Dirac points
- Method applicable to systems with spin-orbit coupling and interactions

## Abstract

Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudo-spin texture. The topological defects appear as vortices in the azimuthal phase of this pseudo-spin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in optical lattices also with spin-orbit coupling and interactions.