Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics

TL;DR

This paper explores how topological defects like vortices emerge and condense during ferroelectric phase transitions in hexagonal manganites, revealing a dual gauge field description and enabling experimental tests of fundamental theories.

Contribution

It demonstrates the emergence of a U(1) symmetry and vortex proliferation in ferroelectrics, connecting topological defect dynamics with the Higgs mechanism and providing a new experimental platform.

Findings

Vortex proliferation occurs at the ferroelectric transition.

Vortices couple to an emergent U(1) gauge field.

Direct imaging confirms the vortex network.

Abstract

Lars Onsager and Richard Feynman envisioned that the three-dimensional (3D) superfluid-to-normal $\lambda$ transition in $^{4}$He occurs through the proliferation of vortices. This process should hold for every phase transition in the same universality class. The role of topological defects in symmetry-breaking phase transitions has become a prime topic in cosmology and high-temperature superconductivity, even though direct imaging of these defects is challenging. Here we show that the U(1) continuous symmetry that emerges at the ferroelectric critical point of multiferroic hexagonal manganites leads to a similar proliferation of vortices. Moreover, the disorder field (vortices) is coupled to an emergent U(1) gauge field, which becomes massive by means of the Higgs mechanism when vortices condense (span the whole system) upon heating above the ferroelectric transition temperature. Direct imaging of the vortex network in hexagonal manganites offers unique experimental access to this dual description of the ferroelectric transition, while enabling tests of the Kibble-Zurek mechanism.