Evidence of hyperdimensional topological defects in a ferroelectric supercrystal phase-transition

TL;DR

This study visualizes a ferroelectric phase transition revealing a 3D lattice of topological defects forming a supercrystal, advancing understanding of complex topological structures in ferroelectric materials.

Contribution

It provides real-time 3D imaging evidence of a supercrystal of topological defects in a ferroelectric phase transition, linking topological theory with experimental observation.

Findings

Observation of a 3D lattice of topological defects

Identification of a supercrystal structure of N=4 defects

Demonstration of defect projection as S^3 hypersphere

Abstract

We perform real-time stereoscopic wide-area imaging of a ferroelectric phase-transition in KTN:Li. Spontaneous polarization is observed to form a thermally hysteretic 3D lattice of mutually interlinked closed-flux patterns that spans the entire sample. Results are compatible with a supercrystal of $N=4$ topological texture defects arising as the three-fold spatial and one-fold time-inversion symmetries are simultaneously broken. Each lattice site of the texture supercrystal emerges as the projection in actual space of an S$^3$ hypersphere, an extended volume Hopf-link fabric able to screen both volume charge and ferroelectric strain.