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

Nature Physics volume 10, pages 970977 (2014) | Download Citation

Abstract

Lars Onsager and Richard Feynman envisaged that the three-dimensional (3D) superfluid-to-normal λ transition in 4He 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) on 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.

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Acknowledgements

We thank S. C. Chae, A. del campo and V. Zapf for stimulating discussion. This project was in part supported by the DOE under the LDRD program at the Los Alamos National Laboratory. The work at Rutgers University was supported by the DOE under Grant No. DE-FG02-07ER46382. Y.K. acknowledges the financial support by the RIKEN iTHES Project. The work was also supported by China Scholarship Council.

Author information

Author notes

    • Shi-Zeng Lin
    •  & Xueyun Wang

    These authors contributed equally to this work.

Affiliations

  1. Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

    • Shi-Zeng Lin
    • , Yoshitomo Kamiya
    • , Gia-Wei Chern
    • , Wojciech H. Zurek
    •  & Cristian D. Batista
  2. Rutgers Centre for Emergent Materials and Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road Piscataway, New Jersey 08854, USA

    • Xueyun Wang
    • , Fei Fan
    • , David Fan
    • , Brian Casas
    • , Yue Liu
    • , Valery Kiryukhin
    •  & Sang-Wook Cheong
  3. iTHES Research Group and Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan

    • Yoshitomo Kamiya
  4. Shaanxi Key Laboratory of Condensed Matter Structures and Properties, School of Science, Northwestern Polytechnical University, Xi’an 710129, China

    • Fei Fan
  5. Montgomery High School, 1016 Route 601, Skillman New Jersey 08558, USA

    • David Fan
  6. Functional Materials Laboratory, Department of Physics, University of South Florida, Tampa, Florida 33613, USA

    • Brian Casas
  7. The MOE key Laboratory of Weak-Light Nonlinear Photonics and TEDA Applied Physics School, Nankai University, Tianjin 300457, China

    • Yue Liu

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Contributions

S-W.C. designed and supervised the experiment. W.H.Z. and C.D.B. discussed the simulations and experiments, and wrote the section on the Kibble–Zurek mechanism. X.W. carried out annealing experiments, AFM and PFM work. F.F. performed PFM work. D.F., B.C. and Y.L. analysed vortex–antivortex optical images and V.K. calculated the experimental correlation functions. S-Z.L., Y.K. and G-W.C. simulated the theoretical results. S-Z.L., X.W., S-W.C., W.H.Z., C.D.B. and V.K. co-wrote the paper. All authors discussed the results.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Sang-Wook Cheong.

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DOI

https://doi.org/10.1038/nphys3142

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