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Quantum criticality of topological phase transitions in three-dimensional interacting electronic systems

Nature Physics volume 10, pages 774778 (2014) | Download Citation

Abstract

Topological phase transitions in condensed matter systems accompany emerging singularities of the electronic wavefunction, often manifested by gap-closing points in momentum space. In conventional topological insulators in three dimensions, the low-energy theory near the gap-closing point can be described by relativistic Dirac fermions coupled to the long-range Coulomb interaction; hence, the quantum critical point of topological phase transitions provides a promising platform to test the intriguing predictions of quantum electrodynamics. Here we discover a class of quantum critical phenomena in topological materials for which either the inversion symmetry or time-reversal symmetry can be broken. At the quantum critical point, the emerging low-energy fermions, dubbed the anisotropic Weyl fermions, show both relativistic and Newtonian dynamics simultaneously. The interplay between the anisotropic dispersion and the Coulomb interaction brings about a screening phenomenon distinct from the conventional Thomas–Fermi screening in metals and logarithmic screening in Dirac fermions.

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Acknowledgements

We are grateful for support from the Japan Society for the Promotion of Science (JSPS) through the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program), and Grant-in-Aids for Scientific Research (Kiban (S), No. 24224009) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT). B-J.Y. and N.N. greatly appreciate the stimulating discussions with A. Aharony, O. Entin-Wohlman, M. Hermele and M.A. Cazalilla. E-G.M. is grateful for invaluable discussion with L. Balents, M. Metlitski and C. Xu and supported by the MRSEC Program of the National Science Foundation under Award No. DMR 1121053. H.I. is supported by a Grant-in-Aid for JSPS Fellows.

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Affiliations

  1. RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan

    • Bohm-Jung Yang
    •  & Naoto Nagaosa
  2. Department of Physics, University of California, Santa Barbara, California 93106, USA

    • Eun-Gook Moon
  3. Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan

    • Hiroki Isobe
    •  & Naoto Nagaosa

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Contributions

N.N. conceived the original ideas. B-J.Y., E-G.M. and H.I. performed the calculations. All authors analysed the data and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Bohm-Jung Yang or Naoto Nagaosa.

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https://doi.org/10.1038/nphys3060

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