### Abstract

We show that a wide class of unconventional quantum criticality emerges when orbital currents cause quantum phase transitions from zero-gap semiconductors such as Dirac fermions to a topological insulator or a Chern insulator. Changes in Fermi-surface topology concomitant with [SU(2) or time-reversal] symmetry breakings generate quantum critical lines (QCLs) even beyond the quantum critical point. This QCL running at temperature T=0 separates two distinct topological phases. This is in contrast to the simple termination of the finite-temperature critical line at the quantum critical point without any extension of it at T=0. Topology change causes the unconventionality beyond the concept of simple spontaneous symmetry breaking assumed in the conventional Landau-Ginzburg-Wilson scenario. The unconventional universality implied by mean-field critical exponents β>1/2 and δ<3 is protected by the existence of the quantum critical line. It emerges for several specific lattice models including the honeycomb, kagome, diamond, and pyrochlore lattices. We also clarify phase diagrams of the topological phases in these lattices at finite temperatures.

Original language | English |
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Article number | 115143 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 88 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2013 Sep 27 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*88*(11), [115143]. https://doi.org/10.1103/PhysRevB.88.115143