### Abstract

The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTl(S_{1-δ}Se_{δ})_{2}, in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum-locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena.

Original language | English (US) |
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Pages (from-to) | 560-564 |

Number of pages | 5 |

Journal | Science |

Volume | 332 |

Issue number | 6029 |

DOIs | |

State | Published - Apr 29 2011 |

### All Science Journal Classification (ASJC) codes

- General

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## Cite this

*Science*,

*332*(6029), 560-564. https://doi.org/10.1126/science.1201607