Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator

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 via odd number of band inversions, driving the system through a topological quantum phase transition. By directly measuring the topological invariants (for the method to directly measure Fu-Kane {$ν_0$}, see Hsieh \textit{et.al.,} Science 323, 919 (2009) at http://www.sciencemag.org/content/323/5916/919.abstract) we report the observation of a phase transition in a tunable spin-orbit system BiTl(S{1-d}Se{d})2 (which is an analog of the most studied topological insulator Bi2Se3, see Xia \textit{et.al.,} Nature Phys. 5, 398 (2009) at http://www.nature.com/nphys/journal/v5/n6/full/nphys1294.html and Spin-Momentum locking at http://www.nature.com/nature/journal/v460/n7259/full/nature08234.html) where the topological insulator state formation is visualized for the first time. In the topological state, vortex-like polarization states are observed to exhibit 3D vectorial textures, which collectively feature a chirality transition of its topological spin-textures as the spin-momentum locked (Z2 topologically ordered) electrons on the surface go through the zero carrier density point. Such phase transition and texture chirality inversion can be the physical basis for observing \textit{fractional charge} (e/2) and other related fractional topological phenomena.