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Topological Insulators

Topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The bulk of such materials is insulating but the surface can conduct electric current with well-defined spin texture. In addition, the relativistic energy-momentum relationship of electrons in these materials provides a great opportunity to study the physics of relativity in a condensed matter system with the velocity of massless particles about 200 times slower than the light speed in vacuum.

Surface conduction of topological insulators.  (A) The spin of electrons on the surface is correlated with their direction of motion. (B) The lattice structure of Bi2Te3 and the predicted relativistic "Dirac cone" like electronic structure formed by the surface electrons. (C) The electronic structure measured by angle-resolved photoemission that confirmed the theoretical prediction and the topological nature of Bi2Te3.


Unlike other materials where the fragile surface states can be easily altered by details in the surface geometry and chemistry, topological insulators are predicted to have unusually robust surface states due to the protection of time-reversal symmetry. These unique states are protected against all time-reversal-invariant perturbations, such as scattering by non-magnetic impurities, crystalline defects, and distortion of the surface itself, and can lead to striking quantum phenomena such as quantum spin Hall effect, an image magnetic monopole induced by an electric charge, and Majorana fermions (whose anti-particle is itself) induced by proximity effect from a superconductor.

Extracting the electronic and structural properties of topological insulators is essential for both the understanding of the underlying physics and potential applications. As a direct method to study the electron band structures of solids, ARPES can yield rich information of the electronic bands of topological insulators, as demonstrated in our results on the realization of the large gap single Dirac cone topological insulator, Bi2Te3.

Crystal and electronic structures of Bi2Te3.  (A) Tetradymite-type crystal structure of Bi2Te3. (B) Calculated bulk conduction band (BCB) and bulk valence band (BVB) dispersions along high symmetry directions of the surface Brillouin zone (BZ) (see inset), with the chemical potential rigidly shifted to match the experimental result. (C) The kz dependence of the calculated bulk Fermi surface (FS) projection on the surface BZ. (D) ARPES measurements of band dispersions along K-Γ-K and M-Γ-M (bottom) directions. (E) Measured wide range FS map covering three BZs, where the red hexagons represent the surface BZ. (F) Photon energy dependent FS maps. The shape of the inner FS changes dramatically with photon energies, indicating a strong kz dependence due to its bulk nature as predicted in panel (C), while the non-varying shape of the outer hexagram FS confirms its surface state origin.


Selected Publications

[1] Y. L. Chen et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178 (2009)

[2] Y. L. Chen et al. Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329, 659 (2010)

[3] Z. K. Liu et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864 (2014)