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Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators


Understanding the structure of the wavefunction is essential for depicting the surface states of a topological insulator. Owing to the inherent strong spin–orbit coupling, the conventional hand-waving picture of the Dirac surface state with a single chiral spin texture is incomplete, as this ignores the orbital components of the Dirac wavefunction and their coupling to the spin textures. Here, by combining orbital-selective angle-resolved photoemission experiments and first-principles calculations, we deconvolve the in-plane and out-of-plane p-orbital components of the Dirac wavefunction. The in-plane orbital wavefunction is asymmetric relative to the Dirac point. It is predominantly tangential (radial) to the k-space constant energy surfaces above (below) the Dirac point. This orbital texture switch occurs exactly at the Dirac point, and therefore should be intrinsic to the topological physics. Our results imply that the Dirac wavefunction has a spin–orbital texture—a superposition of orbital wavefunctions coupled with the corresponding spin textures.

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Figure 1: ARPES energy–momentum intensity plots at the Γ point for s and p photon polarizations.
Figure 2: Deducing the orbital texture from constant energy surface intensity plots.
Figure 3: Sketch of the orbital texture switch deduced from the experimental and theoretical matrix elements.
Figure 4: OPRλ switches sign at the Dirac point.


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We acknowledge helpful discussions with S-C. Zhang, S-R. Park, M. Hermele, A. Essin and G. Chen. The ARPES work was carried out at the Advanced Light Source, LBL, and was supported by the DOE Office of Basic Science by grant DE-FG02-03ER46066 and by the NSF under DMR-1007014. A.Z., X-W.Z. and J-W.L. were supported as part of the Center for Inverse Design, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award number DEAC 36-08GO28308. X-W.Z. also acknowledges the administrative support of REMRSEC under NSF grant number DMR-0820518, Colorado School of Mines, Golden, Colorado. The Rutgers work was supported by IAMDN of Rutgers University, National Science Foundation (NSF DMR-0845464) and Office of Naval Research (ONR N000140910749), and the Brookhaven work was supported by the DOE under contract number DE-AC03-76SF00098. Both LBL and BNL are supported by the DOE, Office of Basic Energy Sciences.

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Authors and Affiliations



Y.C. led the experimental data taking and analysis. J.A.W., Q.W. and T.J.R. helped with the data taking, and S.K.M. with the instrument and decapping procedure. X-W.Z., J-W.L. and A.Z. carried out the density functional calculations. Y.C., X-W.Z., J-W.L. and A.Z. analyzed the results from the first-principles calculations. Z.X., A.Y., J.S. and G.D.G. prepared the single crystal samples, and M.B., N.B. and S.O. prepared the thin film samples. Y.C. and D.S.D. did the majority of the paper writing (with contributions from all coauthors) and D.S.D. directed the overall project.

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Correspondence to Yue Cao or D. S. Dessau.

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The authors declare no competing financial interests.

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Cao, Y., Waugh, J., Zhang, XW. et al. Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators. Nature Phys 9, 499–504 (2013).

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