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

Yue Cao; J. A. Waugh; X. W. Zhang; J. W. Luo; Q. Wang; T. J. Reber; S. K. Mo; Z. Xu; A. Yang; J. Schneeloch; G. D. Gu; M. Brahlek; N. Bansal; S. Oh; A. Zunger; D. S. Dessau

doi:10.1038/nphys2685

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

Yue Cao, J. A. Waugh, X. W. Zhang, J. W. Luo, Q. Wang, T. J. Reber, S. K. Mo, Z. Xu, A. Yang, J. Schneeloch, G. D. Gu, M. Brahlek, N. Bansal, S. Oh, A. Zunger, D. S. Dessau

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122 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	499-504
Number of pages	6
Journal	Nature Physics
Volume	9
Issue number	8
DOIs	https://doi.org/10.1038/nphys2685
State	Published - Aug 2013
Externally published	Yes

Funding

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.

Funders	Funder number
DOE Office of Basic Science	DE-FG02-03ER46066
IAMDN of Rutgers University
Office of Basic Energy Sciences	DEAC 36-08GO28308
REMRSEC	DMR-0820518
US Department of Energy
National Science Foundation	DMR-0845464, 1007014, DMR-1007014, 0845464
Office of Naval Research	N000140910749
U.S. Department of Energy	DE-AC03-76SF00098
Office of Science
Colorado School of Mines

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title = "Mapping the orbital wavefunction of the surface states in three-dimensional topological insulators",

abstract = "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.",

author = "Yue Cao and Waugh, {J. A.} and Zhang, {X. W.} and Luo, {J. W.} and Q. Wang and Reber, {T. J.} and Mo, {S. K.} and Z. Xu and A. Yang and J. Schneeloch and Gu, {G. D.} and M. Brahlek and N. Bansal and S. Oh and A. Zunger and Dessau, {D. S.}",

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AU - Wang, Q.

AU - Reber, T. J.

AU - Mo, S. K.

AU - Xu, Z.

AU - Yang, A.

AU - Schneeloch, J.

AU - Gu, G. D.

AU - Brahlek, M.

AU - Bansal, N.

AU - Oh, S.

AU - Zunger, A.

AU - Dessau, D. S.

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N2 - 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.

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

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