Mapping the unconventional orbital texture in topological crystalline insulators

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Abstract

The newly discovered topological crystalline insulators feature a complex band structure involving multiple Dirac cones1,2,3,4,5,6, and are potentially highly tunable by external electric field, temperature or strain. Theoretically, it has been predicted that the various Dirac cones, which are offset in energy and momentum, might harbour vastly different orbital character7. However, their orbital texture, which is of immense importance in determining a variety of a material’s properties8,9,10 remains elusive. Here, we unveil the orbital texture of Pb1−xSnxSe, a prototypical topological crystalline insulator. By using Fourier-transform scanning tunnelling spectroscopy we measure the interference patterns produced by the scattering of surface-state electrons. We discover that the intensity and energy dependences of the Fourier transforms show distinct characteristics, which can be directly attributed to orbital effects. Our experiments reveal a complex band topology involving two Lifshitz transitions11 and establish the orbital nature of the Dirac bands, which could provide an alternative pathway towards future quantum applications.

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Figure 1: Overall band structure and crystal structure of the topological crystalline insulator Pb1 − xSnxSe.
Figure 2: Representative k- and q-space structure and quasiparticle interference (QPI) dispersion.
Figure 3: Visualizing the Lifshitz transition and extracting the anisotropy of the surface state (SS) dispersion.
Figure 4: Determining the orbital character of the surface state bands.

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Acknowledgements

V.M. gratefully acknowledges funding from the US Department of Energy, Scanned Probe Division under Award Number DE-FG02-12ER46880 for the primary support of I.Z. and Y.O. (experiments, data analysis and writing the paper) and NSF-ECCS-1232105 for the partial support of W.Z. and D.W. (data acquisition). Work at Massachusetts Institute of Technology is supported by US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010526 (L.F.), and NSF DMR 1104498 (M.S.). H.L. acknowledges the Singapore National Research Foundation for support under NRF Award No. NRF-NRFF2013-03. The work at Northeastern University is supported by the US Department of Energy grant number DE-FG02-07ER46352, and benefited from Northeastern University’s Advanced Scientific Computation Center (ASCC), theory support at the Advanced Light Source, Berkeley and the allocation of time at the NERSC supercomputing centre through DOE grant number DE-AC02-05CH11231. W-F.T. and C-Y.H. were supported by the NSC in Taiwan under Grant No. 102-2112-M-110-009. W-F.T. also thanks C. Fang for useful discussions. Work at Princeton University is supported by the US National Science Foundation Grant, NSF-DMR-1006492. F.C. acknowledges the support provided by MOST-Taiwan under project number NSC-102-2119-M-002-004.

Author information

Y.O., I.Z. and V.M. designed the experiments. Samples were obtained from R.S., F.C. and M.Z.H. Theoretical analysis and calculations were done by C-Y.H., M.S., W-F.T., H.L., A.B. and L.F. STM experiments were carried out by Y.O., I.Z., D.W. and W.Z., I.Z., Y.O., H.L., L.F. and V.M. analysed the data and wrote the paper.

Correspondence to Vidya Madhavan.

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Zeljkovic, I., Okada, Y., Huang, C. et al. Mapping the unconventional orbital texture in topological crystalline insulators. Nature Phys 10, 572–577 (2014) doi:10.1038/nphys3012

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