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Spectromicroscopic measurement of surface and bulk band structure interplay in a disordered topological insulator


Topological insulators are bulk semiconductors that manifest in-gap surface states with massless Dirac-like dispersion due to the topological bulk-boundary correspondence principle1,2,3. These surface states can be manipulated by the interface environment to display various emergent phenomena4,5,6,7,8,9,10,11. Here, we use angle-resolved photoemission spectroscopy and scanning tunnelling microscopy to investigate the interplay of crystallographic inhomogeneity with the topologically ordered band structure in a model topological insulator. We develop quantitative analysis methods to obtain spectroscopic information, in spite of a limited dwell time on each measured point. We find that the band energies vary on the scale of 50 meV across the sample surface, and this enables single sample measurements that are analogous to a multi-sample doping series. By focusing separately on the bulk and surface electrons we reveal a hybridization-like interplay between fluctuations in the surface and bulk state energetics.

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Fig. 1: Cross-correlation for ARPES analysis.
Fig. 2: Real-space maps of the electronic band structure.
Fig. 3: Bulk- and surface-ordered binning series.
Fig. 4: Interplay of bulk and surface electronic states.

Data availability

The data represented in Figs. 1c, 2, 3e,i–m and 4c are available as source data with the online version of the paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

All relevant source code or algorithms are available from the corresponding author upon reasonable request.


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This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. Work at NYU was supported by the MRSEC Program of the National Science Foundation under award no. DMR-1420073. Synthesis and analysis instrumentation at NYU is supported by the NSF under MRI-1531664 and by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF4838. The STM work at Rutgers is supported by the NSF under grant no. DMR-1506618. This research is funded in part by the Gordon and Betty Moore Foundation EPiQS Initiative, grant no. GBMF3848, to J.G.C. (instrumentation development) and the Office of Naval Research (ONR) under award no. N00014-17-1-2883 (material synthesis).

Author information

Authors and Affiliations



E.K., L.M., Y.X. and S.A.B. carried out the ARPES experiments, with support from C.J., A.B. and E.R. STM experiments were performed by W.Z., with guidance from W.W. High-quality samples were synthesized by T.S., with guidance from J.C. Computational data analysis and tight binding simulations were implemented by E.K. and Y.X., with assistance from S.A.B. and L.A.W. E.K., L.M., Y.X. and L.A.W. participated in the analysis, figure planning and draft preparation. L.A.W. was responsible for the concept and overall direction, planning and integration among different research units.

Corresponding author

Correspondence to L. Andrew Wray.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–6, Discussion and Table 1.

Source data

Source Data Fig. 1

The cross-correlation values for the template on given example shown in Fig. 1. Row delta is ~0.002 Å−1. Column delta is ~0.0016 eV.

Source Data Fig. 2

Maps data from Fig. 2. Each row (1–4) represents a map (2a–d) with 961 elements. Reshape 31 × 31 to convert to maps.

Source Data Fig. 3

Lines 1, 6 are energy axes used for Figs. 3e, i respectively. Lines 2–5 and 7–9 are the intensity values (a.u.) of the EDCs in Figs. 3e, i respectively. Lines 10–11 are x, y axes for histogram Fig. 3j; rows 12–13 for Fig. 3k. Lines 14–17 indicate which map pixels (0 = not included, 1 = included) are included in the spectra Fig. 3a–d, respectively. Lines 18–20 indicate which map pixels are included in Fig. 3f–h.

Source Data Fig. 4

Line 1 is colour-plot X values (bulk E). Line 2 is colour-plot Y values (surface E). Lines 3-28 are colour-plot Z values (2d-histo count). Lines 29, 30 are center-of-mass (X, Y) values using minimum 10 counts per point (red curve of Fig. 4c). Lines 31, 32 are model (bulk-E, surface-E) values.

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Kotta, E., Miao, L., Xu, Y. et al. Spectromicroscopic measurement of surface and bulk band structure interplay in a disordered topological insulator. Nat. Phys. 16, 285–289 (2020).

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