Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3

Journal name:
Nature Physics
Year published:
Published online

The newly discovered three-dimensional strong topological insulators (STIs) exhibit topologically protected Dirac surface states1, 2. Although the STI surface state has been studied spectroscopically, for example, by photoemission3, 4, 5 and scanned probes6, 7, 8, 9, 10, transport experiments11, 12, 13, 14, 15, 16, 17 have failed to demonstrate the most fundamental signature of the STI: ambipolar metallic electronic transport in the topological surface of an insulating bulk. Here we show that the surfaces of thin (~ 10nm), low-doped Bi2Se3 (1017cm−3) crystals are strongly electrostatically coupled, and a gate electrode can completely remove bulk charge carriers and bring both surfaces through the Dirac point simultaneously. We observe clear surface band conduction with a linear Hall resistivity and a well-defined ambipolar field effect, as well as a charge-inhomogeneous minimum conductivity region18, 19, 20. A theory of charge disorder in a Dirac band19, 20, 21 explains well both the magnitude and the variation with disorder strength of the minimum conductivity (2 to 5 e2/h per surface) and the residual (puddle) carrier density (0.4×1012 to 4×1012cm−2). From the measured carrier mobilities 320–1,500cm2V−1s−1, the charged impurity densities 0.5×1013 to 2.3×1013cm−2 are inferred. They are of a similar magnitude to the measured doping levels at zero gate voltage (1×1013 to 3×1013cm−2), identifying dopants as the charged impurities.

At a glance


  1. Bi2Se3 thin-film device.
    Figure 1: Bi2Se3 thin-film device.

    a,b, Schematics of the p-type doping scheme and gate configuration for charge transfer doping with F4TCNQ organic molecules (a) and polymer electrolyte (PEO+LiClO4) (b) top gating. c,d, Longitudinal resistivity ρxx (c) and  sheet carrier density (d) determined from Hall measurement as a function of back-gate voltage for device 4 (F4TCNQ-doped) at various temperatures from 2 to 50K, as indicated in the figure. The inset of d shows an optical micrograph of the device. The scale bar is 2μm.

  2. Single band conduction in the topological insulator regime.
    Figure 2: Single band conduction in the topological insulator regime.

    a, Hall resistivity ρxy of device 4 as a function of magnetic field B at a temperature of 2K at different carrier densities tuned by the back-gate electrode. b, Polar plot of the normalized longitudinal resistivity ρxx of the dual-gated Bi2Se3 thin-film device as a function of the total magnitude of displacement field (Dtotal)and the gating asymmetry factor α (defined in the text).

  3. Transport properties of the Bi2Se3 surface state.
    Figure 3: Transport properties of the Bi2Se3 surface state.

    a, The conductivity per surface versus carrier density per surface σ(n) at zero magnetic field for five different devices. Devices 1–3 are electrolyte-gated and devices 4 and 5 are F4TCNQ-doped. The inset shows σ(n) near the Dirac point. Dashed lines are fits to equation (1a). Transport data outside the topological regime (n>nbulk=5×1012cm−2) are denoted as dotted curves. b, Hall carrier density per surface versus carrier density measured at the same conditions as in a. Dashed lines show the residual carrier density n* (defined in the text) for different devices. c, Variation of field effect mobility as a function of carrier density. Dashed curves indicate the region |n|<n* within which electron and hole puddles dominate transport.

  4. Charge inhomogeneity and minimum conductivity versus disorder strength.
    Figure 4: Charge inhomogeneity and minimum conductivity versus disorder strength.

    a, Residual carrier density n*versus inverse field effect mobility (1/μFE). b, Minimum conductivity σmin versus 1/μFE. Shaded areas indicate the expectations of the self-consistent theory of ref. 20, open symbols are experimental data.


  1. Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).
  2. Zhang, H. J. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438442 (2009).
  3. Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 11011105 (2009).
  4. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator Bi2Te3. Science 325, 178181 (2009).
  5. Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398402 (2009).
  6. Zhang, T. et al. Experimental demonstration of topological surface states protected by time-reversal symmetry. Phys. Rev. Lett. 103, 266803 (2009).
  7. Alpichshev, Z. et al. STM imaging of electronic waves on the surface of Bi2Te3: Topologically protected surface states and hexagonal warping effects. Phys. Rev. Lett. 104, 016401 (2010).
  8. Hanaguri, T. et al. Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi2Se3. Phys. Rev. B 82, 081305R (2010).
  9. Cheng, P. et al. Landau quantization of topological surface states in Bi2Se3. Phys. Rev. Lett. 105, 076801 (2010).
  10. Beidenkopf, H. et al. Spatial fluctuations of helical Dirac fermions on the surface of topological insulators. Nature Phys. 7, 939943 (2011).
  11. Steinberg, H., Gardner, D. R., Lee, Y. S. & Jarillo-Herrero, P. Surface state transport and ambipolar electric field effect in Bi2Se3 nanodevices. Nano Lett. 10, 50325036 (2010).
  12. Qu, D., Hor, Y. S., Xiong, J., Cava, R. J. & Ong, N. P. Quantum oscillations and Hall anomaly of surface states in the topological insulator Bi2Te3. Science 329, 821824 (2010).
  13. Xiu, F. et al. Manipulating surface states in topological insulator nanoribbons. Nature Nanotech. 6, 216221 (2011).
  14. Analytis, J. G. et al. Two-dimensional surface state in the quantum limit of a topological insulator. Nature Phys. 6, 960964 (2010).
  15. Peng, H. et al. Aharonov–Bohm interference in topological insulator nanoribbons. Nature Mater. 9, 225229 (2010).
  16. Chen, J. et al. Gate–voltage control of chemical potential and weak antilocalization in Bi2Se3. Phys. Rev. Lett. 105, 176602 (2010).
  17. Checkelsky, J. G., Hor, Y. S., Cava, R. J. & Ong, N. P. Surface state conduction observed in voltage-tuned crystals of the topological insulator Bi2Se3. Phys. Rev. Lett. 106, 196801 (2010).
  18. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197200 (2005).
  19. Hwang, E. H., Adam, S. & Das Sarma, S. Carrier transport in two-dimensional graphene layers. Phys. Rev. Lett. 98, 186806 (2007).
  20. Adam, S., Hwang, E. H., Galitski, V. M. & Das Sarma, S. A self-consistent theory for graphene transport. Proc. Natl Acad. Sci. USA 104, 1839218397 (2007).
  21. Culcer, D., Hwang, E. H., Stanescu, T. D. & Das Sarma, S. Two-dimensional surface charge transport in topological insulators. Phys. Rev. B 82, 155457 (2010).
  22. Butch, N. P. et al. Strong surface scattering in ultrahigh-mobility Bi2Se3 topological insulator crystals. Phys. Rev. B 81, 241301 (2010).
  23. Kong, D. et al. Rapid surface oxidation as a source of surface degradation factor for Bi2Se3. ACS Nano 5, 46984703 (2011).
  24. Das, A. et al. Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor. Nature Nanotech. 3, 210215 (2008).
  25. Efetov, D. K. & Kim, P. Controlling electron–phonon interactions in graphene at ultrahigh carrier densities. Phys. Rev. Lett. 105, 256805 (2010).
  26. Lu, C. G., Fu, Q., Huang, S. M. & Liu, J. Polymer electrolyte-gated nanotube field-effect carbon transistor. Nano Lett. 4, 623627 (2004).
  27. Coletti, C. et al. Charge neutrality and band-gap tuning of epitaxial graphene on SiC by molecular doping. Phys. Rev. B 81, 235401 (2010).
  28. Bansal, M., Kim, Y. S., Brahlek, M., Eliav, E. & Oh, S. Thickness-independent surface transport channel in topological insulator Bi2Se3 thin films. Preprint at (2011).
  29. Chen, J. H. et al. Charged impurity scattering in graphene. Nature Phys. 4, 377381 (2008).
  30. Adam, S., Hwang, E. H. & Sarma, S. D. 2D transport and screening in topological insulator surface states. Preprint at (2012).

Download references

Author information

  1. These authors contributed equally to this work

    • Dohun Kim &
    • Sungjae Cho


  1. Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA

    • Dohun Kim,
    • Sungjae Cho,
    • Nicholas P. Butch,
    • Paul Syers,
    • Kevin Kirshenbaum,
    • Johnpierre Paglione &
    • Michael S. Fuhrer
  2. Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-6202, USA

    • Shaffique Adam
  3. Present address: Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-2902, USA

    • Sungjae Cho
  4. Present address: Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA

    • Nicholas P. Butch


D.K. conceived the p-type doping schemes. D.K. and S.C. fabricated devices, performed the electrical measurements with K.K. and analysed the data. N.P.B., P.S. and J.P. prepared single crystal Bi2Se3 starting material. S.A. assisted with the theoretical analysis. D.K., S.C. and M.S.F. wrote the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (656kb)

    Supplementary Information

Additional data