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# Manipulating surface states in topological insulator nanoribbons

## Abstract

Topological insulators display unique properties, such as the quantum spin Hall effect, because time-reversal symmetry allows charges and spins to propagate along the edge or surface of the topological insulator without scattering1,2,3,4,5,6,7,8,9,10,11,12,13,14. However, the direct manipulation of these edge/surface states is difficult because they are significantly outnumbered by bulk carriers9,15,16. Here, we report experimental evidence for the modulation of these surface states by using a gate voltage to control quantum oscillations in Bi2Te3 nanoribbons. Surface conduction can be significantly enhanced by the gate voltage, with the mobility and Fermi velocity reaching values as high as ~5,800 cm2 V−1 s−1 and ~3.7 × 105 m s−1, respectively, with up to ~51% of the total conductance being due to the surface states. We also report the first observation of h/2e periodic oscillations, suggesting the presence of time-reversed paths with the same relative zero phase at the interference point16. The high surface conduction and ability to manipulate the surface states demonstrated here could lead to new applications in nanoelectronics and spintronics.

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## References

1. Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

2. Kane, C. L. & Mele, E. J. Topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).

3. Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009).

4. Moore, J. Topological insulators: the next generation. Nature Phys. 5, 378–380 (2009).

5. Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).

6. Qu, D.-X., 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, 821–824 (2010).

7. Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009).

8. Zhang, T. et al. Experimental demonstration of topological surface states protected by time-reversal symmetry. Phys. Rev. Lett. 103, 266803 (2009).

9. Chen, J. et al. Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3 . Phys. Rev. Lett. 105, 176602 (2010).

10. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

11. Qi, X.-L. & Zhang, S.-C. The quantum spin Hall effect and topological insulators. Phys. Today 63, 33–38 (January 2010).

12. Konig, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

13. Ren, Z., Taskin, A. A., Sasaki, S., Segawa, K. & Ando, Y. Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se. Phys. Rev. B 82, 241306 (2010).

14. Zhang, Y. et al. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nature Phys. 6, 584–588 (2010).

15. 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 . http://arxiv.org/abs/1003.3883v1 (2010).

16. Ihn, T. Topological insulators: oscillations in the ribbons. Nature Mater. 9, 187–188 (2010).

17. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

18. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3 . Science 325, 178–181 (2009).

19. Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009).

20. Wang, Z. et al. Tuning carrier type and density in Bi2Se3 by Ca-doping. Appl. Phys. Lett. 97, 042112 (2010).

21. Checkelsky, J. G. et al. Quantum interference in maroscopic crystals of nonmetallic Bi2Se3 . Phys. Rev. Lett. 103, 246601 (2009).

22. Peng, H. et al. Aharonov–Bohm interference in topological insulator nanoribbons. Nature Mater. 9, 225–229 (2009).

23. Kong, D. S. et al. Few-layer nanoplates of Bi2Se3 and Bi2Te3 with highly tunable chemical potential. Nano Lett. 10, 2245–2250 (2010).

24. Eto, K., Ren, Z., Taskin, A. A., Segawa, K. & Ando, Y. Angular-dependent oscillations of the magnetoresistance in Bi2Se3 due to the three-dimensional bulk Fermi surface. Phys. Rev. B 81, 195309 (2010).

25. Analytis, J. G. et al. Bulk Fermi surface coexistence with Dirac surface state in Bi2Se3: a comparison of photoemission and Shubnikov–de Haas measurements. Phys. Rev. B 81, 205407 (2010).

26. Taskin, A. A. & Ando, Y. Quantum oscillations in a topological insulator Bi1-xSbx . Phys. Rev. B 80, 085303 (2009).

27. Mallinson, R. B., Rayne, J. A. & Ure, R. W. de Haas–van Alphen effect in n-type Bi2Te3 . Phys. Rev. 175, 1049–1056 (1968).

28. Chandrasekhar, V., Rooks, M. J., Wind, S. & Prober, D. E. Observation of Aharonov–Bohm electron interference effects with periods h/e and h/2e in individual micron-size, normal-metal rings. Phys. Rev. Lett. 55, 1610–1613 (1985).

29. Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).

30. Bardarson, J. H., Brouwer, P. W. & Moore, J. E. Aharonov–Bohm oscillations in disordered topological insulator nanowires. Phys. Rev. Lett. 105, 156803 (2010).

## Acknowledgements

The authors thank the Focus Center Research Program-Center on Functional Engineered Nano Architectonics (FENA), Defense Advanced Research Projects Agency (DARPA) and the Australia Research Council (DP0984755, DP0985084) for their financial support. K.L.W. thanks Jeff Rogers (DARPA) and Betsy Weitzman (FENA). Y.W. thanks the Queensland International Fellowship. F.X. acknowledges helpful discussions with Siguang Ma, Yabin Fan and Pramey Upadhyaya (UCLA) and Wei Peng (UC Riverside).

## Author information

Authors

### Contributions

F.X. and L.H. designed and fabricated the devices. F.X., L-T.C., M.L. and A.S. carried out the measurements. L-N.C., Y.W., Z.G.C. and J.Z. synthesized the Bi2Te3 nanoribbons and performed structural analysis. Y.W., G.H., X.K., X.J. and Y.Z. contributed to the measurements and analysis. K.W. supervised the research. F.X., Y.W., L.H., J.Z. and K.W. wrote the paper, with help from all other co-authors.

### Corresponding authors

Correspondence to Faxian Xiu or Kang L. Wang.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 10792 kb)

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Xiu, F., He, L., Wang, Y. et al. Manipulating surface states in topological insulator nanoribbons. Nature Nanotech 6, 216–221 (2011). https://doi.org/10.1038/nnano.2011.19

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• DOI: https://doi.org/10.1038/nnano.2011.19

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