Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Magnetic field-induced helical mode and topological transitions in a topological insulator nanoribbon

Nature Nanotechnology volume 11, pages 345–351 (2016)Cite this article

Subjects

Abstract

The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov–Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Schematics of the Bi2Te3 bandstructure, surface state modes and expected magnetoconductance oscillation patterns in TINRs.
Figure 2: Ambipolar field effect, demonstrating quasi-ballistic conduction and gate-tunable 0- and π-ABOs, demonstrating TSS modes in TINRs.
Figure 3: Analysis of quantized TSS subbands in gate-dependent conductance oscillations and 0- and π-ABO alternations.
Figure 4: Temperature dependence of the AB oscillations in TINRs, confirming quasi-ballistic transport.
Figure 5: Non-local transport in TINRs.

Similar content being viewed by others

References

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

    CAS  Google Scholar 

  2. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  6. Qu, D.-X., Hor, Y., Xiong, J., Cava, R. & Ong, N. Quantum oscillations and hall anomaly of surface states in the topological insulator Bi2Te3 . Science 329, 821–824 (2010).

    Article  CAS  Google Scholar 

  7. Peng, H. L. et al. Aharonov–Bohm interference in topological insulator nanoribbons. Nature Mater. 9, 225–229 (2010).

    Article  CAS  Google Scholar 

  8. Xiu, F. X. et al. Manipulating surface states in topological insulator nanoribbons. Nature Nanotech. 6, 216–221 (2011).

    Article  CAS  Google Scholar 

  9. Tian, M. L. et al. Dual evidence of surface Dirac states in thin cylindrical topological insulator Bi2Te3 nanowires. Sci. Rep. 3, 1212 (2013).

    Article  Google Scholar 

  10. Dufouleur, J. et al. Quasiballistic transport of Dirac fermions in a Bi2Se3 nanowire. Phys. Rev. Lett. 110, 186806 (2013).

    Article  CAS  Google Scholar 

  11. Gooth, J., Hamdou, B., Dorn, A., Zierold, R. & Nielsch, K. Resolving the Dirac cone on the surface of Bi2Te3 topological insulator nanowires by field-effect measurements. Appl. Phys. Lett. 104, 243115 (2014).

    Article  Google Scholar 

  12. Guanhua, Z. et al. Growth of topological insulator Bi2Se3 thin films on SrTiO3 with large tunability in chemical potential. Adv. Funct. Mater. 21, 2351–2355 (2011).

    Article  Google Scholar 

  13. Tian, J. F. et al. Quantum and classical magnetoresistance in ambipolar topological insulator transistors with gate-tunable bulk and surface conduction. Sci. Rep. 4, 4859 (2014).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  15. Cook, A. & Franz, M. Majorana fermions in a topological–insulator nanowire proximity-coupled to an s-wave superconductor. Phys. Rev. B 84, 201105 (2011).

    Article  Google Scholar 

  16. Cook, A. M., Vazifeh, M. M. & Franz, M. Stability of Majorana fermions in proximity-coupled topological insulator nanowires. Phys. Rev. B 86, 155431 (2012).

    Article  Google Scholar 

  17. Rosenberg, G., Guo, H. M. & Franz, M. Wormhole effect in a strong topological insulator. Phys. Rev. B 82, 041104 (2010).

    Article  Google Scholar 

  18. Zhang, Y. & Vishwanath, A. Anomalous Aharonov–Bohm conductance oscillations from topological insulator surface states. Phys. Rev. Lett. 105, 206601 (2010).

    Article  Google Scholar 

  19. Ostrovsky, P. M., Gornyi, I. V. & Mirlin, A. D. Interaction-induced criticality in Z2 topological insulators. Phys. Rev. Lett. 105, 036803 (2010).

    Article  CAS  Google Scholar 

  20. Hong, S. S., Zhang, Y., Cha, J. J., Qi, X. L. & Cui, Y. One-dimensional helical transport in topological insulator nanowire interferometers. Nano Lett. 14, 2815–2821 (2014).

    Article  CAS  Google Scholar 

  21. Cho, S. et al. Aharonov–Bohm oscillations in a quasi-ballistic three-dimensional topological insulator nanowire. Nature Commun. 6, 7634 (2015).

    Article  Google Scholar 

  22. De Juan, F., Ilan, R. & Bardarson, J. H. Robust transport signatures of topological superconductivity in topological insulator nanowires. Phys. Rev. Lett. 113, 107003 (2014).

    Article  Google Scholar 

  23. Ilan, R., Bardarson, J. H., Sim, H.-S. & Moore, J. E. Detecting perfect transmission in Josephson junctions on the surface of three dimensional topological insulators. New J. Phys. 16, 053007 (2014).

    Article  Google Scholar 

  24. Jauregui, L. A., Pettes, M. T., Rokhinson, L. P., Shi, L. & Chen, Y. P. Gate tunable relativistic mass and Berry's phase in topological insulator nanoribbon field effect devices. Sci. Rep. 5, 8452 (2015).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  26. Hamdou, B., Gooth, J., Dorn, A., Pippel, E. & Nielsch, K. Aharonov–Bohm oscillations and weak antilocalization in topological insulator Sb2Te3 nanowires. Appl. Phys. Lett. 102, 223110 (2013).

    Article  Google Scholar 

  27. Matsuo, S. et al. Weak antilocalization and conductance fluctuation in a submicrometer-sized wire of epitaxial Bi2Se3 . Phys. Rev. B 85, 075440 (2012).

    Article  Google Scholar 

  28. Ning, W. et al. One-dimensional weak antilocalization in single-crystal Bi2Te3 nanowires. Sci. Rep. 3, 1564 (2013).

    Article  Google Scholar 

  29. Grbic, B. et al. Aharonov–Bohm oscillations in the presence of strong spin–orbit interactions. Phys. Rev. Lett. 99, 176803 (2007).

    Article  Google Scholar 

  30. Yau, J. B., De Poortere, E. P. & Shayegan, M. Aharonov–Bohm oscillations with spin: evidence for Berry's phase. Phys. Rev. Lett. 88, 146801 (2002).

    Article  Google Scholar 

  31. Yang, M. J., Yang, C. H. & Lyanda-Geller, Y. B. Quantum beating in the conductance of ballistic rings. Physica E 22, 304–307 (2004).

    Article  Google Scholar 

  32. Buttiker, M. Four-terminal phase-coherent conductance. Phys. Rev. Lett. 57, 1761 (1986).

    Article  CAS  Google Scholar 

  33. Couto, N., Sacépé, B. & Morpurgo, A. Transport through graphene on SrTiO3 . Phys. Rev. Lett. 107, 225501 (2011).

    Article  Google Scholar 

  34. Bardarson, J. H. & Moore, J. E. Quantum interference and Aharonov–Bohm oscillations in topological insulators. Rep. Prog. Phys. 76, 056501 (2013).

    Article  Google Scholar 

  35. Gao, B., Chen, Y. F., Fuhrer, M. S., Glattli, D. C. & Bachtold, A. Four-point resistance of individual single-wall carbon nanotubes. Phys. Rev. Lett. 95, 196802 (2005).

    Article  CAS  Google Scholar 

  36. Kobayashi, K., Aikawa, H., Katsumoto, S. & Iye, Y. Probe-configuration-dependent decoherence in an Aharonov–Bohm ring. J. Phys. Soc. Jpn 71, 2094 (2002).

    Article  CAS  Google Scholar 

  37. Hansen, A. E., Kristensen, A., Pedersen, S., Sorensen, C. B. & Lindelof, P. E. Mesoscopic decoherence in Aharonov–Bohm rings. Phys. Rev. B 64, 045327 (2001).

    Article  Google Scholar 

  38. Ferrier, M. et al. Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network. Phys. Rev. Lett. 100, 146802 (2008).

    Article  CAS  Google Scholar 

  39. Ludwig, T. & Mirlin, A. D. Interaction-induced dephasing of Aharonov–Bohm oscillations. Phys. Rev. B 69, 193306 (2004).

    Article  Google Scholar 

  40. Texier, C. & Montambaux, G. Dephasing due to electron–electron interaction in a diffusive ring. Phys. Rev. B 72, 115327 (2005).

    Article  Google Scholar 

  41. Buchholz, S. S., Fischer, S. F., Kunze, U., Reuter, D. & Wieck, A. D. Nonlocal Aharonov–Bohm conductance oscillations in an asymmetric quantum ring. Appl. Phys. Lett. 94, 022107 (2009).

    Article  Google Scholar 

  42. Yacoby, A., Schuster, R. & Heiblum, M. Phase rigidity and h/2e oscillations in a single-ring Aharonov–Bohm experiment. Phys. Rev. B 53, 9583 (1996).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

TI material synthesis, characterization and part of the magneto-transport studies were supported by a DARPA MESO programme (grant no. N66001-11-1-4107). Part of the FET fabrication and characterizations were supported by Intel Corporation. The later stage of this work at Purdue was also supported in part by the National Science Foundation (DMR-1410942). L.A.J. acknowledges support by an Intel PhD fellowship and a Purdue Center for Topological Materials fellowship. L.P.R. was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC-0008630. Y.P.C. and L.A.J. thank M. Franz, J.H. Bardarson, T. Kubis and F.W. Chen for discussions.

Author information

Author notes

  1. Michael T. Pettes

    Present address: Present address: Department of Mechanical Engineering, University of Connecticut, Storrs, Connecticut 06269, USA,

Authors and Affiliations

  1. Birck Nanotechnology Center, Purdue University, West Lafayette, 47907, Indiana, USA

    Luis A. Jauregui, Leonid P. Rokhinson & Yong P. Chen

  2. School of Electrical and Computer Engineering, Purdue University, West Lafayette, 47907, Indiana, USA

    Luis A. Jauregui, Leonid P. Rokhinson & Yong P. Chen

  3. Department of Mechanical Engineering, University of Texas at Austin, Austin, 78712, Texas, USA

    Michael T. Pettes & Li Shi

  4. Department of Physics and Astronomy, Purdue University, West Lafayette, 47907, Indiana, USA

    Leonid P. Rokhinson & Yong P. Chen

  5. Materials Science and Engineering Program, University of Texas at Austin, Austin, 78712, Texas, USA

    Li Shi

Authors
  1. Luis A. Jauregui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael T. Pettes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Leonid P. Rokhinson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Li Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yong P. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

L.A.J. designed and fabricated the devices and carried out the measurements and data analysis. M.T.P. and L.S. synthesized the Bi2Te3 nanoribbons and performed structural analysis. L.P.R. helped with the low-temperature transport experiment. Y.P.C. supervised the research. L.A.J and Y.P.C. wrote the paper with contributions from all co-authors.

Corresponding author

Correspondence to Yong P. Chen.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1914 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jauregui, L., Pettes, M., Rokhinson, L. et al. Magnetic field-induced helical mode and topological transitions in a topological insulator nanoribbon. Nature Nanotech 11, 345–351 (2016). https://doi.org/10.1038/nnano.2015.293

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2015.293

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing