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.

  • Letter
  • Published:

Electrically tunable transverse magnetic focusing in graphene

Nature Physics volume 9, pages 225–229 (2013)Cite this article

Subjects

Abstract

Electrons in a periodic lattice can propagate without scattering for macroscopic distances despite the presence of the non-uniform Coulomb potential due to the nuclei1. Such ballistic motion of electrons allows the use of a transverse magnetic field to focus electrons2. This phenomenon, known as transverse magnetic focusing (TMF), has been used to study the Fermi surface of metals3 and semiconductor heterostructures4, as well as to investigate Andreev reflection3 and spin–orbit interaction5, and to detect composite fermions6,7. Here we report on the experimental observation of TMF in high-mobility mono-, bi- and tri-layer graphene devices. The ability to tune the graphene carrier density enables us to investigate TMF continuously from the hole to the electron regime and analyse the resulting focusing fan. Moreover, by applying a transverse electric field to tri-layer graphene, we use TMF as a ballistic electron spectroscopy method to investigate controlled changes in the electronic structure of a material. Finally, we demonstrate that TMF survives in graphene up to 300 K, by far the highest temperature reported for any system, opening the door to new room-temperature applications based on electron-optics.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

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

Figure 1: TMF schematics.
Figure 2: TMF in MLG, BLG and TLG at 5 K.
Figure 3: Visualizing in situ band structure changes in TLG with TMF.
Figure 4: Temperature dependence of the TMF in MLG and BLG.

Similar content being viewed by others

References

  1. Bloch, F. Über die Quantenmechanik der Elektronen in Kristallgittern. Z. Phys. 52, 555–600 (1929).

    Article  ADS  Google Scholar 

  2. Tsoi, V. S. Focusing of electrons in a metal by a transverse magnetic field. JETP Lett. 19, 70–71 (1974).

    ADS  Google Scholar 

  3. Tsoi, V. S., Bass, J. & Wyder, P. Studying conduction-electron/interface interactions using transverse electron focusing. Rev. Mod. Phys. 71, 1641–1693 (1999).

    Article  ADS  Google Scholar 

  4. Van Houten, H. et al. Coherent electron focusing with quantum point contacts in a two-dimensional electron gas. Phys. Rev. B 39, 8556–8575 (1989).

    Article  ADS  Google Scholar 

  5. Rokhinson, L. P., Larkina, V., Lyanda-Geller, Y. B., Pfeiffer, L. N. & West, K. W. Spin separation in cyclotron motion. Phys. Rev. Lett. 93, 146601 (2004).

    Article  ADS  Google Scholar 

  6. Goldman, V. J., Su, B. & Jain, J. K. Detection of composite fermions by magnetic focusing. Phys. Rev. Lett. 72, 2065–2068 (1994).

    Article  ADS  Google Scholar 

  7. Smet, J. H. et al. Magnetic focusing of composite fermions through arrays of cavities. Phys. Rev. Lett. 77, 2272–2275 (1996).

    Article  ADS  Google Scholar 

  8. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotech. 5, 722–726 (2010).

    Article  ADS  Google Scholar 

  9. Taychatanapat, T., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene. Nature Phys. 7, 621–625 (2011).

    Article  ADS  Google Scholar 

  10. Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011).

    Article  ADS  Google Scholar 

  11. Beenakker, C. W. J., van Houten, H. & van Wees, B. J. Mode interference effect in coherent electron focusing. Europhys. Lett. 4, 359–364 (1988).

    Article  ADS  Google Scholar 

  12. Aidala, K. E. et al. Imaging magnetic focusing of coherent electron waves. Nature Phys. 3, 464–468 (2007).

    Article  ADS  Google Scholar 

  13. Rakyta, P., Kormányos, A., Cserti, J. & Koskinen, P. Exploring the graphene edges with coherent electron focusing. Phys. Rev. B 81, 115411 (2010).

    Article  ADS  Google Scholar 

  14. Silvestrov, P. G. & Efetov, K. B. Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach. Phys. Rev. B 77, 155436 (2008).

    Article  ADS  Google Scholar 

  15. McCann, E. & Fal’ko, V. I. Landau-level degeneracy and quantum Hall effect in a graphite bilayer. Phys. Rev. Lett. 96, 086805 (2006).

    Article  ADS  Google Scholar 

  16. Lu, C. L., Chang, C. P., Huang, Y. C., Chen, R. B. & Lin, M. L. Influence of an electric field on the optical properties of few-layer graphene with AB stacking. Phys. Rev. B 73, 144427 (2006).

    Article  ADS  Google Scholar 

  17. Guinea, F., Neto, A. H. C. & Peres, N. M. R. Electronic states and Landau levels in graphene stacks. Phys. Rev. B 73, 245426 (2006).

    Article  ADS  Google Scholar 

  18. Latil, S. & Henrard, L. Charge carriers in few-layer graphene films. Phys. Rev. Lett. 97, 036803 (2006).

    Article  ADS  Google Scholar 

  19. Partoens, B. & Peeters, F. M. From graphene to graphite: Electronic structure around the K point. Phys. Rev. B 74, 075404 (2006).

    Article  ADS  Google Scholar 

  20. Koshino, M. & McCann, E. Gate-induced interlayer asymmetry in ABA-stacked trilayer graphene. Phys. Rev. B 79, 125443 (2009).

    Article  ADS  Google Scholar 

  21. Cheianov, V. V., Falk´o, V. & Altshuler, B. L. The focusing of electron flow and a veselago lens in graphene p–n junctions. Science 315, 1252–1255 (2007).

    Article  ADS  Google Scholar 

  22. Hwang, E. H. & Das Sarma, S. Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene. Phys. Rev. B 77, 115449 (2008).

    Article  ADS  Google Scholar 

  23. Heremans, J., Fuller, B. K., Thrush, C. M. & Partin, D. L. Temperature dependence of electron focusing in In1−xGax As/InP heterojunctions. Phys. Rev. B 52, 5767–5772 (1995).

    Article  ADS  Google Scholar 

  24. Schiefele, J., Sols, F. & Guinea, F. Temperature dependence of the conductivity of graphene on boron nitride. Phys. Rev. B 85, 195420 (2012).

    Article  ADS  Google Scholar 

  25. Liu, Z. et al. Direct growth of graphene/hexagonal boron nitride stacked layers. Nano Lett. 11, 2032–2037 (2011).

    Article  ADS  Google Scholar 

  26. Mayorov, A. S. et al. Interaction-drive spectrum reconstruction in bilayer graphene. Science 333, 860–863 (2011).

    Article  ADS  Google Scholar 

  27. Weitz, R. T., Allen, M. T., Feldman, B. E., Martin, J. & Yacoby, A. Broken-symmetry states in doubly gated suspended bilayer graphene. Science 330, 812–816 (2010).

    Article  ADS  Google Scholar 

  28. Kotov, V. N., Uchoa, B., Pereira, V. M., Guinea, F. & Castro Neto, A. H. Electron–electron interactions in graphene: Current status and perspectives. Rev. Mod. Phys. 84, 1067–1125 (2012).

    Article  ADS  Google Scholar 

  29. Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nature Phys. 6, 30–33 (2010).

    Article  ADS  Google Scholar 

  30. Levy, N. et al. Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329, 544–547 (2010).

    Article  ADS  Google Scholar 

  31. Gomes, K. K., Mar, W., Ko, W., Guinea, F. & Manoharan, H. C. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank L. Levitov and A. Yacoby for discussions. We acknowledge financial support from National Science Foundation Career Award No. DMR-0845287 and the Office of Naval Research GATE MURI. This work made use of the MRSEC Shared Experimental Facilities supported by the National Science Foundation under award No. DMR-0819762 and of Harvard’s Center for Nanoscale Systems (CNS), supported by the National Science Foundation under grant No. ECS-0335765.

Author information

Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    Thiti Taychatanapat

  2. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Thiti Taychatanapat & Pablo Jarillo-Herrero

  3. National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan

    Kenji Watanabe & Takashi Taniguchi

Authors
  1. Thiti Taychatanapat
    View author publications

    Search author on:PubMed Google Scholar

  2. Kenji Watanabe
    View author publications

    Search author on:PubMed Google Scholar

  3. Takashi Taniguchi
    View author publications

    Search author on:PubMed Google Scholar

  4. Pablo Jarillo-Herrero
    View author publications

    Search author on:PubMed Google Scholar

Contributions

T. Taychatanapat fabricated the samples and performed the experiments. K.W. and T. Taniguchi synthesized the hBN samples. T. Taychatanapat and P.J-H. carried out the data analysis and co-wrote the paper.

Corresponding author

Correspondence to Pablo Jarillo-Herrero.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 2165 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taychatanapat, T., Watanabe, K., Taniguchi, T. et al. Electrically tunable transverse magnetic focusing in graphene. Nature Phys 9, 225–229 (2013). https://doi.org/10.1038/nphys2549

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue date:

  • DOI: https://doi.org/10.1038/nphys2549

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