Journal of Electronic Materials

, Volume 46, Issue 7, pp 3837–3841 | Cite as

Analysis of Scanned Probe Images for Magnetic Focusing in Graphene

  • Sagar Bhandari
  • Gil-Ho Lee
  • Philip Kim
  • Robert M. Westervelt
Open Access


We have used cooled scanning probe microscopy (SPM) to study electron motion in nanoscale devices. The charged tip of the microscope was raster-scanned at constant height above the surface as the conductance of the device was measured. The image charge scatters electrons away, changing the path of electrons through the sample. Using this technique, we imaged cyclotron orbits that flow between two narrow contacts in the magnetic focusing regime for ballistic hBN–graphene–hBN devices. We present herein an analysis of our magnetic focusing imaging results based on the effects of the tip-created charge density dip on the motion of ballistic electrons. The density dip locally reduces the Fermi energy, creating a force that pushes electrons away from the tip. When the tip is above the cyclotron orbit, electrons are deflected away from the receiving contact, creating an image by reducing the transmission between contacts. The data and our analysis suggest that the graphene edge is rather rough, and electrons scattering off the edge bounce in random directions. However, when the tip is close to the edge, it can enhance transmission by bouncing electrons away from the edge, toward the receiving contact. Our results demonstrate that cooled SPM is a promising tool to investigate the motion of electrons in ballistic graphene devices.


Scanning probe microscopy theory ballistic transport graphene simulation magnetic focusing electron trajectories 


  1. 1.
    M.A. Topinka, B.J. Leroy, S.E.J. Shaw, E.J. Heller, R.M. Westervelt, K.D. Maranwoski, and A.C. Gossard, Science 289, 2323 (2000).CrossRefGoogle Scholar
  2. 2.
    K.E. Aidala, R.E. Parrott, T. Kramer, E.J. Heller, R.M. Westervelt, M.P. Hanson, and A.C. Gossard, Nat. Phys. 3, 464 (2007).CrossRefGoogle Scholar
  3. 3.
    P. Fallahi, A.C. Bleszynski, R.M. Westervelt, J. Huang, J.D. Walls, E.J. Heller, M. Hanson, and A.C. Gossard, Nano Lett. 5, 223 (2005).CrossRefGoogle Scholar
  4. 4.
    A.C. Bleszynski-Jayich, F.A. Zwanenburg, R.M. Westervelt, A.L. Roest, E.P.A.M. Bakkers, and L.P. Kouwenhoven, Nano Lett. 7, 295 (2007).CrossRefGoogle Scholar
  5. 5.
    A.C. Bleszynski-Jayich, L.E. Froberg, M.T. Bjork, H.J. Trodahl, L. Samuelson, and R.M. Westervelt, Phys. Rev. B 77, 245327 (2008).CrossRefGoogle Scholar
  6. 6.
    S. Bhandari, G.H. Lee, A. Klales, K. Watanabe, T. Taniguchi, E. Heller, P. Kim, and R.M. Westervelt, Nano Lett. 16, 1690 (2016).CrossRefGoogle Scholar
  7. 7.
    S. Bhandari (Ph.D. thesis, Harvard University, 2015).Google Scholar
  8. 8.
    P.R. Wallace, Phys. Rev. 71, 622 (1947).CrossRefGoogle Scholar
  9. 9.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, Rev. Mod. Phys. 81, 109 (2009).CrossRefGoogle Scholar
  10. 10.
    A.K. Geim and K.S. Novoselov, Nat. Mater. 6, 183 (2007).CrossRefGoogle Scholar
  11. 11.
    M.L. Boas, Mathematical Methods in the Physical Sciences, 3rd ed. (London: Wiley, 2006), p. 714.Google Scholar

Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Sagar Bhandari
    • 1
  • Gil-Ho Lee
    • 2
  • Philip Kim
    • 1
    • 2
  • Robert M. Westervelt
    • 1
    • 2
  1. 1.School of Engineering and Applied SciencesHarvard UniversityCambridgeUSA
  2. 2.Department of PhysicsHarvard UniversityCambridgeUSA

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