Magnetic quantum ratchet effect in graphene

Journal name:
Nature Nanotechnology
Volume:
8,
Pages:
104–107
Year published:
DOI:
doi:10.1038/nnano.2012.231
Received
Accepted
Published online

Abstract

A periodically driven system with spatial asymmetry can exhibit a directed motion facilitated by thermal or quantum fluctuations1. This so-called ratchet effect2 has fascinating ramifications in engineering and natural sciences3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. Graphene19 is nominally a symmetric system. Driven by a periodic electric field, no directed electric current should flow. However, if the graphene has lost its spatial symmetry due to its substrate or adatoms, an electronic ratchet motion can arise. We report an experimental demonstration of such an electronic ratchet in graphene layers, proving the underlying spatial asymmetry. The orbital asymmetry of the Dirac fermions is induced by an in-plane magnetic field, whereas the periodic driving comes from terahertz radiation. The resulting magnetic quantum ratchet transforms the a.c. power into a d.c. current, extracting work from the out-of-equilibrium electrons driven by undirected periodic forces. The observation of ratchet transport in this purest possible two-dimensional system indicates that the orbital effects may appear and be substantial in other two-dimensional crystals such as boron nitride, molybdenum dichalcogenides and related heterostructures. The measurable orbital effects in the presence of an in-plane magnetic field provide strong evidence for the existence of structure inversion asymmetry in graphene.

At a glance

Figures

  1. Dirac electrons drive a ratchet.
    Figure 1: Dirac electrons drive a ratchet.

    The ratchet wheel (analogue of electric current) turns as the a.c. electric field E(t) from the terahertz radiation drives the electrons in graphene. The ratchet-and-pawl mechanism is induced by the static magnetic field B and the spatial asymmetry of graphene induced by the hydrogen adatoms (blue spheres). The resulting spatial distribution of the electron density is shown in red. If the electrons, at any time, are driven to the right by the electric field, their orbitals are shifted upwards due to a quantum analogue of the Lorentz force (left panel). Consequently, their mobility decreases; that is, friction increases. Half a period later, when electrons are caused to flow to the left, their orbitals are shifted downwards and the mobility increases (right panel).

  2. Temperature dependence of current density jx measured in sample A.
    Figure 2: Temperature dependence of current density jx measured in sample A.

    The a.c. electric field is aligned along the x-axis and the magnetic field along the y-axis. Data are obtained for an electric field amplitude of ~10 kV cm−1 and a static magnetic field By = ±7 T. Left inset: magnetic field dependence of jx(|By|= [jx(By < 0) − jx(By > 0)]/2 for samples A, B, C and D. Data for samples A, B and C are obtained at T = 150 K and data for sample D at 4.2 K. Note that curves for samples A, B and D in the inset are multiplied by a factor of 3. Right inset: experimental geometry. The normal incidence of radiation on the sample excludes current generation at zero magnetic field26, 27, 28.

  3. Sensitivity of ratchet current to a.c. electric field direction.
    Figure 3: Sensitivity of ratchet current to a.c. electric field direction.

    a, Temperature dependence of variable j1 and constant j2 contributions to ratchet current jx(|By|) measured in sample A for |By| = 7 T and electric field amplitude ~10 kV cm−1. Left inset: dependence of jx(|By|) on the electric field orientation given by the azimuth angle β between E and By (right inset). Data are obtained for T = 115 K. The solid line is a fit after equation (1). b, Mobility and density of Dirac fermions as a function of temperature determined in sample A by Hall measurements. The decrease in mobility for T > ~100 K is attributed to phonon scattering, as the Bloch–Grüneisen temperature for this sample is TBG  66 K.

  4. Magnetic field dependence of the current density jy([verbar]By[verbar]).
    Figure 4: Magnetic field dependence of the current density jy(|By|).

    Measurements are taken along magnetic field By in sample C for clockwise and anticlockwise rotating in-plane electric field E(t) with amplitude ~7 kV cm−1. Solid lines show the linear fit of jy(|By|). Inset: experimental geometry.

References

  1. Hänggi, P. & Marchesoni, F. Artificial Brownian motors: controlling transport on the nanoscale. Rev. Mod. Phys. 81, 387442 (2009).
  2. Feynman, R. P., Leighton, R. B. & Sands, M. The Feynman Lectures on Physics Vol. 1 (Addison-Wesley, 1966).
  3. Hänggi, P., Marchesoni, F. & Nori, F. Brownian motors. Annal. Physik 14, 13 (2005).
  4. Linke, H. et al. Experimental tunneling ratchets. Science 286, 23142317 (1999).
  5. Koumura, N., Zijlstra, R. W. J., van Delden, R. A., Harada, N. & Feringa, B. L. Light-driven monodirectional molecular rotor. Nature 401, 152155 (1999).
  6. Bermudez, V. et al. Influencing intramolecular motion with an alternating electric field. Nature 406, 608611 (2000).
  7. Serreli, V., Lee, C., Kay, E. R. & Leigh, D. A. A molecular information ratchet. Nature 445, 523527 (2007).
  8. Mahmud, G. et al. Directing cell motions on micropatterned ratchets. Nature Phys. 5, 606612 (2009).
  9. Villegas, J. E. et al. A superconducting reversible rectifier that controls the motion of magnetic flux quanta. Science 302, 11881191 (2003).
  10. Togawa, Y. et al. Direct observation of rectified motion of vortices in a niobium superconductor. Phys. Rev. Lett. 95, 087002 (2005).
  11. Cole, D. et al. Ratchet without spatial asymmetry for controlling the motion of magnetic flux quanta using time-asymmetric drives. Nature Mater. 5, 305311 (2006).
  12. Roeling, E. M. et al. Organic electronic ratchets doing work. Nature Mater. 10, 5155 (2011).
  13. Salger, T. et al. Directed transport of atoms in a Hamiltonian quantum ratchet. Science 326, 12411243 (2009).
  14. Blickle, V. & Bechinger, C. Realization of a micrometre-sized stochastic heat engine. Nature Phys. 8, 143146 (2012).
  15. Olbrich, P. et al. Ratchet effects induced by terahertz radiation in heterostructures with a lateral periodic potential. Phys. Rev. Lett. 103, 090603 (2009).
  16. O'Hare, A., Kusmartsev, F. V. & Kugel, K. I. A stable ‘flat’ form of two-dimensional crystals: could graphene, silicene, germanene be minigap semiconductors? Nano Lett. 12, 10451052 (2012).
  17. Smirnov, S., Bercioux, D., Grifoni, M. & Richter, K. Quantum dissipative Rashba spin ratchets. Phys. Rev. Lett. 100, 230601 (2008).
  18. Costache, M. V. & Valenzuela, S. O. Experimental spin ratchet. Science 330, 16451648 (2010).
  19. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109162 (2009).
  20. Das Sarma, S., Adam, S., Huang, E. H. & Rossi, E. Electronic transport in two dimensional graphene. Rev. Mod. Phys. 83, 407470 (2011).
  21. Rozhkov, A. V., Giavaras, G., Bliokh, Y. P., Freilikher, V. & Nori, F. Electronic properties of mesoscopic graphene structures: charge confinement and control of spin and charge transport. Phys. Rep. 503, 77114 (2011).
  22. Ganichev, S. D. & Prettl, W. Intense Terahertz Excitation of Semiconductors (Oxford Univ. Press, 2006).
  23. Ganichev, S. D. Tunnel ionization of deep impurities in semiconductors induced by terahertz electric fields. Physica B 273–274, 737742 (1999).
  24. Schneider, P. et al. Spin relaxation times of 2D holes from spin sensitive bleaching of inter-subband absorption. J. Appl. Phys. 96, 420424 (2004).
  25. Tzalenchuk, A. et al. Towards a quantum resistance standard based on epitaxial graphene. Nature Nanotech. 5, 186189 (2010).
  26. Karch, J. et al. Dynamic Hall effect driven by circularly polarized light in a graphene layer. Phys. Rev. Lett. 97, 227402 (2010).
  27. Karch, J. et al. Terahertz radiation driven chiral edge currents in graphene. Phys. Rev. Lett. 107, 276601 (2011).
  28. Ganichev, S. D., Ivchenko, E. L. & Prettl, W. Photogalvanic effects in quantum wells. Physica E 14, 166171 (2002).
  29. Lara-Avila, S. et al. Non-volatile photochemical gating of an epitaxial graphene. Adv. Mater. 23, 878882 (2011).
  30. Falko, V. I. Rectifying properties of 2D inversion layers in a parallel magnetic field. Fiz. Tvedr. Tela 31, 2932 (1989) [Sov. Phys. Solid State, 561–563 (1989)].
  31. Tarasenko, S. A. Electron scattering in quantum wells subjected to an in-plane magnetic field. Phys. Rev. B 77, 085328 (2008).
  32. Tarasenko, S. A. Direct current driven by ac electric field in quantum wells. Phys. Rev. B 83, 035313 (2011).
  33. Konschuh, S., Gmitra, M. & Fabian, J. Tight-binding theory of the spin–orbit coupling in graphene. Phys. Rev. B 82, 245412 (2010).
  34. Yazyev, O. & Helm, L. Defect-induced magnetism in graphene. Phys. Rev. B 75, 125408 (2007).
  35. Castro Neto, A. H. & Guinea, F. Impurity induced spin–orbit coupling in graphene. Phys. Rev. Lett. 103, 206804 (2009).
  36. Ertler, C., Konschuh, S., Gmitra, M. & Fabian, J. Electron spin relaxation in graphene: the role of the substrate. Phys. Rev. B 80, 041405(R) (2009).

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Author information

Affiliations

  1. Terahertz Center, University of Regensburg, 93040 Regensburg, Germany

    • C. Drexler,
    • P. Olbrich,
    • J. Karch,
    • M. Hirmer,
    • F. Müller,
    • M. Gmitra,
    • J. Fabian &
    • S. D. Ganichev
  2. Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia

    • S. A. Tarasenko
  3. Linköping University, S-58183 Linköping, Sweden

    • R. Yakimova
  4. Chalmers University of Technology, S-41296 Göteborg, Sweden

    • S. Lara-Avila &
    • S. Kubatkin
  5. The Richard E. Smalley Institute for Nanoscale Science and Technology, Rice University, Houston, Texas 77005, USA

    • M. Wang,
    • R. Vajtai,
    • P. M. Ajayan &
    • J. Kono

Contributions

S.D.G. and S.A.T. conceived the experiments. C.D., P.O., J.Ka., M.H., F.M. and S.D.G. designed the experimental set-up and performed the measurements. C.D., P.O., S.D.G. and S.A.T. analysed the data. R.Y., S.L-A., S.K., J.Ko., P.M.A., M.W. and R.V. grew, fabricated and characterized samples. S.A.T. developed the microscopic theory. J.F. and M.G. performed the first-principles calculations. S.D.G., S.A.T., J.F., C.D., P.O. and M.G. co-wrote the paper. All authors commented on the manuscript.

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