Magnetic quantum ratchet effect in graphene

Journal name:
Nature Nanotechnology
Year published:
Published online


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


  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.


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Author information


  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


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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