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Electron–hole collision limited transport in charge-neutral bilayer graphene

Abstract

Ballistic transport occurs whenever electrons propagate without collisions deflecting their trajectory. It is normally observed in conductors with a negligible concentration of impurities, at low temperature, to avoid electron–phonon scattering. Here, we use suspended bilayer graphene devices to reveal a new regime, in which ballistic transport is not limited by scattering with phonons or impurities, but by electron–hole collisions. The phenomenon manifests itself in a negative four-terminal resistance that becomes visible when the density of holes (electrons) is suppressed by gate-shifting the Fermi level in the conduction (valence) band, above the thermal energy. For smaller densities, transport is diffusive, and the measured conductivity is reproduced quantitatively, with no fitting parameters, by including electron–hole scattering as the only process causing velocity relaxation. Experiments on a trilayer device show that the phenomenon is robust and that transport at charge neutrality is governed by the same physics. Our results provide a textbook illustration of a transport regime that had not been observed previously and clarify the nature of conduction through charge-neutral graphene under conditions in which carrier density inhomogeneity is immaterial. They also demonstrate that transport can be limited by a fully electronic mechanism, originating from the same microscopic processes that govern the physics of Dirac-like plasmas.

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Figure 1: Ballistic transport in multi-terminal suspended bilayer devices.
Figure 2: Electron–hole scattering in bilayer graphene.
Figure 3: Electron–hole scattering in Bernal-stacked trilayer graphene.
Figure 4: Temperature dependence of the mobility and conductivity at charge neutrality.

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References

  1. Sharvin, Y. V. A possible method for studying Fermi surfaces. J. Exp. Theor. Phys. 21, 655–656 (1965).

    ADS  Google Scholar 

  2. 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 

  3. 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 

  4. Beenakker, C. W. J. & Vanhouten, H. Quantum transport in semiconductor nanostructures. Solid State Phys. 44, 1–228 (1991).

    Article  Google Scholar 

  5. Taychatanapat, T., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Electrically tunable transverse magnetic focusing in graphene. Nat. Phys. 9, 225–229 (2013).

    Article  Google Scholar 

  6. Lee, M. et al. Ballistic miniband conduction in a graphene superlattice. Science 353, 1526–1529 (2016).

    Article  ADS  Google Scholar 

  7. van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848–850 (1988).

    Article  ADS  Google Scholar 

  8. Wharam, D. A. et al. One-dimensional transport and the quantisation of the ballistic resistance. J. Phys. C 21, L209 (1988).

    Article  Google Scholar 

  9. Predel, H. et al. Effects of electron–electron scattering on electron-beam propagation in a two-dimensional electron gas. Phys. Rev. B 62, 2057–2064 (2000).

    Article  ADS  Google Scholar 

  10. Ki, D.-K. & Morpurgo, A. F. High-quality multiterminal suspended graphene devices. Nano Lett. 13, 5165–5170 (2013).

    Article  ADS  Google Scholar 

  11. Ochoa, H., Castro, E. V., Katsnelson, M. I. & Guinea, F. Temperature-dependent resistivity in bilayer graphene due to flexural phonons. Phys. Rev. B 83, 235416 (2011).

    Article  ADS  Google Scholar 

  12. Laitinen, A. et al. Coupling between electrons and optical phonons in suspended bilayer graphene. Phys. Rev. B 91, 121414 (2015).

    Article  ADS  Google Scholar 

  13. Koshino, M. & Ando, T. Transport in bilayer graphene: calculations within a self-consistent Born approximation. Phys. Rev. B 73, 245403 (2006).

    Article  ADS  Google Scholar 

  14. 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 

  15. Gorbachev, R. V., Tikhonenko, F. V., Mayorov, A. S., Horsell, D. W. & Savchenko, A. K. Weak localization in bilayer graphene. Phys. Rev. Lett. 98, 176805 (2007).

    Article  ADS  Google Scholar 

  16. Li, J. et al. Effective mass in bilayer graphene at low carrier densities: the role of potential disorder and electron–electron interaction. Phys. Rev. B 94, 161406 (2016).

    Article  ADS  Google Scholar 

  17. Baber, W. G. The contribution to the electrical resistance of metals from collisions between electrons. Proc. R. Soc. Lond. A 158, 0383–0396 (1937).

    Article  ADS  Google Scholar 

  18. Thompson, A. H. Electron–electron scattering in TiS2 . Phys. Rev. Lett. 35, 1786–1789 (1975).

    Article  ADS  Google Scholar 

  19. Kukkonen, C. A. & Maldague, P. F. Electron-hole scattering and the electrical resistivity of the semimetal TiS2 . Phys. Rev. Lett. 37, 782–785 (1976).

    Article  ADS  Google Scholar 

  20. Gantmakher, V. F. & Levinson, I. B. Effect of collisions between current carriers on dissipative conductivity. Sov. Phys. JETP 47, 133–137 (1978).

    ADS  Google Scholar 

  21. Entin, M. V. et al. The effect of electron–hole scattering on transport properties of a 2D semimetal in the HgTe quantum well. J. Exp. Theor. Phys. 117, 933–943 (2013).

    Article  ADS  Google Scholar 

  22. González, J., Guinea, F. & Vozmediano, M. A. H. Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction. Phys. Rev. B 59, R2474–R2477 (1999).

    Article  ADS  Google Scholar 

  23. Sheehy, D. E. & Schmalian, J. Quantum critical scaling in graphene. Phys. Rev. Lett. 99, 226803 (2007).

    Article  ADS  Google Scholar 

  24. Son, D. T. Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction. Phys. Rev. B 75, 235423 (2007).

    Article  ADS  Google Scholar 

  25. Fritz, L., Schmalian, J., Müller, M. & Sachdev, S. Quantum critical transport in clean graphene. Phys. Rev. B 78, 085416 (2008).

    Article  ADS  Google Scholar 

  26. Kashuba, A. B. Conductivity of defectless graphene. Phys. Rev. B 78, 085415 (2008).

    Article  ADS  Google Scholar 

  27. Hartnoll, S. A. Theory of universal incoherent metallic transport. Nat. Phys. 11, 54–61 (2015).

    Article  Google Scholar 

  28. 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 

  29. Freitag, F., Trbovic, J., Weiss, M. & Schönenberger, C. Spontaneously gapped ground state in suspended bilayer graphene. Phys. Rev. Lett. 108, 076602 (2012).

    Article  ADS  Google Scholar 

  30. Velasco, J. Jr et al. Transport spectroscopy of symmetry-broken insulating states in bilayer graphene. Nat. Nanotech. 7, 156–160 (2012).

    Article  ADS  Google Scholar 

  31. Castro, E. V. et al. Limits on charge carrier mobility in suspended graphene due to flexural phonons. Phys. Rev. Lett. 105, 266601 (2010).

    Article  ADS  Google Scholar 

  32. Crossno, J. et al. Observation of the Dirac fluid and the breakdown of the Wiedemann–Franz law in graphene. Science 351, 1058–1061 (2016).

    Article  ADS  Google Scholar 

  33. Guinea, F., Castro Neto, A. & Peres, N. Electronic states and Landau levels in graphene stacks. Phys. Rev. B 73, 245426 (2006).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. Koshino, M. & Ando, T. Orbital diamagnetism in multilayer graphenes: systematic study with the effective mass approximation. Phys. Rev. B 76, 085425 (2007).

    Article  ADS  Google Scholar 

  36. Partoens, B. & Peeters, F. Normal and Dirac fermions in graphene multilayers: tight-binding description of the electronic structure. Phys. Rev. B 75, 193402 (2007).

    Article  ADS  Google Scholar 

  37. Koshino, M. Interlayer screening effect in graphene multilayers with ABA and ABC stacking. Phys. Rev. B 81, 125304 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  39. Mayorov, A. S. et al. How close can one approach the Dirac point in graphene experimentally? Nano Lett. 12, 4629–4634 (2012).

    Article  ADS  Google Scholar 

  40. Fradkin, E. Critical behavior of disordered degenerate semiconductors. II. Spectrum and transport properties in mean-field theory. Phys. Rev. B 33, 3263–3268 (1986).

    Article  ADS  Google Scholar 

  41. Katsnelson, M. I. Zitterbewegung, chirality, and minimal conductivity in graphene. Eur. Phys. J. B 51, 157–160 (2006).

    Article  ADS  Google Scholar 

  42. Tworzydło, J., Trauzettel, B., Titov, M., Rycerz, A. & Beenakker, C. W. J. Sub-poissonian shot noise in graphene. Phys. Rev. Lett. 96, 246802 (2006).

    Article  ADS  Google Scholar 

  43. Das Sarma, S., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011).

    Article  ADS  Google Scholar 

  44. Lucas, A., Crossno, J., Fong, K. C., Kim, P. & Sachdev, S. Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene. Phys. Rev. B 93, 075426 (2016).

    Article  ADS  Google Scholar 

  45. Bandurin, D. A. et al. Negative local resistance caused by viscous electron backflow in graphene. Science 351, 1055–1058 (2016).

    Article  ADS  Google Scholar 

  46. Levitov, L. & Falkovich, G. Electron viscosity, current vortices and negative nonlocal resistance in graphene. Nat. Phys. 12, 672–676 (2016).

    Article  Google Scholar 

  47. Grushina, A. L. et al. Insulating state in tetralayers reveals an even–odd interaction effect in multilayer graphene. Nat. Commun. 6, 6419 (2015).

    Article  ADS  Google Scholar 

  48. Nam, Y., Ki, D.-K., Koshino, M., McCann, E. & Morpurgo, A. F. Interaction-induced insulating state in thick multilayer graphene. 2D Mater. 3, 045014 (2016).

    Article  Google Scholar 

  49. Tombros, N. et al. Large yield production of high mobility freely suspended graphene electronic devices on a polydimethylglutarimide based organic polymer. J. Appl. Phys. 109, 093702 (2011).

    Article  ADS  Google Scholar 

  50. Ki, D.-K., Fal’ko, V. I., Abanin, D. A. & Morpurgo, A. F. Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene. Nano Lett. 14, 2135–2139 (2014).

    Article  ADS  Google Scholar 

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Acknowledgements

We gratefully acknowledge A. Ferreira for continued technical support of the experiments. We are also grateful to D. Abanin, V. Fal’ko, T. Giamarchi, L. S. Levitov, M. Müller, M. Polini, J. Song, D. Valentinis, D. van der Marel and J. Wallbank for very helpful discussions. Financial support from the Swiss National Science Foundation, the NCCR QSIT, and the EU Graphene Flagship Project are also gratefully acknowledged.

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Y.N., D.-K.K. and D.S.-D. fabricated devices and Y.N. and D.-K.K. performed measurements. A.F.M. derived the expression for the conductivity and supervised the analysis of the data done by Y.N. Y.N., D.-K.K. and A.F.M. wrote the manuscript. All authors discussed the results and contributed to their interpretation.

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Correspondence to Alberto F. Morpurgo.

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Nam, Y., Ki, DK., Soler-Delgado, D. et al. Electron–hole collision limited transport in charge-neutral bilayer graphene. Nature Phys 13, 1207–1214 (2017). https://doi.org/10.1038/nphys4218

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