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Conductance fluctuations in graphene nanoribbons

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Abstract

Over the past few years, the amazing properties of graphene have led to predictions for its use in a variety of areas, not the least of which is in semiconductor devices. But, the transport is an important aspect of any possible application. At low temperature, fluctuations are observed in the conductance through nanoribbons. These fluctuations arise from the presence of a random potential in the semiconductor, which arises from e.g. impurities present in the material structure. In this work, we examine the nature of these fluctuations in nanoribbons using an atomic basis quantum transport simulation.

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References

  1. Fowler, A.B., Hartstein, A., Webb, R.A.: Conductance in restricted-dimensionality accumulation layers. Phys. Rev. Lett. 48, 196 (1982)

    Article  Google Scholar 

  2. Ferry, D.K., Goodnick, S.M., Bird, J.P.: Transport in Nanostructures, 2nd edn. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  3. Thornton, T.J., Pepper, M., Ahmed, H., Davies, G.J., Andrews, D.: Universal conductance fluctuations and electron coherence lengths in a narrow two-dimensional electron gas. Phys. Rev. B 36, 4514 (1987)

    Article  Google Scholar 

  4. Lee, P.A., Stone, A.D.: Universal conductance fluctuations in metals. Phys. Rev. Lett. 55, 1622 (1985)

    Article  Google Scholar 

  5. Lee, P.A., Stone, A.D., Fukuyama, H.: Universal conductance fluctuations in metals: effects of finite temperature, interactions, and magnetic field. Phys. Rev. B 35, 1039 (1987)

    Article  Google Scholar 

  6. 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, 109 (2009)

    Article  Google Scholar 

  7. Berger, C., et al.: Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191 (2006)

    Article  Google Scholar 

  8. Morozov, S.V., Novoselov, K.S., Katsnelson, M.I., Schedin, F., Ponomarenko, L.A., Jiang, D., Geim, A.: Strong suppression of weak localization in Graphene. Phys. Rev. Lett. 97, 016801 (2006)

    Article  Google Scholar 

  9. Grincwajg, A., Edwards, G., Ferry, D.K.: Conductance fluctuations in microstructures: crossover between different transport regimes. Phys. B 218, 92 (1996)

    Article  Google Scholar 

  10. Liu, B., Akis, R., Ferry, D.K.: Conductance fluctuation in semiconductor nanostructure. J. Phys. 25, 395802 (2013)

    Google Scholar 

  11. Rycerz, A., Tworzydlo, J., Beenakker, C.W.J.: Anomalously large conductance fluctuations in weakly disordered graphene. Europhys. Lett. 79, 570003 (2007)

    Article  Google Scholar 

  12. Kechedzhi, K., Kashuba, O., Fal’ko, V.I.: Quantum kinetic equation and universal conductance fluctuations in graphene. Phys. Rev. B 77, 193403 (2008)

    Article  Google Scholar 

  13. Kharitonov, MYu., Efetov, K.B.: Universal conductance fluctuations in graphene. Phys. Rev. B 78, 033404 (2008)

    Article  Google Scholar 

  14. Staley, N.E., Puls, C.P., Liu, Y.: Suppression of conductance fluctuation in weakly disordered mesoscopic graphene samples near the charge neutral point. Phys. Rev. B 77, 155429 (2008)

    Article  Google Scholar 

  15. Ojeda-Aristizabal, C., Monteverde, M., Weil, R., Ferrier, M., Guéron, S., Bouchiat, H.: Conductance fluctuations and field asymmetry of rectification in graphene. Phys. Rev. Lett. 104, 186802 (2010)

    Article  Google Scholar 

  16. Bohra, G., Somphonsane, R., Aoki, N., Ochiai, Y., Akis, R., Ferry, D.K., Bird, J.P.: Nonergodicity and microscopic symmetry breaking of the conductance fluctuations in disordered mesoscopic graphene. Phys. Rev. B 86, 161405 (2012)

    Article  Google Scholar 

  17. Huang, L., Lai, Y.-C., Ferry, D.K., Goodnick, S.M.: Transmission and scarring in graphene quantum dots. J. Phys. 21, 344203 (2009)

    Google Scholar 

  18. Speyer, G., Akis, R., Ferry, D.K.: Complexities of the molecular conductance problem. In: Lyshevski, S.E. (ed.) Nano and Molecular Electronics, pp. 209–276. CRC Press, Boca Raton (2007)

  19. Ando, T.: Quantum point contacts in magnetic fields. Phys. Rev. B 44, 8017 (1991)

    Article  Google Scholar 

  20. Usuki, T., Saito, M., Takatsu, M., Kiehl, R.A., Yokoyama, N.: Numerical analysis of ballistic-electron transport in magnetic fields by using a quantum point contact and a quantum wire. Phys. Rev. B 52, 8244 (1995)

    Article  Google Scholar 

  21. Akis, R., Ferry, D.K.: Use of the scattering matrix for device simulations. J. Comput. Electron. 12(3), 356–362 (2013)

    Article  Google Scholar 

  22. Akis, R., Ferry, D.K., Bird, J.P.: Magnetotransport fluctuations in regular semiconductor ballistic quantum dots. Phys. Rev. B 54, 17705 (1996)

    Article  Google Scholar 

  23. Wallace, P.R.: The band theory of graphite. Phys. Rev. 71, 622 (1947)

    Article  MATH  Google Scholar 

  24. Son, Y.-W., Cohen, M.L., Louie, S.G.: Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 97, 216803 (2006)

    Article  Google Scholar 

  25. Ferry, D.K.: Semiconductors, Sec. 5.10. Macmillan, Reading (1991)

    Google Scholar 

  26. Hellmann, H.: Einführung in die Quantenchemie, p. 285. Franz Deuticke, Leipzig (1937)

    Google Scholar 

  27. Feynman, R.P.: Forces in molecules. Phys. Rev. 56(4), 340 (1939)

    Article  MATH  Google Scholar 

  28. Fischetti, M.V., Kim, J., Narayanan, S., Ong, Z.Y., Sachs, C., Ferry, D.K., Aboud, S.J.: Pseudopotential-based studies of electron transport in graphene and graphene nanoribbons. J. Phys. 25(47), 473202 (2013)

    Google Scholar 

  29. Terrones, H., Lv, R., Terrones, M., Dresselhaus, M.S.: The role of defects and doping in 2D graphene sheets and 1D nanoribbons. Rept. Progr. Phys. 75(6), 062501 (2012)

    Article  Google Scholar 

  30. Büttiker, M.: The quantum hall effect in open conductors. In: Willardson, R.K., Beer, A.C., Weber, E.R. (eds.) Semiconductors and Semimetals, vol. 35. Academic Press, New York (1992)

  31. Akis, R., Barnes, C., Kirczenow, G.: Edge states, band structure, and the hall effect in two-dimensional lattice structures: quantum dot arrays and the tight-binding model. Can. J. Phys. 73, 147 (1995)

    Article  Google Scholar 

  32. Elhassan, M., et al.: Magnetically induced Bragg scattering of electrons in quantum-dot crystals. Phys. Rev. B 70, 205341 (2004)

    Article  Google Scholar 

  33. Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)

    Article  Google Scholar 

  34. Mott, N.F.: Electrons in disordered structures. Adv. Phys. 16, 49 (1967)

    Article  Google Scholar 

  35. Ferry, D.K.: Semiconductors, Ch. 14. Macmillan, New York (1991)

    Google Scholar 

  36. Stopa, M., Aoyagi, Y.: Effect of donor layer ordering on the formation of single mode quantum wires. Physica B 227, 61 (1996)

    Article  Google Scholar 

  37. Sule, N., Hagness, S.C., Knezevic, I.: Clustered impurities and carrier transport in supported graphene. Phys. Rev. B 89, 165402 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge helpful discussions with J. P. Bird, M. Fischetti, S. Aboud, and Y.-W. Son on magneto-transport in graphene and atomic-basis band structure simulations.

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Correspondence to D. K. Ferry.

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Liu, B., Akis, R. & Ferry, D.K. Conductance fluctuations in graphene nanoribbons. J Comput Electron 13, 950–959 (2014). https://doi.org/10.1007/s10825-014-0613-9

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