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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Fowler, A.B., Hartstein, A., Webb, R.A.: Conductance in restricted-dimensionality accumulation layers. Phys. Rev. Lett. 48, 196 (1982)
Ferry, D.K., Goodnick, S.M., Bird, J.P.: Transport in Nanostructures, 2nd edn. Cambridge University Press, Cambridge (2009)
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)
Lee, P.A., Stone, A.D.: Universal conductance fluctuations in metals. Phys. Rev. Lett. 55, 1622 (1985)
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)
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)
Berger, C., et al.: Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191 (2006)
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)
Grincwajg, A., Edwards, G., Ferry, D.K.: Conductance fluctuations in microstructures: crossover between different transport regimes. Phys. B 218, 92 (1996)
Liu, B., Akis, R., Ferry, D.K.: Conductance fluctuation in semiconductor nanostructure. J. Phys. 25, 395802 (2013)
Rycerz, A., Tworzydlo, J., Beenakker, C.W.J.: Anomalously large conductance fluctuations in weakly disordered graphene. Europhys. Lett. 79, 570003 (2007)
Kechedzhi, K., Kashuba, O., Fal’ko, V.I.: Quantum kinetic equation and universal conductance fluctuations in graphene. Phys. Rev. B 77, 193403 (2008)
Kharitonov, MYu., Efetov, K.B.: Universal conductance fluctuations in graphene. Phys. Rev. B 78, 033404 (2008)
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)
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)
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)
Huang, L., Lai, Y.-C., Ferry, D.K., Goodnick, S.M.: Transmission and scarring in graphene quantum dots. J. Phys. 21, 344203 (2009)
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)
Ando, T.: Quantum point contacts in magnetic fields. Phys. Rev. B 44, 8017 (1991)
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)
Akis, R., Ferry, D.K.: Use of the scattering matrix for device simulations. J. Comput. Electron. 12(3), 356–362 (2013)
Akis, R., Ferry, D.K., Bird, J.P.: Magnetotransport fluctuations in regular semiconductor ballistic quantum dots. Phys. Rev. B 54, 17705 (1996)
Wallace, P.R.: The band theory of graphite. Phys. Rev. 71, 622 (1947)
Son, Y.-W., Cohen, M.L., Louie, S.G.: Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 97, 216803 (2006)
Ferry, D.K.: Semiconductors, Sec. 5.10. Macmillan, Reading (1991)
Hellmann, H.: Einführung in die Quantenchemie, p. 285. Franz Deuticke, Leipzig (1937)
Feynman, R.P.: Forces in molecules. Phys. Rev. 56(4), 340 (1939)
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)
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)
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)
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)
Elhassan, M., et al.: Magnetically induced Bragg scattering of electrons in quantum-dot crystals. Phys. Rev. B 70, 205341 (2004)
Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)
Mott, N.F.: Electrons in disordered structures. Adv. Phys. 16, 49 (1967)
Ferry, D.K.: Semiconductors, Ch. 14. Macmillan, New York (1991)
Stopa, M., Aoyagi, Y.: Effect of donor layer ordering on the formation of single mode quantum wires. Physica B 227, 61 (1996)
Sule, N., Hagness, S.C., Knezevic, I.: Clustered impurities and carrier transport in supported graphene. Phys. Rev. B 89, 165402 (2014)
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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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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DOI: https://doi.org/10.1007/s10825-014-0613-9