Localization of Charge Carriers in Monolayer Graphene Gradually Disordered by Ion Irradiation

Erez Zion¹, Avner Haran², Alexander Butenko¹, Leonid Wolfson³, Yuri Kaganovskii³, Tal Havdala¹, Amos Sharoni¹, Doron Naveh², Vladmir Richter⁴, Moshe Kaveh³, Eugene Kogan³, Issai Shlimak^3*

¹1Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, Israel.
¹Department of Physics and Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, Israel.
²Faculty of Engineering, Bar-Ilan University, Ramat-Gan, Israel.
³Jack and Pearl Resnick Institute, Department of Physics, Bar-Ilan University, Ramat-Gan, Israel.
⁴Solid State Institute and Physics Department, Technion-Israel Institute of Technology, Haifa, Israel.

DOI: 10.4236/graphene.2015.43005                

Abstract

Gradual localization of charge carriers is studied in a series of microsize samples of monolayer graphene fabricated on the common large scale film and irradiated by different doses of C⁺ ions with energy 35 keV. Measurements of the temperature dependence of conductivity and magneto-resistance in fields up to 4 T show that at low disorder, the samples are in the regime of weak localization and antilocalization. Further increase of disorder leads to strong localization regime, when conductivity is described by the variable-range-hopping (VRH) mechanism. A crossover from the Mott regime to the Efros-Shklovskii regime of VRH is observed with decreasing temperature. Theoretical analysis of conductivity in both regimes shows a remarkably good agreement with experimental data.

Keywords

Graphene, Localization, Hopping Conductivity, Ion Irradiation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Morozov, S.V., Novoselov, K.S., Katsnelson, M.I., Schedin, F., Ponomarenko, L.A., Jiang, D. and Geim, A.K. (2006) Strong Suppression of Weak Localization in Graphene. Physical Review Letters, 97, Article ID: 016801. http://dx.doi.org/10.1103/physrevlett.97.016801
[2]	Wu, X.S., Li, X.B., Song, Z.M., Berger, C. and de Heer, W.A. (2007) Weak Antilocalization in Epitaxial Graphene: Evidence for Chiral Electrons. Physical Review Letters, 98, Article ID: 136801. http://dx.doi.org/10.1103/physrevlett.98.136801
[3]	Tikhonenko, F.V., Kozikov, A.A., Savchenko, A.K. and Gorbachev, R.V. (2009) Transition between Electron Localization and Antilocalization in Graphene. Physical Review Letters, 103, Article ID: 226801. http://dx.doi.org/10.1103/PhysRevLett.103.226801
[4]	Chen, Y.-F., Bae, M.-H., Chialvo, C., Dirks, T., Bezryadin, A. and Mason, N. (2010) Magnetoresistance in Single-Layer Graphene: Weak Localization and Universal Conductance Fluctuation Studies. Journal of Physics: Condensed Matter, 22, Article ID: 205301. http://dx.doi.org/10.1088/0953-8984/22/20/205301
[5]	Lundeberg, M.B. and Folk, J.A. (2010) Rippled Graphene in an In-Plane Magnetic Field: Effects of a Random Vector Potential. Physical Review Letters, 105, Article ID: 146804. http://dx.doi.org/10.1103/physrevlett.105.146804
[6]	Buchowicz, G., Stone, P.R., Robinson, J.T., Cress, C.D., Beeman, J.W. and Dubon, O.D. (2011) Correlation between Structure and Electrical Transport in Ion-Irradiated Graphene Grown on Cu Foils. Applied Physics Letters, 98, Article ID: 032102. http://dx.doi.org/10.1063/1.3536529
[7]	Jobst, J., Waldmann, D., Gornyi, I.V., Mirlin, A.D. and Weber, H.B. (2012) Electron-Electron Interaction in the Magnetoresistance of Graphene. Physical Review Letters, 108, Article ID: 106601. http://dx.doi.org/10.1103/PhysRevLett.108.106601
[8]	Moktadir, Z., Hang, S.J. and Mizuta, H. (2014) Defect-Induced Fermi Level Pinning and Suppression of Ambipolar Behaviour in Graphene. http://arxiv.org/abs/1410.4400
[9]	Shlimak, I., Haran, A., Zion, E., Havdala, T., Kaganovskii, Yu., Butenko, A.V., Wolfson, L., Richter, V., Naveh, D., Sharoni, A., Kogan, E. and Kaveh, M. (2015) Raman Scattering and Electrical Resistance of Highly Disordered Graphene. Physical Review B, 91, Article ID: 045414. http://dx.doi.org/10.1103/physrevb.91.045414
[10]	Altshuler, B.L., Aronov, A.G. and Khmelnitsky, D.E. (1982) Effects of Electron-Electron Collisions with Small Energy Transfers on Quantum Localization. Journal of Physics C: Solid State Physics, 15, Article ID: 7367. http://dx.doi.org/10.1088/0022-3719/15/36/018
[11]	Morpurgo, A.F. and Guinea, F. (2006) Intervalley Scattering, Long-Range Disorder, and Effective Time-Reversal Symmetry Breaking in Graphene. Physical Review Letters, 97, Article ID: 196804. http://dx.doi.org/10.1103/PhysRevLett.97.196804
[12]	Aleiner, I.L. and Efetov, K.B. (2006) Effect of Disorder on Transport in Graphene. Physical Review Letters, 97, Article ID: 236801. http://dx.doi.org/10.1103/PhysRevLett.97.236801
[13]	Altland, A. (2006) Low-Energy Theory of Disordered Graphene. Physical Review Letters, 97, Article ID: 236802. http://dx.doi.org/10.1103/PhysRevLett.97.236802
[14]	Ostrovsky, P.M., Gornyi, I.V. and Mirlin, A.D. (2006) Electron Transport in Disordered Graphene. Physical Review B, 74, Article ID: 235443. http://dx.doi.org/10.1103/PhysRevB.74.235443
[15]	McCann, E., Kechedzhi, K., Fal’ko, V.I., Suzuura, H., Ando, T. and Altshuler, B.L. (2006) Weak-Localization Magnetoresistance and Valley Symmetry in Graphene. Physical Review Letters, 97, Article ID: 146805. http://dx.doi.org/10.1103/PhysRevLett.97.146805
[16]	Kechedzhi, K., McCann, E., Fal’ko, V.I., Suzuura, H., Ando, T. and Altshuler, B.L. (2007) Weak Localization in Monolayer and Bilayer Graphene. The European Physical Journal Special Topics, 148, 39-54. http://dx.doi.org/10.1140/epjst/e2007-00224-6
[17]	Tikhonenko, F.V., Kozikov, A.A., Savchenko, A.K. and Gorbachev, R.V. (2009) Transition between Electron Localization and Antilocalization in Graphene. Physical Review Letters, 103, Article ID: 226801. http://dx.doi.org/10.1103/PhysRevLett.103.226801
[18]	Pal, A.N., Kochat, V. and Ghosh, A. (2012) Direct Observation of Valley Hybridization and Universal Symmetry of Graphene with Mesoscopic Conductance Fluctuations. Physical Review Letters, 109, Article ID: 196601. http://dx.doi.org/10.1103/PhysRevLett.109.196601
[19]	Baker, A.M.R., Alexander-Webber, J.A., Altebaeumer, T., Janssen, T.J.B.M., Tzalenchuk, A., Lara-Avila, S., Kubatkin, S., Yakimova, R., Lin, C.-T., Li, L.-J. and Nicholas, R.J. (2012) Weak Localization Scattering Lengths in Epitaxial, and CVD Graphene. Physical Review B, 86, Article ID: 235441. http://dx.doi.org/10.1103/PhysRevB.86.235441
[20]	Stauber, T., Peres, N.M.R. and Guinea, F. (2007) Electronic Transport in Graphene: A Semiclassical Approach Including Midgap States. Physical Review B, 76, Article ID: 205423. http://dx.doi.org/10.1103/physrevb.76.205423
[21]	Hwang, E.H. and Das Sarma, S. (2008) Acoustic Phonon Scattering Limited Carrier Mobility in Two-Dimensional Extrinsic Graphene. Physical Review B, 77, Article ID: 115449. http://dx.doi.org/10.1103/PhysRevB.77.115449
[22]	Tikhonov, K.S., Zhao, W.L.Z. and Finkelstein, A.M. (2014) Dephasing Time in Graphene Due to Interaction with Flexural Phonons. Physical Review Letters, 113, Article ID: 076601. http://dx.doi.org/10.1103/PhysRevLett.113.076601
[23]	Bishop, D.J., Tsui, D.C. and Dines, R.C. (1980) Nonmetallic Conduction in Electron Inversion Layers at Low Temperatures. Physical Review Letters, 44, Article ID: 1153.
[24]	Gantmakher, V.F. (2005) Electrons and Disorder in Solids. Oxford University Press, Oxford. http://dx.doi.org/10.1093/acprof:oso/9780198567561.001.0001
[25]	Shklovskii, B.I. and Efros, A.L. (1984) Electronic Properties of Doped Semiconductors. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-662-02403-4
[26]	Moser, J., Tao, H., Roche, S., Alzina, F., Sotomayor Torres, C.M. and Bachtold, A. (2010) Magnetotransport in Disordered Graphene Exposed to Ozone: From Weak to Strong Localization. Physical Review B, 81, Article ID: 205445. http://dx.doi.org/10.1103/PhysRevB.81.205445
[27]	Joung, D. and Khondaker, S. (2012) Efros-Shklovskii Variable-Range Hopping in Reduced Graphene Oxide Sheets of Varying Carbon sp2 Fraction. Physical Review B, 86, Article ID: 235423. http://dx.doi.org/10.1103/PhysRevB.86.235423
[28]	Hong, X., Cheng, S.-H., Herding, C. and Zhu, J. (2011) Colossal Negative Magnetoresistance in Dilute Fluorinated Graphene. Physical Review B, 83, Article ID: 085410. http://dx.doi.org/10.1103/PhysRevB.83.085410
[29]	Zhang, H.J., Lu, J.M., Wu, S., Wang, Z., Zhang, T., Sun, M.Y., Zheng, Y., Chen, Q.H., Wang, N., Lin, J.J. and Sheng, P. (2013) Large-Scale Mesoscopic Transport in Nanostructured Graphene. Physical Review Letters, 110, Article ID: 066805. http://dx.doi.org/10.1103/physrevlett.110.066805
[30]	Shlimak, I., Kaveh, M., Yosefin, M., Lea, M. and Fozooni, P. (1992) Crossover Phenomenon for Hopping Conduction in Strong Magnetic Fields. Physical Review Letters, 68, Article ID: 3076.
[31]	Singh, M., Tarutani, Y., Kabasava, U. and Takagi, K. (1994) Temperature and Electric-Field Dependence of Hopping Transport in Low-Dimensional Devices. Physical Review B, 50, 7007-7015. http://dx.doi.org/10.1103/PhysRevB.50.7007
[32]	Lien, N.V. (1995) Crossovers in Two-Dimensional Variable Range Hopping. Physics Letters A, 207, 379-384.
[33]	Dunlap, W.C. (1955) Amphoteric Impurity Action in Germanium. Physical Review, 100, 1629-1633. http://dx.doi.org/10.1103/PhysRev.100.1629
[34]	Fistul, V. (2004) Impurities in Semiconductors: Solubility, Migration and Interactions. CRS Press, Boca Raton. http://dx.doi.org/10.1201/9780203299258