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Localisation and finite-size effects in graphene flakes

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http://dx.doi.org/10.1209/0295-5075/104/17012
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2013-10
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EPL Association, European Physical Society
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Abstract
We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as 1/6 of the band width of clean graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene flakes of size approximate to 200 x 200 nm(2) or larger are needed. For smaller samples, due to the surprisingly large extent of the electronic wave functions, a regime of apparently extended (or even critical) states is identified. Our results complement earlier studies of macroscopically large samples and can explain the divergence of results for finite-size graphene flakes.
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© EPLA, 2013. CGS and RAR are grateful to the CSC and UCM for hospitality, respectively, and to Ministerio de Educación, Comunidad de Madrid and the European Social Fund for funding the research stays at Madrid and Warwick during which much of this work was done. Work at Madrid was supported by MICINN (project MAT2010-17180). Caculations were done at i) CSC Warwick (MidPlus, EP SRC EP/K000128/1), ii) cluster for physics (UCM, Feder FUNDS and CEI Moncloa) and iii) Centro Nacional de Supercomputaci´on - Barcelona Supercomputing Center.
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[1] Anderson P. W., Phys. Rev., 109 (1958) 1492. [2] Lee P. A. and Ramakrishnan T. V., Rev. Mod. Phys., 57 (1985) 287. [3] Kramer B. and MacKinnon A., Rep. Prog. Phys., 56 (1993) 1469. [4] Evers F. and Mirlin A. D., Rev. Mod. Phys., 80 (2008) 1355. [5] Abrahams E., Anderson P. W., Licciardello D. C. and Ramakrishnan T. V., Phys. Rev. Lett., 42 (1979) 673. [6] Belitz D. and Kirkpatrick T. R., Rev. Mod. Phys., 66 (1994) 261. [7] Izrailev F. M. and Krokhin A. A., Phys. Rev. Lett., 82 (1999) 4062. [8] Bellani V., Diez E., Hey R., Toni L., Tarricone L., Parravicini G. B., Domínguez-Adame F. and Gomez Alcala R. , Phys. Rev. Lett., 82 (1999) 2159. [9] Punnoose A. and Finkel’stein A. M., Science, 310 (2005) 289. [10] Novoselov K. S., Geim A. K., Morozov S. V., Jiang D., Zhang Y., Dubonos S. V., Grigorieva I. V. and Firsov A. A., Science, 306 (2004) 666. [11] Geim A. K., Science, 324 (2009) 1530. [12] Ando T., Nakanishi T. and Saito R., J. Phys. Soc. Jpn., 67 (1998) 2857. [13] Schreiber M. and Ottomeier M., J. Phys.: Condens. Matter, 4 (1992) 1959. [14] Xiong S.-J. and Xiong Y., Phys. Rev. B, 76 (2007) 214204. [15] Bardarson J. H., Tworzydlo J., Brouwer P. W. and Beenakker C. W. J., Phys. Rev. Lett., 99 (2007) 106801. [16] Nomura K., Koshino M. and Ryu S., Phys. Rev. Lett., 99 (2007) 146806. [17] Lherbier A., Biel B., Niquet Y.-M. and Roche S., Phys. Rev. Lett., 100 (2008) 036803. [18] Schubert G., Schleede J. and Fehske H., Phys. Rev. B, 79 (2009) 235116. [19] Gunlycke D. and White C. T., Phys. Rev. B, 81 (2010) 075434. [20] Amini M., Jafari S. A. and Shahbazi F., EPL, 87 (2009) 37002. [21] Amanatidis I. and Evangelou S. N., Phys. Rev. B, 79 (2009) 205420. [22] Song Y., Song H. and Feng S., J. Phys.: Condens. Matter, 23 (2011) 205501. [23] Barrios-Vargas J. E. and Naumis G. G., J. Phys.: Condens. Matter, 24 (2012) 255305. [24] Amanatidis H., Kleftogiannis I., Katsanos D. and Evangelou S., arXiv:1302.2470 (2013). [25] Hilke M., arXiv:0912.0769 (2009). [26] Schleede J., Schubert G. and Fehske H., EPL, 90 (2010) 17002. [27] Amini M., Jafari S. A. and Shahbazi F., EPL, 90 (2010) 17003. [28] Lee K. L., Grémaud B., Miniatura C. and Delande D., Phys. Rev. B, 87 (2013) 144202. [29] Bang J. and Chang K. J., Phys. Rev. B, 81 (2010) 193412. [30] Schubert G. and Fehske H., Phys. Rev. Lett., 108 (2012) 066402. [31] Rodriguez A., Chakrabarti A. and Römer R. A., Phys. Rev. B, 86 (2012) 085119. [32] Eilmes A., Fischer A. M. and Rómer R. A., Phys. Rev. B, 77 (2008) 245117. [33] Frahm K., Müller-Groeling A., Pichard J. L. and Weinmann D., Europhys. Lett., 31 (1995) 169. [34] Ndawana M. L., Römer R. A. and Schreiber M., Eu rophys. Lett., 68 (2004) 678. [35] Gonzalez-Santander C., PhD Thesis, Universidad Complutense de Madrid (2013). [36] MacKinnon A. and Kramer B., Phys. Rev. Lett., 47 (1981) 1546. [37] Slevin K. and Ohtsuki T., Phys. Rev. Lett., 82 (1999) 382. [38] Rodriguez A., Vasquez L. J., Slevin K. and Römer R. A., Phys. Rev. B, 84 (2011) 134209. [39] Rodriguez A., Vasquez L. J., Slevin K. and Römer R. A., Phys. Rev. Lett., 105 (2010) 046403. [40] Gershgorin S., Izv. Akad. SSSR, Otd. Mat. Estest. Nauk V, II (1931) 749. [41] Wallace P. R., Phys. Rev., 71 (1947) 622. [42] Grimm U., Romer R. A. ¨ and Schliecker G., Ann. Phys. (Leipzig), 7 (1998) 389. [43] Leadbeater M., Romer R. A. ¨ and Schreiber M., Eur. Phys. J. B, 8 (1999) 643. [44] Nakada K., Fujita M., Dresselhaus G. and Dres selhaus M. S., Phys. Rev. B, 54 (1996) 17954. [45] MacKinnon A. and Kramer B., Z. Phys. B, 53 (1983) 1. [46] Brey L. and Fertig H. A., Phys. Rev. B, 73 (2006) 235411. [47] Wang X., Ouyang Y., Jiao L., Wang H., Xie L., Wu J., Guo J. and Dai H., Nature, 6 (2011) 563. [48] Li X., Wang X., Zhang L., Lee S. and Dai H., Science, 319 (2008) 1229. [49] Miao F., Wijeratne S., Zhang Y., Coskun U. C., Bao W. and Lau C. N., Science, 317 (2007) 1530. [50] Ponomarenko L. A., Schedin F., Katsnelson M. I., Yang R., Hill E. W. and Novoselov K. S. and Geim A. K., Science, 320 (2008) 356.
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https://hdl.handle.net/20.500.14352/33701
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