Abstract
We have investigated electrical transport and shot noise in graphene field effect devices. In large width over length ratio W/L graphene strips, we have measured shot noise at low frequency (f=600–850 MHz) in the temperature range of 4.2–30 K. We observe a minimum conductivity of \(\frac{4e^{2}}{\pi h}\) and a finite and gate dependent Fano factor reaching the universal value of \(\frac{1}{3}\) at the Dirac point, i.e. where the density of states vanishes. These findings are in good agreement with the theory describing that transport at the Dirac point should occur via evanescent waves in perfect graphene samples with large W/L. Moreover, we show and discuss how disorder and non-parallel leads affect both conductivity and shot noise.
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References
A.K. Geim, K.S. Novoselov, Nat. Mat. 6, 183 (2007)
M.I. Katsnelson, Eur. Phys. J. B 51, 157 (2006)
J. Tworzydło, B. Trauzettel, M. Titov, A. Rycerz, C.W.J. Beenakker, Phys. Rev. Lett. 96, 246802 (2006)
Y.M. Blanter, M. Büttiker, Phys. Rep. 336, 1 (2000)
L. Saminadayar, D.C. Glattli, Y. Jin, B. Etienne, Phys. Rev. Lett. 79, 2526 (1997)
R. de Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, D. Mahalu, Nature 389, 162 (1997)
M. Henny, S. Oberholzer, C. Strunk, T. Heinzel, K. Ensslin, M. Holland, C. Schönenberger, Science 284, 296 (1999)
W.D. Oliver, J. Kim, R.C. Liu, Y. Yamamoto, Science 284, 299 (1999)
S.S. Safonov, A.K. Savchenko, D.A. Bagrets, O.N. Jouravlev, Y.V. Nazarov, E.H. Linfield, D.A. Ritchie, Phys. Rev. Lett. 91, 136801 (2003)
P. Roche, J. Ségala, D.C. Glattli, J.T. Nicholls, M. Pepper, A.C. Graham, K.J. Thomas, M.Y. Simmons, D.A. Ritchie, Phys. Rev. Lett. 93, 116602 (2004)
L. DiCarlo, Y. Zhang, D.T. McClure, D.J. Reilly, C.M. Marcus, L.N. Pfeiffer, K.W. West, Phys. Rev. Lett. 97, 036810 (2006)
S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1995)
C.W.J. Beenakker, M. Büttiker, Phys. Rev. B 46, 1889 (1992)
K. Nagaev, Phys. Lett. A 169, 103 (1992)
A. Shimizu, M. Ueda, Phys. Rev. Lett. 69, 1403 (1992)
A.H. Steinbach, J.M. Martinis, M.H. Devoret, Phys. Rev. Lett. 76, 3806 (1996)
H. Schomerus, Phys. Rev. B 76, 045433 (2007)
E.B. Sonin, Phys. Rev. B 77, 233408 (2008)
K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438, 197 (2005)
Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E.H. Whang, S. Das Sarma, H.L. Stormer, P. Kim, Phys. Rev. Lett. 99, 246803 (2007)
J.H. Bardarson, J. Tworzydło, P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. Lett. 99, 106801 (2007)
A. Schuessler, P.M. Ostrovsky, I.V. Gornyi, A.D. Mirlin, arXiv:0809.3782 (2008)
M.A. Laakso, T.T. Heikkilä, arXiv:0806.4528 (2008)
I. Snyman, C.W.J. Beenakker, Phys. Rev. B 75, 045322 (2007)
M.I. Katsnelson, Eur. Phys. J. B 52, 151 (2006)
V.V. Cheianov, V.I. Fal’ko, Phys. Rev. B 74, 041403(R) (2006)
D.A. Abanin, L.S. Levitov, Science 317, 641 (2007)
C.W.J. Beenakker, Phys. Rev. Lett. 97, 067007 (2006)
Q. Zhang, D. Fu, B. Wang, D.Y. Xing, Phys. Rev. Lett. 101, 047005 (2008)
J.P. Robinson, H. Schomerus, Phys. Rev. B 76, 115430 (2007)
X. Jehl, M. Sanquer, R. Calemczuk, D. Mailly, Nature 405, 50 (2000)
F. Wu, L. Roschier, T. Tsuneta, M. Palaanen, T.H. Wang, P.J. Hakonen, AIP Conf. Proc. 850, 1482 (2006)
F. Wu, P. Queipo, A. Nasibulin, T. Tsuneta, T.H. Wang, E. Kauppinen, P.J. Hakonen, Phys. Rev. Lett. 99, 156803 (2007)
R. Danneau, F. Wu, M.F. Craciun, S. Russo, M.Y. Tomi, J. Salmilehto, A.F. Morpurgo, P.J. Hakonen, Phys. Rev. Lett. 100, 196802 (2008)
J.B. Oostinga, H.B. Heersche, X. Liu, A.F. Morpurgo, L.M.K. Vandersypen, Nat. Mat. 7, 151 (2008)
C.W.J. Beenakker, C. Schönenberger, Phys. Today 56, 37 (2003)
V.A. Khlus, Zh. Ekps. Teor. Fiz. 93, 2179 (1987) [Sov. Phys. JETP 66, 1243 (1987)]
F. Schedin, A.K. Geim, S.V. Morozov, E.W. Hill, P. Blake, M.I. Katsnelson, K.S. Novoselov, Nat. Mat. 6, 652 (2007)
F. Miao, S. Wijeratne, Y. Zhang, U.C. Coskun, W. Bao, C.N. Lau, Science 317, 1530 (2007)
M.A. Laakso, private communication
K. Ziegler, Physica E 40, 2622 (2007)
M. Henny, S. Oberholzer, C. Strunk, C. Schönenberger, Phys. Rev. B 59, 2871 (1999)
F. Wu, T. Tsuneta, R. Tarkiainen, D. Gunnarsson, T.-H. Wang, P.J. Hakonen, Phys. Rev. B 75, 125419 (2007)
L. Dicarlo, J.R. Williams, Y. Zhang, D.T. McClure, C.M. Marcus, Phys. Rev. Lett. 100, 156801 (2008)
C.H. Lewenkopf, E.R. Mucciolo, A.H. Castro Neto, Phys. Rev. B 77, 081410(R) (2008)
N.M.R. Peres, F. Guinea, A.H. Castro Neto, Phys. Rev. B 73, 125411 (2006)
A. Carpio, L.L. Bonilla, F. de Juan, M.A.H. Vozmediano, New J. Phys. 10, 053021 (2008)
V.M. Pereira, F. Guinea, J.M.B. Lopes dos Santos, N.M.R. Peres, A.H. Castro Neto, Phys. Rev. Lett. 96, 036801 (2006)
P. Le Doussal, L. Radzihovsky, Phys. Rev. Lett. 69, 1209 (1992)
J.C. Meyer, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, T.J. Booth, S. Roth, Nature 446, 60 (2007)
A. Fasolino, A.H. Los, M.I. Katsnelson, Nat. Mat. 6, 858 (2007)
M. Ishigami, J.H. Chen, W.G. Cullen, M.S. Fuhrer, E.D. Williams, Nano Lett. 7, 1643 (2007)
E. Stolyarova, K.T. Rim, S. Ryu, J. Maultzsch, P. Kim, L.E. Brus, T.F. Heinz, M.S. Hybertsen, G.W. Flynn, Proc. Natl. Acad. Sci. USA 104, 9209–9212 (2007)
F. Varchon, P. Mallet, J.-Y. Veuillen, L. Magaud, Phys. Rev. B 77, 235412 (2008)
F. de Juan, A. Cortijo, M.A.H. Vozmediano, Phys. Rev. B 76, 165409 (2007)
E.-A. Kim, A.H. Castro Neto, arXiv:0702562 (2007)
E.H. Hwang, S. Adam, S. Das Sarma, Phys. Rev. Lett. 98, 186806 (2007)
K. Nomura, A.H. MacDonald, Phys. Rev. Lett. 96, 256602 (2006)
S.V. Morozov, K.S. Novoselov, M.I. Katsnelson, F. Schedin, D.C. Elias, J.A. Jaszczak, A.K. Geim, Phys. Rev. Lett. 100, 016602 (2008)
J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J.H. Smet, K. von Klitzing, A. Yacoby, Nat. Phys. 4, 144 (2008)
S. Fratini, F. Guinea, Phys. Rev. B 77, 195415 (2008)
K.I. Bolotin, K.J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, H.L. Stormer, Solid State Commun. 146, 351 (2008)
J. Moser, A. Barreiro, A. Bachtold, Appl. Phys. Lett. 91, 163513 (2007)
M. Titov, Europhys. Lett. 79, 17004 (2007)
A.F. Morpurgo, F. Guinea, Phys. Rev. Lett. 97, 196804 (2006)
M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006)
A. Rycerz, J. Tworzydło, C.W.J. Beenakker, Europhys. Lett. 79, 57003 (2007)
P. San-Jose, E. Prada, D.S. Golubev, Phys. Rev. B 76, 195445 (2007)
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This work was supported by the Academy of Finland, the EU CARDEQ contract FP6-IST-021285-2 and the NANOSYSTEMS contract with the Nokia Research Center.
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Danneau, R., Wu, F., Craciun, M.F. et al. Evanescent Wave Transport and Shot Noise in Graphene: Ballistic Regime and Effect of Disorder. J Low Temp Phys 153, 374–392 (2008). https://doi.org/10.1007/s10909-008-9837-z
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DOI: https://doi.org/10.1007/s10909-008-9837-z