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Review Article | Open Access
Charge Transport in Disordered Graphene-Based Low Dimensional Materials
Abstract
Two-dimensional graphene, carbon nanotubes, and graphene nanoribbons represent a novel class of low dimensional materials that could serve as building blocks for future carbon-based nanoelectronics. Although these systems share a similar underlying electronic structure, whose exact details depend on confinement effects, crucial differences emerge when disorder comes into play. In this review, we consider the transport properties of these materials, with particular emphasis on the case of graphene nanoribbons. After summarizing the electronic and transport properties of defect-free systems, we focus on the effects of a model disorder potential (Anderson-type), and illustrate how transport properties are sensitive to the underlying symmetry. We provide analytical expressions for the elastic mean free path of carbon nanotubes and graphene nanoribbons, and discuss the onset of weak and strong localization regimes, which are genuinely dependent on the transport dimensionality. We also consider the effects of edge disorder and roughness for graphene nanoribbons in relation to their armchair or zigzag orientation.
References
1
Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998.
2
Loiseau, A.; Launois, P.; Petit, P., Roche, S.; Salvetat, J. -P. Understanding Carbon Nanotubes from Basics to Applications; Lecture Notes in Physics, Vol. 677; Springer-Verlag: Berlin, Heidelberg, 2006.
3
Jorio, A.; Dresselhaus, G.; Dresselhaus, M. S. Carbon Nanotubes: Advanced Topics in the Synthesis, Structure, Properties and Applications; Springer-Verlag: Berlin, Heidelberg, 2007.
4
Charlier, J. C.; Blase, X.; Roche, S. Electronic and transport properties of nanotubes. Rev. Mod. Phys. 2007, 79, 677–732.
5
Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Filrsov, A. A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666–669.
6
Berger, C.; Song, Z. M.; Li, X. B.; Wu, X. S.; Brown, N.; Naud, C.; Mayou, D.; Li, T. B.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. Electronic confinement and coherence in patterned epitaxial graphene. Science 2006, 312, 1191–1196.
7
Zhang, Y. B.; Tan, Y. W.; Stormer, H. L.; Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 2005, 438, 201–204.
8
Zhang, Y.; Jiang, Z.; Small, J. P.; Purewal, M. S.; Tan, Y. -W.; Fazlollahi, M.; Chudow, J. D.; Jaszczak, J. A.; Stormer, H. L.; Kim, P. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 2006, 96, 136806.
9
Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater. 2007, 6, 183–191.
10
Öezyilmaz, B.; Jarillo-Herrero, P.; Efetov, D.; Kim, P. Electronic transport in locally gated graphene nanoconstrictions. Appl. Phys. Lett. 2007, 91, 192107.
11
Öezyilmaz, B.; Jarillo-Herrero, P.; Efetov, D.; Abanin, D. A.; Levitov, L. S.; Kim, P. Electronic transport and quantum Hall effect in bipolar graphene p–n–p junctions. Phys. Rev. Lett. 2007, 99, 166804.
12
Jiang, Z; Zhang, Y; Stormer, H. L.; Kim, P. Quantum Hall states near the charge-neutral Dirac point in graphene. Phys. Rev. Lett. 2007, 99, 106802.
13
Novoselov, K. S.; Jiang, Z.; Zhang, Y.; Morozov, S. V.; Stormer, H. L.; Zeitler, U.; Maan, J. C.; Boebinger, G. S.; Kim, P.; Geim, A. K. Room-temperature quantum Hall effect in graphene. Science 2007, 315, 1379.
14
Wu, X.; Li, X.; Song, Z.; Berger, C.; de Heer, W. A. Weak antilocalization in epitaxial graphene: Evidence for chiral electrons. Phys. Rev. Lett. 2007, 98, 136801.
15
Castro Neto, A. H; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The electronic properties of graphene. arXiv: 0709.1163v2.
16
Dayen, J. -F.; Mahmood, A.; Golubev, D. S.; Roch-Jeune, I.; Salles, P.; Dujardin, E. Side-gated transport in FIB-fabricated multilayered graphene nanoribbons. arXiv: 0712.2314v2, 2008.https://doi.org/10.1002/smll.200700913
17
Lemme, M. C.; Echtermeyer, T. J.; Baus, M.; Kurz, H. A graphene field-effect device. IEEE Elect. Dev. L. 2007, 28, 282–284.
18
Han, M. Y.; Öezyilmaz, B.; Zhang, Y.; Kim, P. Energy band-gap engineering of graphene nanoribbons. Phys. Rev. Lett. 2007, 98, 206805.
19
Chen, Z.; Lin, Y. -M.; Rooks, M. J.; Avouris, P. Graphene nano-ribbon electronics. Physica E 2007, 40, 228–232.
20
Echtermeyer, T. J.; Lemme, M. C.; Bolten, J.; Baus, M.; Ramsteiner, M.; Kurz, H. Graphene field-effect devices. Eur. Phys. J. Special Topics 2007, 148, 19–26.
21
Morozov, S. V.; Novoselov, K. S.; Katsnelson, M. I.; Schedin, F.; Elias, D. C.; Jaszczak, J. A.; Geim, A. K. Giant intrinsic carrier mobilities in graphene and its bilayer Phys. Rev. Lett. 2008, 100, 016602.
22
Javey, A.; Guo, J.; Wang, Q.; Lundstrom, M.; Dai, H. Ballistic carbon nanotube field-effect transistors. Nature 2003, 424, 654–657.
23
Javey, A.; Guo, J.; Farmer, D. B.; Wang, Q.; Wang, D.; Gordon, R. G.; Lundstrom, M.; Dai, H. Carbon nanotube field-effect transistors with integrated ohmic contacts and high-κ gate dielectrics. Nano Lett. 2004, 4, 447–450.
24
Li, X. L.; Wang, X. R.; Zhang, L.; Lee, S.; Dai, H. J. Chemically derived, ultrasmooth graphene nanoribbon semiconductors. Science 2008, 319, 1229–1232.
25
Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 1958, 109, 1492–1505.
26
McClure, J. W. Diamagnetism of graphite. Phys. Rev. 1956, 104, 666–671.
27
Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys. Rev. B 1996, 54, 17954.
28
Wakabayashi, K.; Fujita, M; Ajiki, H.; Sigrist, M. Electronic and magnetic properties of nanographite ribbons. Phys. Rev. B 1999, 59, 8271–8282.
29
Wakabayashi, K. Theory of ballistic electron emission microscopy. Phys. Rev. B 2001, 64, 125408.
30
Ezawa, M. Peculiar width dependence of the electronic properties of carbon nanoribbons. Phys. Rev. B 2006, 73, 045432.
31
Peres, N. M. R; Castro Neto, A. H.; Guinea, F. Conductance quantization in mesoscopic graphene. Phys. Rev. B 2006, 73, 195411.
32
Brey, L.; Fertig, H. A. Electronic states of graphene nanoribbons studied with the Dirac equation. Phys. Rev. B 2006, 73, 235411.
33
Muñoz-Rojas F.; Jacob, D.; Fernádez-Rossier, J.; Palacios, J. J. Coherent transport in graphene nanoconstrictions. Phys. Rev. B 2006, 74, 195417.
34
Wang, Z. F.; Li, Q.; Zheng, H.; Ren, H.; Su, H.; Shi, Q. W.; Chen, J. Tuning the electronic structure of graphene nanoribbons through chemical edge modification: A theoretical study. Phys. Rev. B 2007, 75, 113406.
35
Zheng, H.; Wang, Z. F.; T. Luo, T.; Shi, Q. W.; Chen, J. Analytical study of electronic structure in armchair graphene nanoribbons. Phys. Rev. B 2007, 75, 165414.
36
Areshkin, D. A.; Gunlycke, D.; White, C. T. Ballistic transport in graphene nanostrips in the presence of disorder: Importance of edge effects. Nano Lett. 2007, 7, 204–210.
37
Gunlycke, D.; Areshkin, D. A.; White, C. T. Semi-conducting graphene nanostrips with edge disorder. Appl. Phys. Lett. 2007, 90, 142104.
38
Gunlycke, D.; Lawler, H. M.; White, C. T. Room-temperature ballistic transport in narrow graphene strips. Phys. Rev. B 2007, 75, 085418.
39
Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. Peculiar localized state at zigzag graphite edge. J. Phys. Soc. Jpn. 1996, 65, 1920–1923.
40
Fabrizio, M.; Parola, A.; Tosatti, E. Strong-coupling phases of two Hubbard chains with interchain hopping. Phys. Rev. B 1992, 46, 3159–3162.
41
Gopalan, S.; Rice, T. M.; Sigrist, M. Spin ladders with spin gaps: A description of a class of cuprates. Phys. Rev. B 1994, 49, 8901–8910.
42
Choi, H. J.; Ihm, J.; Louie, S. G.; Cohen, M. L. Defects, quasibound states, and quantum conductance in metallic carbon nanotubes. Phys. Rev. Lett. 2000, 84, 2917–2920.
43
Kim, G.; Lee, S. B.; Kim, T. -S.; Ihm, J. Fano resonance and orbital filtering in multiply connected carbon nanotubes. Phys. Rev. B 2005, 71, 205415.
44
Kim, G.; Jeong, B. W.; Ihm, J. Deep levels in the band gap of the carbon nanotube with vacancy-related defects Appl. Phys. Lett. 2006, 88, 193107.
45
Zhou, T.; Wu, J.; Duan, W.; Gu, B. -L. Physical mechanism of transport blocking in metallic zigzag carbon nanotubes. Phys. Rev. B 2007, 75, 205410.
46
Sánchez-Portal, D.; Ordejón, P.; Artacho, E.; Soler, J. M. Density-functional method for very large systems with LCAO basis sets. Int. J. Quantum Chem. 1997, 65, 453–461.
47
Malysheva, L.; Onipko, A. Spectrum of π electrons in graphene as a macromolecule. Phys. Rev. Lett. 2008, 100, 186806.
48
Cresti, A.; Grosso G.; Pastori Parravicini, G. Electronic states and magnetotransport in unipolar and bipolar graphene ribbons. Phys. Rev. B 2008, 77, 115408.
49
Sutton, A.P. Electronic Structure of Materials; Clarendon Press: Oxford, 1994, p. 41.
50
Rycerz, A.; Tworzydlo, J.; Beenaker, C. W. J. Valley filter and valley valve in graphene. Nat. Phys. 2007, 3, 172–175.
51
Akhmerov, A. R.; Bardarson, J. H.; Rycerz, A.; Beenaker, C. W. J. Theory of the valley-valve effect in graphene nanoribbons. Phys. Rev. B 2008, 77, 205416.
52
Li, Z.; Qian, H.; Wu, J.; Gu, B. -L.; Duan, W. Role of symmetry in the transport properties of graphene nanoribbons under bias. Phys. Rev. Lett. 2008, 100, 206802.
53
Cresti, A.; Grosso, G.; Pastori Parravicini, G. Valley-valve effect and even-odd chain parity in p–n graphene junctions. Phys. Rev. B 2008, 77, 233402.
54
Cresti, A; Grosso, G.; Pastori Parravicini, G. Fieldeffect resistance of gated graphitic polymeric ribbons: Numerical simulations. Phys. Rev. B 2008, 78, 115433.
55
Miyamoto, Y.; Nakada, K.; Fujita, M. First-principles study of edge states of H-terminated graphitic ribbons. Phys. Rev. B 1999, 59, 9858–9861.
56
Kawai, T.; Miyamoto, Y.; Sugino, O.; Koga, Y. Graphitic ribbons without hydrogen-termination: Electronic structures and stabilities. Phys. Rev. B 2000, 62, R16349.
57
Son, Y. -W.; Cohen, M. L.; Louie, S. G. Half-metallic graphene nanoribbons. Nature 2006, 444, 347–349.
58
Barone, V.; Hod, O.; Scuseria, G. E. Electronic structure and stability of semiconducting graphene nanoribbons Nano Lett. 2006, 6, 2748–2754.
59
Son, Y. -W.; Cohen, M. L.; Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803.
60
White, C. T.; Li, J.; Gunlycke, D.; Mintmire, J. W. Hidden one-electron interactions in carbon nanotubes revealed in graphene nanostrips. Nano Lett. 2007, 7, 825–830.
61
Fujita, M.; Igami, M.; Nakada, K. Lattice distortion in nanographite ribbons. J. Soc. Phys. Jpn. 1997, 66, 1864–1867.
62
Sasaki, K.; Murakami, S.; Saito, R. Stabilization mechanism of edge states in graphene. Appl. Phys. Lett. 2006, 88, 113110.
63
Gunlycke, D.; White, C. T. Tight-binding energy dispersions of armchair-edge graphene nanostrips. Phys. Rev. B 2008, 77, 115116.
64
Klusek, Z.; Waqar, Z.; Denisov, E. A.; Kompaniets, T. N.; Makarenko, I. W.; Titkov, A. N.; Bhatti, A. S. Observations of local electron states on the edges of the circular pits on hydrogen-etched graphite surface by scanning tunneling spectroscopy. Appl. Surf. Sci. 2000, 161, 508–514.
65
Niimi, Y.; Matsui, T.; Kambara, H.; Tagami, K.; Tsukada, M.; Fukuyama, H. Scanning tunneling microscopy and spectroscopy studies of graphite edges. Appl. Surf. Sci. 2005, 241, 43–48.
66
Kobayashi, Y.; Fukui, K.; Enoki, T.; Kusakabe, K.; Kaburagi, Y. Observation of zigzag and armchair edges of graphite using scanning tunneling microscopy and spectroscopy. Phys. Rev. B 2005, 71, 193406.
67
Wallace, P. R. The band theory of graphite. Phys. Rev. 1947, 71, 622–634.
68
Reich, S.; Maultzsch, J.; Thomsen, C.; Ordejón P. Tight-binding description of graphene. Phys. Rev. B 2002, 66, 035412.
69
Grüneis, A.; Attaccalite, C.; Wirtz, L.; Shiozawa, H.; Saito, R.; Pichler, T.; Rubio, A. arXiv: 0808.1467v2, 2008.
70
Fiori, G.; Iannaccone, G. Simulation of graphene nanoribbon field-effect transistors. IEEE Elect. Dev. L. 2007, 28, 760–762.
71
Sun, L.; Li, Q.; Ren, H.; Shi, Q. W.; Yang, J.; Hou, J. G. Strain effect on energy gaps of armchair graphene nanoribbons. arXiv: cond-mat/0703795, 2007.
72
Gunlycke, D.; Areshkin, D. A.; Li, J.; Mintmire, J. W.; White, C. T. Graphene nanostrip digital memory device. Nano Lett. 2007, 7, 3608–3611.
73
Palacios, J. J.; Fernández-Rossier, J.; Brey, L. Vacancy-induced magnetism in graphene and graphene ribbons. Phys. Rev. B 2008, 77, 195428.
74
Fernández-Rossier, J. Prediction of hidden multiferroic order in graphene zigzag ribbons. Phys. Rev. B 2008, 77, 075430.
75
Nemec, N.; Tománek, D.; Cuniberti, G. Contact dependence of carrier injection in carbon nanotubes: An ab initio study. Phys. Rev. Lett. 2006, 96, 076802.
76
Nemec, N.; Tománek, D.; Cuniberti, G. Modeling extended contacts for nanotube and graphene devices. Phys. Rev. B 2008, 77, 125420.
77
Tworzydlo, J.; Trauzettel, B.; Titov, M.; Rycerz, A.; Beenakker, C. W. J. Sub-Poissonian shot noise in graphene. Phys. Rev. Lett. 2006, 96, 246802.
78
Kastnelson, M. I. Zitterbewegung, chirality, and minimal conductivity in graphene. Eur. Phys. J. B 2006, 51, 157–160.
79
Cresti, A.; Grosso, G.; Pastori Parravicini, G. Numerical study of electronic transport in gated graphene ribbons. Phys. Rev. B 2007, 76, 205433.
80
Schomerus, H. Effective contact model for transport through weakly-doped graphene. Phys. Rev. B 2007, 76, 045433.
81
San-Jose, P.; Prada, E.; Golubev, D. S. Universal scaling of current fluctuations in disordered graphene. Phys. Rev. B 2007, 76, 195445.
82
Lewenkopf, C. H.; Mucciolo, E. R.; Castro Neto, A. H. Numerical studies of conductivity and Fano factor in disordered graphene. Phys. Rev. B 2008, 77, 081410.
83
Miao, F.; Wijeratne, S.; Zhang, Y.; Coskun, U. C.; Bao, W.; Lau, C. N. Phase-coherent transport in graphene quantum billiards. Science 2007, 317, 1530–1533.
84
DiCarlo, L.; Williams, J. R.; Zhang, Y.; McClure, D. T.; Marcus, C. M. Shot noise in graphene. Phys. Rev. Lett. 2008, 100, 156801.
85
Danneau, R.; Wu, F.; Craciun, M. F.; Russo, S.; Tomi, M. Y.; Salmilehto, J.; Morpurgo A. F.; Hakonen, P. J. Shot noise in ballistic graphene. Phys. Rev. Lett. 2008, 100, 196802.
86
Nemec, N; Cuniberti, G. Hofstadter butterflies of bilayer graphene. Phys. Rev. B 2007, 75, 201404.
87
Nemec, N; Cuniberti, G. Hofstadter butterflies of carbon nanotubes: Pseudofractality of the magnetoelectronic spectrum. Phys. Rev. B 2006, 74, 165411.
88
Brey, L.; Fertig, H. A. Electronic states of graphene nanoribbons studied with the Dirac equation. Phys. Rev. B 2006, 73, 235411.
89
Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005, 438, 197–200.
90
Gusynin, V. P.; Sharapov, S. G. Unconventional integer quantum Hall effect in graphene. Phys. Rev. Lett. 2005, 95, 146801.
91
Cresti, A. Proposal for a graphene-based current nanoswitch. Nanotechnology 2008, 19, 265401.
92
Moser, J.; Barreiro, A.; Bachtold, A. Current-induced cleaning of graphene. App. Phys. Lett. 2007, 91, 163513.
93
Ando, T.; Nakanishi, T.; Saito, R. Berry's phase and absence of back scattering in carbon nanotubes. J. Phys. Soc. Jpn. 1998, 67, 2857–2862.
94
White, C. T.; Todorov, T. N. Carbon nanotubes as long ballistic conductors. Nature 1998, 393, 240–242.
95
McCann, E.; Kechedzhi, K.; Fal'ko, V. I.; Suzuura, H.; Ando, T.; Altshuler, B. L. Weak-localization magnetoresistance and valley symmetry in graphene. Phys. Rev. Lett. 2006, 97, 146805.
96
Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D. Electron transport in disordered graphene. Phys. Rev. B 2006, 74, 235443.
97
Morpurgo A. F.; Guinea, F. Intervalley scattering, long-range disorder, and effective time-reversal symmetry breaking in graphene. Phys. Rev. Lett. 2006, 97, 196804.
98
Khveshchenko, D. V. Effects of long-range correlated disorder on Dirac fermions in graphene. Phys. Rev. B 2007, 75, 241406.
99
Suzuura, H.; Ando, T. Weak-localization in metallic carbon nanotubes. J. Phys. Soc. Jpn. 2006, 75, 024703.
100
Aleiner, I. L.; Efetov, K. B. Effect of disorder on transport in graphene. Phys. Rev. Lett. 2006, 97, 236801.
101
Nomura, K.; Koshino, M.; Ryu, S. Topological delocalization of two-dimensional massless Dirac fermions. Phys. Rev. Lett. 2007, 99, 146806.
102
Anderson, P. W. Localized magnetic states in metals. Phys. Rev. 1961, 124, 41–52.
103
Abrahams, E.; Anderson, P. W.; Licciardello, D. C.; Ramakrishnan T. V. Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 1979, 42, 673–676
104
Lee, P. A.; Fisher, D. S. Anderson localization in two dimensions. Phys. Rev. Lett. 1981, 47, 882–885.
105
Lee, P. A.; Ramakrishnan, T. V. Disordered electronic systems. Rev. Mod. Phys. 1985, 57, 287–337.
106
Roche, S.; Saito, R. Magnetoresistance of carbon nanotubes: From molecular to mesoscopic fingerprints. Phys. Rev. Lett. 2001, 87, 246803.
107
Fedorov, G.; Lassagne, B.; Sagnes, M.; Raquet, B.; Broto, J. -M.; Triozon, F.; Roche, S.; Flahaut, E. Gate-dependent magnetoresistance phenomena in carbon nanotubes. Phys. Rev. Lett. 2005, 94, 066801.
108
Gomez-Navarro, C.; Pablo, P. J. De; Gómez-Herrero, J.; Biel, B.; Garcia-Vidal, F. J.; Rubio, A.; Flores, F. Tuning the conductance of single-walled carbon nanotubes by ion irradiation in the Anderson localization regime. Nat. Mater. 2005, 4, 534–539.
109
Biel, B.; Garcia-Vidal, F. J.; Rubio, A.; Flores, F. Anderson localization in carbon nanotubes: Defect density and temperature effects. Phys. Rev. Lett. 2005, 95, 266801.
110
Strunk, C.; Stojetz, B.; Roche, S. Quantum interference in multiwall carbon nanotubes. Semicond. Sci. Technol. 2006, 21, S38–S45.
111
Fedorov, G.; Tselev, A.; Jimenez, D.; Latil, S.; Kalugin, N.; Barbara, P.; Roche, S. Magnetically induced field effect in carbon nanotube devices. Nano Lett. 2007, 7, 960–964.
112
Lassagne, B.; Cleuziou, J. -P., Nanot, S.; Escofier, W.; Avriller, R.; Roche, S.; Forro, L.; Raquet, B.; Broto, J. -M. Aharonov-Bohm conductance modulation in ballistic carbon nanotubes. Phys. Rev. Lett. 2007, 98, 176802.
113
Stojetz, B.; Roche, S.; Miko, C.; Triozon, F.; Forro, L.; Strunk, C. Competition between magnetic field dependent band structure and coherent backscattering in multiwall carbon nanotubes. New J. Phys. 2007, 9, 56.
114
Biel, B.; Garcia-Vidal, F. J.; Rubio, A.; Flores, F. Ab initio study of transport properties in defected carbon nanotubes: An O(N) approach. J. Phys. : Condens. Matter 2008, 20, 294214.
115
Flores, F.; Biel, B.; Rubio, A.; Garcia-Vidal, F. J.; Gomez-Navarro, C.; de Pablo, P. J.; Gomez-Herrero, J. Anderson localization regime in carbon nanotubes: Size dependent properties. J. Phys. : Condens. Matter 2008, 20, 304211.
116
Hügle, S.; Egger, R. van Hove singularities in disordered multichannel quantum wires and nanotubes. Phys. Rev. B 2002, 66, 193311.
117
Nemec, N., Richter, K.; Cuniberti, G. Diffusion and localization in carbon nanotubes and graphene nanoribbons. New J. Phys. 2008, 10, 065014.
118
Abrikosov, A.; Gor'kov, L. P.; Dzyaloshiuskii, I. E. Quantum Field Theoretical Methods in Statistical Physics; Pergamon: Oxford, 1965.
119
López Sancho, M. P.; López Sancho, J. M.; Rubio, J. Highly convergent schemes for the calculation of bulk and surface Green functions. J. Phys. F: Met. Phys. 1985, 15, 851–858.
120
Nemec, N. Quantum transport in carbon-based nanostructures. PhD Thesis, Universität Regensburg, 2007.
121
Lherbier, A.; Persson, M.; Niquet, Y. M.; Triozon, F.; Roche, S. Quantum transport length scales in silicon-based semiconducting nanowires: Surface roughness effects. Phys. Rev. B. 2008, 77, 085301.
122
Triozon, F.; Roche, S.; Rubio, A.; Mayou, D. Electrical transport in carbon nanotubes: Role of disorder and helical symmetries. Phys. Rev. B 2004, 69, 121410.
123
Tikhonenko, F. V.; Horsell, D. W.; Gorbachev, R. V.; Savchenko, A. K. Weak localization in graphene flakes. Phys. Rev. Lett. 2008, 100, 056802.
124
Morozov, S. V.; Novoselov, K. S.; Katsnelson, M. I.; Schedin, F.; Ponomarenko, L. A.; Jiang, D.; Geim, A. K. Strong suppression of weak localization in graphene. Phys. Rev. Lett. 2006, 97, 016801.
125
Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge University Press: New York, NY, 1995.
126
Thouless, D. J. Maximum metallic resistance in thin wires. Phys. Rev. Lett. 1977, 39, 1167–1169.
127
Beenakker, C. W. J. Random-matrix theory of quantum transport. Rev. Mod. Phys. 1997, 69, 731–808.
128
Avriller, R.; Latil, S.; Triozon, F.; Blase, X.; Roche, S. Chemical disorder strength in carbon nanotubes: xMagnetic tuning of quantum transport regimes. Phys. Rev. B 2006, 74, 121406.
129
Niimi, Y.; Matsui, T.; Kambara, H.; Tagami, K.; Tsukada, M.; Fukuyama, H. Scanning tunneling microscopy and spectroscopy of the electronic local density of states of graphite surfaces near monoatomic step edges. Phys. Rev. B. 2006, 73, 085421.
130
Enoki, T.; Kobayashi, Y.; Katsuyama, C.; Osipov, V. Y.; Baidakova, M. V.; Takai, K.; Fukui, K.; Vul', A. Y. Structures and electronic properties of surface/edges of nanodiamond and nanographite. Diamond Relat. Mater. 2007, 16, 2029–2034.
131
Kobayashi, Y.; Fukui, K.; Enoki, T.; Kusakabe, K. Edge state on hydrogen-terminated graphite edges investigated by scanning tunneling microscopy. Phys. Rev. B 2006, 73, 125415.
132
Enoki, T.; Kobayashi, Y.; Fukui, K. I. Electronic structures of graphene edges and nanographene. Int. Rev. Phys. Chem. 2007, 26, 609–645.
133
Banerjee, S.; Sardar, M.; Gayathri, N.; Tyagi, A. K.; Raj, B. Conductivity landscape of highly oriented pyrolytic graphite surfaces containing ribbons and edges. Phys. Rev. B 2005, 72, 075418.
134
Banerjee, S.; Sardar, M.; Gayathri, N.; Tyagi, A. K.; Raj, B. Enhanced conductivity in graphene layers and at their edges. Appl. Phys. Lett. 2006, 88, 602111.
135
Cançado, L. G.; Pimenta, M. A.; Neves, B. R.; Dantas, M. S.; Jorio, A. Influence of the atomic structure on the Raman spectra of graphite edges. Phys. Rev. Lett. 2004, 93, 247401.
136
de Heer, W. A.; Berger, C.; Wu, X.; First, P. N.; Conrad, E. H.; Li, X.; Li, T.; Sprinkle, M.; Hass, J.; Sadowski, M. L.; Potemski, M.; Martinez, G. Epitaxial graphene. Solid State Commun. 2007, 143, 92–100.
137
Wang, X.; Ouyang, Y.; Li, X.; Wang, H.; Guo, J.; Dai, H. Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors. Phys. Rev. Lett. 2008, 100, 206803.
138
Tapasztó, L.; Dobrik, G.; Lambin, P.; Biró, L. P. Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography. Nature Nanotech. 2008, 3, 397–401.
139
Querlioz, D.; Apertet, Y.; Valentin, A.; Huet, K.; Bournel, A.; Galdin-Retailleau, S.; Dollfus, P. Suppression of the orientation effects on bandgap in graphene nanoribbons in the presence of edge disorder. Appl. Phys. Lett. 2008, 92, 042108.
140
Evaldsson, M.; Zozoulenko, I. V.; Xu, H.; Heinzel, T. Edge disorder induced Anderson localization and conduction gap in graphene nanoribbons. arXiv: 0805.4326v1, 2008.https://doi.org/10.1103/PhysRevB.78.161407
141
Mucciolo, E. R.; Castro Neto, A. H.; Lewenkopf, C. H. Conductance quantization and transport gap in disordered graphene nanoribbons. arXiv: 0806.3777, 2008.https://doi.org/10.1103/PhysRevB.79.075407
142
Martin, I.; Blanter, Y. M. Transport in disordered graphene nanoribbons. arXiv: 0705.0532v2, 2008.
143
Li, T. C.; Lu, S. -P. Quantum conductance of graphene nanoribbons with edge defects. Phys. Rev. B. 2008, 77, 085408.
144
Yoon, Y.; Guo, J. Effect of edge roughness in graphene nanoribbon transistors. Appl. Phys. Lett. 2007, 91, 073103.
145
Fiori, G.; Yoon, Y.; Hong, S.; Iannaccone, G.; Guo, J. Performance comparison of graphene nanoribbon Schottky barrier and MOS FETs. In Int. Electron Device Meeting (IEDM) Tech. Dig. 2007, pp. 757–760.
146
Basu, D.; Gilbert, M. J.; Register, L. F.; Banerjee, S. K.; MacDonald, A. H. Effect of edge roughness on electronic transport in graphene nanoribbon channel metal-oxide-semiconductor field-effect transistors. Appl. Phys. Lett. 2008, 92, 042114.
147
Wimmer, M.; Adagideli, I.; Berber, S.; Tománek, D; Richter, K. Spin transport in rough graphene nanoribbons. Phys. Rev. Lett. 2008, 100, 177207.
148
Yoon, Y.; Fiori, G.; Hong, S.; Iannaccone, G.; Guo, J. Performance comparison of graphene nanoribbon FETs with Schottky contacts and doped reservoirs. IEEE Transactions on Electron Devices 2008, 55, 2314–2323.
149
Ouyang, Y.; Wang, X.; Dai, H.; Guo, J. Carrier scattering in graphene nanoribbon transistors. Appl. Phys. Lett. 2008, 92, 243124.
150
Shon N. H.; Ando, T. Quantum transport in two-dimensional graphite system. J. Phys. Soc. Jpn. 1998, 67, 2421–2429.
151
Nomura K.; MacDonald, A. H. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 2006, 96, 256602.
152
Lherbier, A.; Biel, B.; Niquet, Y. M.; Roche, S. Transport length scales in disordered graphene-based materials: Strong localization regimes and dimensionality effects. Phys. Rev. Lett. 2008, 100, 036803.
153
Peres, N. M. R.; Guinea, F.; Castro Neto, A. H. Electronic properties of disordered two-dimensional carbon. Phys. Rev. B 2008, 73, 125411.
154
Hwang, E. H.; Adam, S.; Das Sarma, S. Carrier transport in two-dimensional graphene layers Phys. Rev. Lett. 2007, 98, 186806.
155
Dong, H. M.; Xu, W.; Zeng, Z.; Peeters, F. M. Quantum and transport conductivities in monolayer graphene. Phys. Rev. B 2008, 77, 235402.
156
Nomura, K.; Ryu S.; Koshino, M.; Mudry, C.; Furusaki A. Quantum Hall effect of massless Dirac fermions in a vanishing magnetic field. Phys. Rev. Lett. 2008, 100, 246806.
157
Kim, E. -A.; Castro Neto, A. H. Graphene as an electronic membrane. arXiv: cond-mat/0702562v2, 2008.
158
Suzuura, H.; Ando, T. Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice. Phys. Rev. Lett. 2002, 89, 266603.
159
Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D. Quantum criticality and minimal conductivity in graphene with long-range disorder. Phys. Rev. Lett. 2007, 98, 256801.
160
Bardarson, J. H.; Tworzyd–o, J.; Brouwer, P. W.; Beenakker, C. W. J. One-parameter scaling at the Dirac point in graphene. Phys. Rev. Lett. 2007, 99, 106801.
161
Guinea, F.; Katsnelson, M. I.; Vozmediano, M. A. H. Midgap states and charge inhomogeneities in corrugated graphene. Phys. Rev. B 2008, 77, 075422.
162
Novikov, D. S. Numbers of donors and acceptors from transport measurements in graphene. Appl. Phys. Lett. 2007, 91, 102102.
163
Adam, S.; Hwang, E. H.; Galitski, V. M.; Das Sarma, S. A self-consistent theory for graphene transport. PNAS. 2007, 104, 18392.
164
Lherbier, A.; Blase X., M.; Niquet, Y. M.; Triozon, F.; Roche S. Charge transport in chemically doped 2D graphene. Phys. Rev. Lett. 2008, 101, 036808.
165
Tan, Y. W.; Zhang, Y.; Bolotin, K.; Zhao, Y.; Adam, S.; Hwang, E. H.; Das Sarma, S.; Stormer, H. L.; Kim, P. Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 2007, 99, 246803.
166
Koshino, M.; Ando, T. Hall plateau diagram for the Hofstadter butterfly energy spectrum. Phys. Rev. B 2006, 73, 155304.
Pages 361-394
Cite this article:
Cresti A, Nemec N, Biel B, et al. Charge Transport in Disordered Graphene-Based Low Dimensional Materials. Nano Research, 2008, 1(5): 361-394. https://doi.org/10.1007/s12274-008-8043-2
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