[ Pobierz całość w formacie PDF ]
at the level of 2.5%, approximately five times larger than
mean free path =c* 0.06 m, and a mobility
expected for simple tight binding theory.17 This may be
1.1 m2 Vs-1. The linewidths are significantly smaller than
linked to the intrinsic single-particle band structure, with
those observed by Jiang et al.9, which may explain why these
some indications of this in the comparison of ab initio and
authors did not observe the electron-hole asymmetry.
tight binding dispersions,19 although these calculations sug-
In conclusion, therefore, we have measured cyclotron
gest values of c* as low as 0.87 106 ms-1. By contrast, the
K
resonance in a monolayer graphene system, which demon-
magnitude of the asymmetry is comparable, but of the oppo-
strates that the electron velocity is significantly enhanced
site sign to that predicted 3% using random phase
relative to the value expected from previous calculations and
approximation methods, which take account of dynamical
measurements for thicker graphitic systems. In addition, we
screening,21 and which also predict an overall 13% en-
have demonstrated a considerable asymmetry in the carrier
hancement of the velocity. It is also possible that the gating
velocity for the electron- and holelike parts of the dispersion
process itself will lead to some changes in the bonding,
relation close to the K point of the Brillouin zone. These
due to the changes in surface field, and that this is linked to
measurements suggest that there are still considerable uncer-
the velocity enhancement in thinner layers.
tainties in understanding the band structure of monolayer
In addition to conventional single-particle effects, it may
graphene, which may lead to significant changes in any
also be possible that many-body corrections could influence
theories24 based on perfect particle-antiparticle symmetry.
the value and asymmetry of the electron velocity. Kohn s
theorem22 has long been known to exclude the influence of
Part of this work has been supported by EuroMagNET
electron-electron interactions on long-wavelength excitations
under the EU Contract No. RII3-CT-2004-506239 of the 6th
for conventional parabolic systems. Calculations for
Framework Structuring the European Research Area, Re-
graphene23 suggest, however, that, although there are several
search Infrastructures Action.
12
*r.nicholas1@physics.ox.ac.uk E. McCann and V. I. Fal ko, Phys. Rev. Lett. 96, 086805 2006 .
1 13
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, F. Guinea, A. H. Castro Neto, and N. M. R. Peres, Phys. Rev. B
S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 73, 245426 2006 .
14
666 2004 . G. Li and E. Y. Andrei, arXiv:0705.1185 unpublished .
2 15
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. M. Milnera, J. Kurti, M. Hulman, and H. Kuzmany, Phys. Rev.
Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Lett. 84, 1324 2000 .
16
Nature London 438, 197 2005 . A. G. Souza Filho, S. G. Chou, G. G. Samsonidze, G. Dressel-
3
Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature London haus, M. S. Dresselhaus, L. An, J. Liu, A. K. Swan, M. S. nl,
438, 201204 2005 . B. B. Goldberg, A. Jorio, A. Grneis, and R. Saito, Phys. Rev. B
4
Y. Zhang, Z. Jiang, J. P. Small, M. S. Purewal, Y. W. Tan, M. 69, 115428 2004 .
17
Fazlollahi, J. D. Chudow, J. A. Jaszczak, H. L. Stormer, and P. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Prop-
Kim, Phys. Rev. Lett. 96, 136806 2006 . erties of Carbon Nanotubes Imperial College Press, London,
5
K. S. Novoselov and A. K. Geim, Nat. Mater. 6, 183 2007 . 1998 .
6 18
P. R. Wallace, Phys. Rev. 71, 622 1947 . R. Saito, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Appl.
7
S. Y. Zhou, G.-H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru, Phys. Lett. 60, 2204 1992 .
19
R. D. Diehl, Y. Kopelevich, D. H. Lee, S. G. Louie, and A. S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejon, Phys. Rev. B
Lanzara, Nat. Phys. 2, 595 2006 . 66, 035412 2002 .
8 20
M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. L.-J. Li, T.-W. Lin, J. Doig, I. B. Mortimer, J. G. Wiltshire, R. A.
deHeer, Phys. Rev. Lett. 97, 266405 2006 . Taylor, J. Sloan, M. L. H. Green, and R. J. Nicholas, Phys. Rev.
9
Z. Jiang, E. A. Henriksen, L. C. Tung, Y. J. Wang, M. E. B 74, 245418 2006 .
21
Schwartz, M. Y. Han, P. P. Kim, and H. L. Stormer, Phys. Rev. T. Miyake and S. Saito, Phys. Rev. B 68, 155424 2003 .
22
Lett. 98, 197403 2007 . W. Kohn, Phys. Rev. 123, 1242 1961 .
10 23
J. W. McClure, Phys. Rev. 104, 666 1956 . A. Iyengar, J. H. Wang, H. A. Fertig, and L. Brey, arXiv:cond-
11
K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal ko, M. I. mat/0608364.
24
Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. Geim, Nat. V. V. Cheianov, V. Fal ko, and B. L. Altshuler, Science 315, 1252
Phys. 2, 177 2006 . 2007 .
081406-4 [ Pobierz całość w formacie PDF ]
zanotowane.pl doc.pisz.pl pdf.pisz.pl wyciskamy.pev.pl
at the level of 2.5%, approximately five times larger than
mean free path =c* 0.06 m, and a mobility
expected for simple tight binding theory.17 This may be
1.1 m2 Vs-1. The linewidths are significantly smaller than
linked to the intrinsic single-particle band structure, with
those observed by Jiang et al.9, which may explain why these
some indications of this in the comparison of ab initio and
authors did not observe the electron-hole asymmetry.
tight binding dispersions,19 although these calculations sug-
In conclusion, therefore, we have measured cyclotron
gest values of c* as low as 0.87 106 ms-1. By contrast, the
K
resonance in a monolayer graphene system, which demon-
magnitude of the asymmetry is comparable, but of the oppo-
strates that the electron velocity is significantly enhanced
site sign to that predicted 3% using random phase
relative to the value expected from previous calculations and
approximation methods, which take account of dynamical
measurements for thicker graphitic systems. In addition, we
screening,21 and which also predict an overall 13% en-
have demonstrated a considerable asymmetry in the carrier
hancement of the velocity. It is also possible that the gating
velocity for the electron- and holelike parts of the dispersion
process itself will lead to some changes in the bonding,
relation close to the K point of the Brillouin zone. These
due to the changes in surface field, and that this is linked to
measurements suggest that there are still considerable uncer-
the velocity enhancement in thinner layers.
tainties in understanding the band structure of monolayer
In addition to conventional single-particle effects, it may
graphene, which may lead to significant changes in any
also be possible that many-body corrections could influence
theories24 based on perfect particle-antiparticle symmetry.
the value and asymmetry of the electron velocity. Kohn s
theorem22 has long been known to exclude the influence of
Part of this work has been supported by EuroMagNET
electron-electron interactions on long-wavelength excitations
under the EU Contract No. RII3-CT-2004-506239 of the 6th
for conventional parabolic systems. Calculations for
Framework Structuring the European Research Area, Re-
graphene23 suggest, however, that, although there are several
search Infrastructures Action.
12
*r.nicholas1@physics.ox.ac.uk E. McCann and V. I. Fal ko, Phys. Rev. Lett. 96, 086805 2006 .
1 13
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, F. Guinea, A. H. Castro Neto, and N. M. R. Peres, Phys. Rev. B
S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 73, 245426 2006 .
14
666 2004 . G. Li and E. Y. Andrei, arXiv:0705.1185 unpublished .
2 15
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. M. Milnera, J. Kurti, M. Hulman, and H. Kuzmany, Phys. Rev.
Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Lett. 84, 1324 2000 .
16
Nature London 438, 197 2005 . A. G. Souza Filho, S. G. Chou, G. G. Samsonidze, G. Dressel-
3
Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature London haus, M. S. Dresselhaus, L. An, J. Liu, A. K. Swan, M. S. nl,
438, 201204 2005 . B. B. Goldberg, A. Jorio, A. Grneis, and R. Saito, Phys. Rev. B
4
Y. Zhang, Z. Jiang, J. P. Small, M. S. Purewal, Y. W. Tan, M. 69, 115428 2004 .
17
Fazlollahi, J. D. Chudow, J. A. Jaszczak, H. L. Stormer, and P. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Prop-
Kim, Phys. Rev. Lett. 96, 136806 2006 . erties of Carbon Nanotubes Imperial College Press, London,
5
K. S. Novoselov and A. K. Geim, Nat. Mater. 6, 183 2007 . 1998 .
6 18
P. R. Wallace, Phys. Rev. 71, 622 1947 . R. Saito, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Appl.
7
S. Y. Zhou, G.-H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru, Phys. Lett. 60, 2204 1992 .
19
R. D. Diehl, Y. Kopelevich, D. H. Lee, S. G. Louie, and A. S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejon, Phys. Rev. B
Lanzara, Nat. Phys. 2, 595 2006 . 66, 035412 2002 .
8 20
M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. L.-J. Li, T.-W. Lin, J. Doig, I. B. Mortimer, J. G. Wiltshire, R. A.
deHeer, Phys. Rev. Lett. 97, 266405 2006 . Taylor, J. Sloan, M. L. H. Green, and R. J. Nicholas, Phys. Rev.
9
Z. Jiang, E. A. Henriksen, L. C. Tung, Y. J. Wang, M. E. B 74, 245418 2006 .
21
Schwartz, M. Y. Han, P. P. Kim, and H. L. Stormer, Phys. Rev. T. Miyake and S. Saito, Phys. Rev. B 68, 155424 2003 .
22
Lett. 98, 197403 2007 . W. Kohn, Phys. Rev. 123, 1242 1961 .
10 23
J. W. McClure, Phys. Rev. 104, 666 1956 . A. Iyengar, J. H. Wang, H. A. Fertig, and L. Brey, arXiv:cond-
11
K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal ko, M. I. mat/0608364.
24
Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. Geim, Nat. V. V. Cheianov, V. Fal ko, and B. L. Altshuler, Science 315, 1252
Phys. 2, 177 2006 . 2007 .
081406-4 [ Pobierz całość w formacie PDF ]