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Integral quantum Hall effect in graphene: Zero and finite Hall field

Title:

Integral quantum Hall effect in graphene: Zero and finite Hall field

Krstajić, P. M. and Vasilopoulos, P. (2011) Integral quantum Hall effect in graphene: Zero and finite Hall field. Physical Review B, 83 (7). 075427-1. ISSN 1098-0121

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Official URL: http://dx.doi.org/10.1103/PhysRevB.83.075427

Abstract

We study the influence of a finite Hall field EH on the Hall conductivity σyx in graphene. Analytical expressions are derived for σyx using the Kubo-Greenwood formula. For vanishing EH, we obtain the well-known expression σyx=4(N+1/2)e2/h. The inclusion of the dispersion of the energy levels, previously not considered, and their width, due to scattering by impurities, produces the plateau of the n=0 Landau level. Further, we evaluate the longitudinal resistivity ρxx and show that it exhibits an oscillatory behavior with the electron concentration. The peak values of ρxx depend strongly on the impurity concentration and their potential. For a finite EH, the result for σyx is the same as that for EH=0, provided EH is not strong, but the values and positions of the resistivity maxima are modified due to the EH-dependent dispersion of the energy levels.

Divisions:Concordia University > Faculty of Arts and Science > Physics
Item Type:Article
Refereed:Yes
Authors:Krstajić, P. M. and Vasilopoulos, P.
Journal or Publication:Physical Review B
Date:2011
Keywords:PACS number(s): 71.10.Pm, 72.25.−b, 73.21.−b
ID Code:7120
Deposited By:DANIELLE DENNIE
Deposited On:07 Mar 2011 12:49
Last Modified:07 Mar 2011 12:49
References:
1.A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009).

2.Y. Zheng and T. Ando, Phys. Rev. B 65, 245420 (2002).

3.V. P. Gusynin and S. G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005).

4.N. M. R. Peres, F. Guinea, and A. H. Castro Neto, Phys. Rev. B 73, 125411 (2006).

5.A. M. J. Schakel, Phys. Rev. D 43, 1428 (1991).

6.K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature (London) 438, 197 (2005).

7.Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London) 438, 201 (2005).

8.K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim, and A. K. Geim, Science 315, 1379 (2005).

9.S. Masubuchi, K. Suga, M. Ono, K. Kindo, S. Takeyama, and T. Machida, J. Phys. Soc. Jpn. 77, 113707 (2008).

10.X. Wu, Y. Hu, M. Ruan, N. K. Madiomanana, J. Hankinson, M. Sprinkle, C. Berger, and W. A. de Heer, Appl. Phys. Lett. 95, 223108 (2009).

11.D. L. Miller, K. D. Kubista, G. M. Rutter, M. Ruan, W. A. de Heer, P. N. First, and J. A. Stroscio, Science 324, 924 (2009).

12.Z. Jiang, Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Solid State Commun. 143, 14 (2007).

13.Y. Zhang, Z. Jiang, J. P. Small, M. S. Purewal, Y.-W. Tan, M. Fazlollahi, J. D. Chudow, J. A. Jaszczak, H. L. Stormer, and P. Kim, Phys. Rev. Lett. 96, 136806 (2006).

14.V. P. Gusynin and S. G. Sharapov, Phys. Rev. Lett. 95, 146801 (2005); Phys. Rev. B 73, 245411 (2006).

15.A. H. Castro Neto, F. Guinea, and N. M. R. Peres, Phys. Rev. B 73, 205408 (2006).

16.I. F. Herbut, Phys. Rev. B 75, 165411 (2007).

17.P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. 77, 195430 (2008).

18.T. Champel and S. Florens, Phys. Rev. B 82, 045421 (2010).

19.T. Kramer, C. Kreisbeck, V. Krueckl, E. J. Heller, R. E. Parrott, and C.-T. Liang, Phys. Rev. B 81, 081410(R) (2010).

20.M. Koshino and T. Ando, Phys. Rev. B 75, 033412 (2007).

21.M. E. Raikh and T. V. Shahbazyan, Phys. Rev. B 47, 1522 (1993).

22.O. G. Balev and P. Vasilopoulos, Phys. Rev. B 47, 16410 (1993).

23.P. S. Zyryanov and M. Klinger, Quantum Theory of Electron Transport Phenomena in Crystalline Semiconductors [in Russian] (Nauka, Moscow, 1976).

24.A. H. MacDonald, T. M. Rice, and W. F. Brinkman, Phys. Rev. B 28, 3648 (1983).

25.V. Lukose, R. Shankar, and G. Baskaran, Phys. Rev. Lett. 98, 116802 (2007).

26.N. M. R. Peres and E. V. Castro, J. Phys. C 19, 406231 (2007).

27.M. Charbonneau, K. M. Van Vliet, and P. Vasilopoulos, J. Math. Phys. 23, 318 (1982); P. Vasilopoulos, Phys. Rev. B 32, 771 (1985).

28.O. G. Balev and P. Vasilopoulos, Phys. Rev. B 54, 4863 (1996).

29.T. Ando, J. Phys. Soc. Jpn. 75, 074716 (2006).

30.N. M. R. Peres, J. M. B. Lopes dos Santos, and T. Stauber, Phys. Rev. B 76, 073412 (2007).

31.E. Fradkin, Phys. Rev. B 33, 3257 (1986).

32.A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).

33.S. Adam, E. H. Hwang, V. M. Galitski, and S. D. Sarma, Proc. Natl. Acad. Sci. USA 104, 18392 (2007).

34.K. Nomura and A. H. MacDonald, Phys. Rev. Lett. 98, 076602 (2007).

35.J.-H. Chen, G. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, and M. Ishigami, Nature Phys. 4, 377 (2008).

36.Strictly speaking, for E≠0, there is a Drude type contribution to the conductivity σdif, stemming from the second term in Eq. (4) or the term ∝δn,n' in Eq. (8) (see Ref. 27). However, this σdif is about five orders of magnitude smaller than σcol evaluated in the text and is therefore neglected. For E=0, though, this σdif vanishes.

37.C. H. Lewenkopf, E. R. Mucciolo, and A. H. Castro Neto, Phys. Rev. B 77, 081410(R) (2008).

38.I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, Orlando, 1980).

39.P. Vasilopoulos and C. M. Van Vliet, Phys. Rev. B 34, 1057 (1986).

40.Z. Jiang, Y. Zhang, H. L. Stormer, and P. Kim, Phys. Rev. Lett. 99, 106802 (2007).

41.A. J. M. Giesbers, L. A. Ponomarenko, K. S. Novoselov, A. K. Geim, M. I. Katsnelson, J. C. Maan, and U. Zeitler, Phys. Rev. B 80, 201403(R) (2009).

42.T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982).

43.J. G. Checkelsky, L. Li, and N. P. Ong, Phys. Rev. Lett. 100, 206801 (2008).

44.S. Cho and M. S. Fuhrer, Phys. Rev. B 77, 081402(R) (2008).

45.Y. Barlas, R. Côté, K. Nomura, and A. H. MacDonald, Phys. Rev. Lett. 101, 097601 (2008).
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