A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

• Authors: Wenhua Hai , Zejun Li , Kewen Xiao
• Languages of publication: EN

Abstracts

EN

It is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen “pseudo-atom”. From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-AlxGa1−x
As heterojunction. The results are in good agreement with the existing experimental data.

Keywords

EN

quantum Hall effect; hydrogen pseudo-atom; band-like structure; exact pair state; 2D electron gas

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 6
• Pages: 1509-1517

Dates

published

1 - 12 - 2011

online

15 - 10 - 2011

Contributors

author

Wenhua Hai

• Department of physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, 410081, China

author

Zejun Li

• Department of physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, 410081, China

author

Kewen Xiao

• Department of physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, 410081, China

References

• [1] D. C. Tsui, H. L. Stormer, A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982) http://dx.doi.org/10.1103/PhysRevLett.48.1559[Crossref]
• [2] H. L. Stormer, A. Chang, D. C. Tsui, J. C. M. Hwang, A. C. Gossard, W. Wiegmann, Phys. Rev. Lett. 50, 1953 (1983) http://dx.doi.org/10.1103/PhysRevLett.50.1953[Crossref]
• [3] W. Pan, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin, K. W. West, Phys. Rev. Lett. 90, 016801 (2003) http://dx.doi.org/10.1103/PhysRevLett.90.016801[Crossref]
• [4] K. von Klitzing, G. Dorda, M. Pepper, Phys. Rev. Lett. 45, 494 (1980) http://dx.doi.org/10.1103/PhysRevLett.45.494[Crossref]
• [5] K. von Klitzing, Rev. Mod. Phys. 58, 519 (1986) http://dx.doi.org/10.1103/RevModPhys.58.519[Crossref]
• [6] T. Chakraborty, Adv. Phys. 49, 959 (2000) http://dx.doi.org/10.1080/00018730050198161[Crossref]
• [7] A. Hansen, J. Kertész, Philos. Mag. B 77, 1301 (1998)
• [8] R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983) http://dx.doi.org/10.1103/PhysRevLett.50.1395[Crossref]
• [9] R. B. Laughlin, Phys. Rev. B 23, R5632 (1981) http://dx.doi.org/10.1103/PhysRevB.23.5632[Crossref]
• [10] F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983) http://dx.doi.org/10.1103/PhysRevLett.51.605[Crossref]
• [11] B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984) http://dx.doi.org/10.1103/PhysRevLett.52.1583[Crossref]
• [12] R. G. Clark, J. R. Mallet, S. R. Haynes, J. J. Harris, C. T. Foxon, Phys. Rev. Lett. 60, 1747 (1988) http://dx.doi.org/10.1103/PhysRevLett.60.1747[Crossref]
• [13] J. R. Simmons, H-P. Wei, L. W. Engel, D. C. Tsui, M. Shayegan, Phys. Rev. Lett. 63, 1731 (1989) http://dx.doi.org/10.1103/PhysRevLett.63.1731[Crossref]
• [14] R. E. Prange, S. Girvin, The Quantum Hall Effect, 2nd edition (Springer Verlag, New York, 1990) http://dx.doi.org/10.1007/978-1-4612-3350-3[Crossref]
• [15] J. K. Jain, Phys. Rev. Lett. 63, 199 (1989) http://dx.doi.org/10.1103/PhysRevLett.63.199[Crossref]
• [16] J. K. Jain, Phys. Rev. B 41, 7653 (1990) http://dx.doi.org/10.1103/PhysRevB.41.7653[Crossref]
• [17] S. C. Zhang, T. H. Hansson, S. Kivelson, Phys. Rev. Lett. 62, 82 (1989) http://dx.doi.org/10.1103/PhysRevLett.62.82[Crossref]
• [18] S. C. Zhang, T. H. Hansson, S. Kivelson, Phys. Rev. Lett. 62, 980 (1989) http://dx.doi.org/10.1103/PhysRevLett.62.980.3[Crossref]
• [19] D. H. Lee, S. C. Zhang, Phys. Rev. Lett. 66, 1220 (1991) http://dx.doi.org/10.1103/PhysRevLett.66.1220[Crossref]
• [20] J. P. Eisenstein, H. L. Stormer, Science 248, 1510 (1990) http://dx.doi.org/10.1126/science.248.4962.1510[Crossref]
• [21] C. C. Chang, J. K. Jain, Phys. Rev. Lett. 92, 196806 (2004) http://dx.doi.org/10.1103/PhysRevLett.92.196806[Crossref]
• [22] A. Fukuda et al., Physica E 40, 1261 (2008) http://dx.doi.org/10.1016/j.physe.2007.08.119[Crossref]
• [23] S. Fujita, Y. Tamura, A. Suzuki, Mod. Phys. Lett. B 15, 817 (2001) http://dx.doi.org/10.1142/S0217984901002610[Crossref]
• [24] W. Pan, H. L. Stormer, D. C. Tsui, L. N. Pfeiffer, K. W. Baldwin, K. W. West, Int. J. Mod. Phys. B 16, 2940 (2002) http://dx.doi.org/10.1142/S0217979202013250[Crossref]
• [25] M. A. Hidalgo, R. Cangas, Physica E 42, 1329 (2010) http://dx.doi.org/10.1016/j.physe.2009.11.017[Crossref]
• [26] M. Taut, Phys. Rev. A 48, 3561 (1993) http://dx.doi.org/10.1103/PhysRevA.48.3561[Crossref]
• [27] M. Taut, J. Phys. A-Match. Gen. 27, 1045 (1994) http://dx.doi.org/10.1088/0305-4470/27/3/040[Crossref]
• [28] M. Taut, J. Phys. A-Match. Gen. 28, 2081 (1995) http://dx.doi.org/10.1088/0305-4470/28/7/026[Crossref]
• [29] R. Pino, V. M. Villalba, Phys. Status Solidi B 211, 641 (1999) http://dx.doi.org/10.1002/(SICI)1521-3951(199902)211:2<641::AID-PSSB641>3.0.CO;2-Y[Crossref]
• [30] W. Hai et al., Int. J. Theor. Phys. 39, 1405 (2000) http://dx.doi.org/10.1023/A:1003603323772[Crossref]
• [31] M. Alberg, L. Wilets, Phys. Lett. A 286, 7 (2001) http://dx.doi.org/10.1016/S0375-9601(01)00385-1[Crossref]
• [32] M. Ahmad, H. Zaman, N. Rehman, Cent. Eur. J. Phys. 8, 422 (2010) http://dx.doi.org/10.2478/s11534-009-0083-z[Crossref]
• [33] M. Ayub, H. Zaman, M. Ahmad, Cent. Eur. J. Phys. 8, 135 (2010) http://dx.doi.org/10.2478/s11534-009-0110-0[Crossref]
• [34] J. M. Shi, F. M. Peeters, J. T. Devreese, Phys. Rev. B 48, 5202 (1993) http://dx.doi.org/10.1103/PhysRevB.48.5202[Crossref]
• [35] J. Zeng, Quantum Mechanics (Science Press, Beijing, 2000) (in Chinese)
• [36] L. Landau, Z. Phys. 64, 629 (1930) http://dx.doi.org/10.1007/BF01397213[Crossref]
• [37] C. Kittel, Introduction to Solid State Physics, 5th edition (John Wiley, New York, 1976) [WoS]
• [38] P. W. Barmby et al., J. Phys.-Condens. Mat. 6, 7867 (1994) http://dx.doi.org/10.1088/0953-8984/6/39/008[Crossref]
• [39] W. Hai, arXiv:cond-mat/0406771v2 [cond-mat.meshall]

Identifiers

DOI

10.2478/s11534-011-0069-5