Quantum of the Magnetic Flux Characteristic forExperiments Performed on the Integer and Fractional Quantum Hall Effects
Author(s)
Stanisław Olszewski*
ABSTRACT
Experimentally the plateaus characteristic for the integer quantum Hall effect is obtained in vicinity of specific values of the magnetic induction. The paper demonstrates that the ratios of these induction values to carrier concentration in the planar crystalline samples approach systematically the quanta of the magnetic flux important for the behavior of superconductors. Moreover, the same quanta can be deduced from the Landau levels theory and their application in the magnetoresistance theory gives results being in accordance with experiments. The quanta of the magnetic flux similar to those for the integer quantum Hall effect can be obtained also for the fractional quantum Hall effect. This holds on condition the experimental ratio of the magnetic flux to carrier concentration is multiplied by the filling factor of the Landau level.
Cite this paper
S. Olszewski, "Quantum of the Magnetic Flux Characteristic forExperiments Performed on the Integer and Fractional Quantum Hall Effects," Journal of Modern Physics, Vol. 4 No. 11, 2013, pp. 14-20. doi: 10.4236/jmp.2013.411A1003.
S. Olszewski, "Quantum of the Magnetic Flux Characteristic forExperiments Performed on the Integer and Fractional Quantum Hall Effects," Journal of Modern Physics, Vol. 4 No. 11, 2013, pp. 14-20. doi: 10.4236/jmp.2013.411A1003.
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[1] J. C. Slater, “Quantum Theory of Molecules and Solids,” Vol. 3, McGraw-Hill, New York, 1967. [2] J. M. Ziman, “Principles of the Theory of Solids,” Cambridge University Press, 1972.
http://dx.doi.org/10.1017/CBO9781139644075 [3] M. Cyrot and R. Pavuna, “Introduction to Superconductivity and High Tc Materials,” World Scientific, Singapore, 1992. [4] S. A. Kivelson and V. L. Pokrovsky, Physical Review B, Vol. 40, 1989, p. 1373.
http://dx.doi.org/10.1103/PhysRevB.40.1373 [5] J. K. Jain, S. A. Kivelson and D. J. Thouless, Physical Review Letters, Vol. 71, 1993, p. 3003.
http://dx.doi.org/10.1103/PhysRevLett.71.3003 [6] A. H. MacDonald, “Quantum Hall Effect: A Perspective,” Kluwer, Milano, 1989.
http://dx.doi.org/10.1007/978-94-010-9709-3 [7] R. E. Prange and S. M. Girvin, “The Quantum Hall Effect,” 2nd Edition, Springer, New York, 1990.
http://dx.doi.org/10.1007/978-1-4612-3350-3 [8] S. Das Sarma and A. Pinczuk, “Perspectives in Quantum Hall Effects,” Wiley, New York, 1997. [9] S. Olszewski and M. Gluzinski, Zeitschrift für Naturforschung A, Vol. 66, 2011, p. 311. [10] S. Olszewski, Acta Physica Polonica A, Vol. 120, 2011, p. 525. [11] S. Olszewski, Reviews in Theoretical Science, Vol. 1, 2013, p. 344. http://dx.doi.org/10.1166/rits.2013.1011 [12] S. Olszewski, Quantum Matter, Vol. 2, 2013, p. 102.
http://dx.doi.org/10.1166/qm.2013.1030 [13] C. Kittel, “Quantum Theory of Solids,” 2nd Edition, Wiley, New York, 1987. [14] C. Kittel, “Introduction to Solid State Physics,” 7th Edition, Wiley, New York, 1996. [15] J. Singleton, “Band Theory and Electronic Properties of Solids,” Oxford University Press, Oxford, 2001. [16] Th. Englert, D. C. Tsui, A. C. Gossard and Ch. Uihlein, Surface Science, Vol. 113, 1982, p. 295.
http://dx.doi.org/10.1016/0039-6028(82)90604-5 [17] D. C. Tsui, H. L. Stormer and A. C. Gossard, Physical Review Letters, Vol. 48, 1982, p. 1559.
http://dx.doi.org/10.1103/PhysRevLett.48.1559 [18] M. A. Paalanen, D. C. Tsui and A. C. Gossard, Physical Review B, Vol. 25, 1982, p. 5566.
http://dx.doi.org/10.1103/PhysRevB.25.5566 [19] D. C. Tsui, H. L. Stormer, J. C. M. Hwang, J. S. Brooks and M. J. Naughton, Physical Review B, Vol. 28, 1983, p. 2274. http://dx.doi.org/10.1103/PhysRevB.28.2274 [20] H. L. Stormer, D. C. Tsui, A. C. Gossard and J. C. M. Hwang, Physica B, Vol. 117/118, 1983, p. 688.
http://dx.doi.org/10.1016/0378-4363(83)90624-1 [21] A. M. Chang, P. Berglund, D. C. Tsui, H. L. Stormer and J. C. M. Hwang, Physical Review Letters, Vol. 53, 1984, p. 997. http://dx.doi.org/10.1103/PhysRevLett.53.997 [22] H. P. Wei, D. C. Tsui and A. M. M. Pruisken, Physical Review B, Vol. 33, 1985, p. 1488.
http://dx.doi.org/10.1103/PhysRevB.33.1488 [23] G. S. Boebinger, A. M. Chang, H. L. Stormer and D. C. Tsui, Physical Review B, Vol. 32, 1985, p. 4268.
http://dx.doi.org/10.1103/PhysRevB.32.4268 [24] R. J. Clark, R. J. Nicholas, A. Usher, C. T. Foxon and J. J. Harris, Surface Science, Vol. 170, 1986, p. 141.
http://dx.doi.org/10.1016/0039-6028(86)90953-2 [25] R. L. Willett, J. P. Eisenstein, H. L. Stormer, D. C. Tsui, A. C. Gossard and J. H. English, Physical Review Letters, Vol. 59, 1987, p. 1776.
http://dx.doi.org/10.1103/PhysRevLett.59.1776 [26] J. P. Eisenstein, H. L. Stormer, L. Pfeiffer, and K. W. West, Physical Review Letters, Vol. 62, 1989, p. 1540.
http://dx.doi.org/10.1103/PhysRevLett.62.1540 [27] G. S. Boebinger, H. W. Jiang, L. N. Pfeiffer and K. W. West, Physical Review Letters, Vol. 64, 1990, p. 1793.
http://dx.doi.org/10.1103/PhysRevLett.64.1793 [28] A. M. Chang, “The Quantum Hall Effect,” In: R. E. Prange and S. M. Girvin, Eds., The Quantum Hall Effect, Chapter 6, 2nd Edition, Springer, New York, 1990.
http://dx.doi.org/10.1007/978-1-4612-3350-3 [29] J. P. Eisenstein and H. L. Stormer, Science, Vol. 248, 1990, p. 1510.
http://dx.doi.org/10.1126/science.248.4962.1510 [30] M. E. Cage in “The Quantum Hall Effect,” In: R. E. Prange and S. M. Girvin, Eds., The Quantum Hall Effect, Chapter 2, 2nd Edition, Springer, New York, 1990.
http://dx.doi.org/10.1007/978-1-4612-3350-3 [31] M. B. Santos, Y. W. Suen, M. Shayegan, Y. P. Li, L. W. Engel and D. C. Tsui, Physical Review Letters, Vol. 68, 1992, p. 1188.
http://dx.doi.org/10.1103/PhysRevLett.68.1188 [32] J. P. Eisenstein, G. S. Boebinger, L. N. Pfeiffer, K. W. West and Song He, Physical Review Letters, Vol. 68, 1992, p. 1383.
http://dx.doi.org/10.1103/PhysRevLett.68.1383 [33] V. Goldman, J. K. Wang, B. Su and M. Shayegan, Physical Review Letters, Vol. 70, 1993, p. 647.
http://dx.doi.org/10.1103/PhysRevLett.70.647 [34] T. Sajoto, Y. P. Li, L. W. Engel, D. C. Tsui and M. Shayegan, Physical Review Letters, Vol. 70, 2321, 1993.
http://dx.doi.org/10.1103/PhysRevLett.70.2321 [35] H. C. Manoharan and M. Shayegan, Physical Review B, Vol. 50, 1994, p. 17662.
http://dx.doi.org/10.1103/PhysRevB.50.17662 [36] P. T. Coleridge, A. S. Sachrajda, H. Lafontaine and Y. Feng, Physical Review B, Vol. 54, 1996, p. 14518.
http://dx.doi.org/10.1103/PhysRevB.54.14518 [37] H. C. Manoharan, Y. W. Suen, M. B. Santos and M. Shayegan, Physical Review Letters, Vol. 77, 1996, p. 1813. http://dx.doi.org/10.1103/PhysRevLett.77.1813 [38] M. Shayegan, “Perspectives of Quantum Hall Effects,” In: S. Das Sarma and A. Pinczuk, Eds., Perspectives in Quantum Hall Effects, Chapter 9, Wiley, New York, 1997. [39] D. C. Tsui, Reviews of Modern Physics, Vol. 71, 1999, p. 891. http://dx.doi.org/10.1103/RevModPhys.71.891 [40] C. T. Liang, C. G. Smith, M. Y. Simmons and D. A. Ritchie, Physical Review B, Vol. 64, 2001, Article 233319. http://dx.doi.org/10.1103/PhysRevB.64.233319 [41] K. Vyborny, L. Smrcka and R. A. Deutschmann, Physical Review B, Vol. 66, 2002, Article 205318.
http://dx.doi.org/10.1103/PhysRevB.66.205318 [42] B. S. Deaver and W. M. Fairbank, Physical Review Letters, Vol. 7, 1961, p. 43.
http://dx.doi.org/10.1103/PhysRevLett.7.43 [43] S. Olszewski, Quantum Matter, in press. [44] H. Aoki, Reports on Progress in Physics, Vol. 80, 1987, p. 655. http://dx.doi.org/10.1088/0034-4885/50/6/002 [45] T. M. Lu, W. Pan, D. C. Tsui, C.-H. Lee, and C. W. Liu, Physical Review B, Vol. 85, 2012, Article 121307.