Theory of the Integer and Fractional Quantum Hall Effects

Name: Theory of the Integer and Fractional Quantum Hall Effects
SKU: 26651
Price: 210.00 USD
Availability: InStock

$210.00

Shosuke Sasaki
Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, Machikaneyama, Toyonaka, Osaka, Japan

Series: Classical and Quantum Mechanics, Physics Research and Technology
BISAC: SCI057000

This book aims to describe the physics of the integer and fractional quantum Hall effects (QHE) from a theoretical side.

In the classical Hall effect, the Hall resistance is proportional to the applied magnetic field strength and varies continuously. So, the discovery of a stepwise change of the Hall resistance by von Klitzing in an ultra-thin layer of a MOSFET was a big surprise.

The QHE is a macroscopic phenomenon and shows the exact quantum structure, which is one of the most fundamental phenomena in physics.

The fractional quantum Hall effect has been explained assuming quasi-particles with fractional charges or Jain’s composite fermions, the existence of which has not been verified experimentally. The author has been developing a theory based on a standard treatment of an interacting electron system without assuming any quasi-particle.

This book will be easily understood by undergraduate students. Knowledge of quantum field theory is needed to study Chapter 9. (Imprint: Nova)

Binding

Clear

Add to Wishlist

ISBN: N/A Categories: Classical and Quantum Mechanics, Physics and Astronomy, Physics Research and Technology, Quantum Theory Tags: 9781634844628, 9781634849388, quantum theory

Table of Contents
Publish with Us

Table of Contents

Preface

Chapter 1. Formulation of the Problem

Chapter 2. Integer Quantum Hall Effect

Chapter 3. Coulomb Energy in the FQH States

Chapter 4. Binding Energy of Electron Pair

Chapter 5. Valle, Flat and Peak Structures in the Energy Spectrum

Chapter 6. Effect of Higher Order Perturbation and Contribution from Upper Landau Levels

Chapter 7. Plateaus of Quantum Hall Resistance

Chapter 8. Accuracy of Hall Resistance Confinement

Chapter 9. Spin Polarization in the Fractional Quantum Hall States

Chapter 10. FQHE under a Tilted Magnetic Field

Chapter 11. Further Experiments

Chapter 12. Discussions on Traditional Theories

Chapter 13. Summary

References

Appendix

Index

References

[1] von Klitzing, K; Dorda, G; Pepper, M. Phys. Rev. Lett., 45 (1980), 494.
[2] von Klitzing, K. The quantized Hall effect, Rev. Mod. Phys., 58, no. 3, 519, (1986).
[3] von Klitzing, K. Nobel lectures, Physics, 1981-1990, (World Scientific), pp 317.
[4] Tsui, DC; Gossard, AC. Appl. Phys. Lett., 37 (1981), 550.
[5] Tsui, DC; Stormer, HL; Gossard, AC. Phys. Rev., B 25 (1982), 1405.
[6] Tsui, DC; Stormer, HL; Gossard, AC. Phys. Rev. Lett., 48 (1982), 1559.
[7] Willet, R; Eisenstein, JP; Stormer, HL; Tsui, DC; Gossard, AC; English, JH. Phys. Rev. Lett., 59, (1987), 1776.
[8] Eisenstein, JP; Stormer, HL. Science, 248, (1990), 1461.
[9] Stormer, HL. Nobel lectures, Physics 1996-2000, (World Scientific), pp 295-325.
[10] Novoselov, KS; Jiang, Z; Zhang, Y; Morozov, SV; Stormer, HL; Zeitler, U; Maan, JC; Boebinger, GS; Kim, P; Geim, AK. Science Express on 15 February 2007. Vol. 315. no. 5817, p. 1379. DOI: 10.1126/science.1137201.
[11] Woszczyna, M; Friedemann, M; Götz, M; Pesel, E; Pierz, K; Weimann, T; Ahlers, FJ. “Precision quantization of Hall resistance in transferred grapheme” Appl. Phys. Lett., 100, 164106 (2012); http://dx.doi.org/10.1063/1.4704190.
[12] Banghert, E; von Klitzing, K; Landwehr, G. in Proceeding of the 12-th ICPS, (1974).
[13] Broido, DA; Sham, LJ. Phys. Rev., B31, 888, (1985).
[14] Raphael, Wagner; Master, thesis. University of Basel (2009).
[15] Ando, T; Matsumoto, Y; Uemura, Y. J. Phys. Soc. Jpn., 39 (2), 279-288, (1975).
[16] Jeckelmann, B; Jeanneret, B. The Quantum Hall Effect as an Electrical Resistance Standard; Seminaire Poincare, 2 (2004), 39 – 51.
[17] Büttiker, M. Phys. Rev. B, 38, (1988), 9375.
[18] Kawano, Y; Komiyama, S. Spatial distribution of nonequilibrium electrons in quantum Hall devices: Imaging via cyclotron emission Phys. Rev., B68, 085328-1-5, (2003).
[19] Laughlin, RB. Phys. Rev. B, 27, (1983), 3383.
[20] Laughlin, RB. Phys. Rev. Lett., 50, (1983), 1395.
[21] Haldane, FDM. Phys. Rev. Lett., 51, (1983), 605.
[22] Halperin, BI. Phys. Rev. Lett., 52, (1984), 1583.
[23] Girvin, SM. Phys. Rev. B, 29, (1984), 6012.
[24] Jain, JK. Phys. Rev. Lett., 63, (1989), 199; Phys. Rev. B 41 (1990), 7653.
[25] Tao, R; Thouless, DJ. Phys. Rev. B, 28, (1983), 1142.
[26] Tao, R. Phys. Rev. B, 29, (1984), 636.
[27] Shosuke Sasaki, Physica B, vol. 281-282, pp. 838–839, 2000.
[28] Shosuke Sasaki, Proceedings of the 25th Intl. Conf. on the Physics of Semiconductors, Springer (2000), pp 925-926.
[29] Shosuke Sasaki. Surface Science: New Research, Nova Science Publishers, Chapter 4 (2005) 103-161.
[30] Shosuke Sasaki. Journal of Physics, vol. 100, Article ID 042021, 4 pages, 2008.
[31] Shosuke Sasaki. Advances in Condensed Matter Physics, vol. 2012, Article ID 281371, 13 pages. doi:10.1155/2012/281371.
[32] Shosuke Sasaki. http://arxiv.org/abs/0708.1541. (2007).
[33] Shosuke Sasaki. http://arxiv.org/abs/cond-mat/0703360. (2007).
[34] Pan, W; Stormer, HL; Tsui, DC; Pfeiffer, LN; Baldwin, KW; West, KW. Phys. Rev. Lett., 88 (2002) 176802.
[35] Pan, W; Stormer, HL; Tsui, DC; Pfeiffer, LN; Baldwin, KW; West, KW. arXiv:cond-mat/0303429v1 [cond-mat.mes-hall] 20 Mar (2003).
[36] Wojs, A; Quinn, JJ. Phys. Rev.B, 61, (2000), 2846.
[37] Wojs, A; Yi, KS; Quinn, JJ. Phys. Rev. B, 69, (2004), 205322.
[38] Smet, JH. Nature, (London) 422, 391.
[39] Peterson, MR; Jain, JK. cond-mat/ 0309291 (2003).
[40] Pashitskii, EA. Low Temp. Phys., 31, 171.
[41] Pan, W; Stormer, HL; Tsui, DC; Pfeiffer, LN; Baldwin, KW; West, KW. arXiv:cond-mat/0303428v1 20 Mar (2003).
[42] Pan, W; Du, RR; Stormer, HL; Tsui, DC; Pfeiffer, LN; Baldwin, KW; West, KW. Phys. Rev. Lett., 83, 820–823, (1999).
[43] Lilly, MP; Cooper, KB; Eisenstein, JP; Pfeiffer, LN; West, KW. Phys. Rev. Lett., 82, 394–397 (1999), 83, 824-827, (1999).
[44] Eisenstein, JP; Cooper, KB; Pfeiffer, LN; West, KW. Phys. Rev. Lett., 88, 076801 (2002)
[45] Dean, CR; Piot, BA; Hayden, P; Das Sarma, S; Gervais, G; Pfeiffer, LN; West, KW. Phys. Rev. Lett., 100, 146803, (2008).
[46] Xia, JS; Pan, W; Vicente, CL; Adams, ED; Sullivan, NS; Stormer, HL; Tsui, DC; Pfeiffer, LN; Baldwin, KW; West, KW. Phys. Rev. Lett., 93, 176809, (2004).
[47] Csáthy, GA; Xia, JS; Vicente, CL; Adams, ED; Sullivan, NS; Stormer, HL; Tsui, DC; Pfeiffer, LN; West, KW. Phys. Rev. Lett., 94, 146801, (2005).
[48] Pan, W; Xia, JS; Stormer, HL; Tsui, DC; Vicente, C; Adams, ED; Sullivan, NS; Pfeiffer, LN; Baldwin, KW; West, KW. Phys. Rev., B 77, 075307, (2008)
[49] Choi, HC; Kang, W; Das Sarma, S; Pfeiffer, LN; West, KW. Phys. Rev. B, 77, 081301(R) (2008).
[50] Stormer, HL; Tsui, DC; Gossard, AC. The fractional quantum Hall effect Rev. Mod. Phys., Vol. 71, S298-S305, (1999).
[51] Aleiner, LL; Glazman, LI. Phys. Rev. Phys. Rev., B 52, 11296–11312, (1995).
[52] Koulakov, AA; Fogler, MM; Shklovskii, BI. Phys. Rev. Lett., 76, 499–502, (1996).
[53] Moessner Chalker, R; JT. Phys. Rev., B 54, 5006–5015, (1996).
[54] Rezayi, EH; Haldane, FDM. Kun Yang, Phys. Rev. Lett., 83, 1219–1222, (1999).
[55] Haldane, FDM; Rezayi, EH. Phys. Rev. Lett., 60, 956–959, (1988).
[56] Moore, G; Read, N. Nucl. Phys., B 360, 362–396, (1991).
[57] Read, N. Physica B: Condensed Matter, 298, 121–128, (2001).
[58] Bardeen, J; Cooper, LN; Schrieffer, JR. Phys. Rev., 106 162 (1957); 108, 1175, (1957).
[59] Greiter, M; Wen, XG; Wilczek, F. Phys. Rev. Lett., 66, 3205–3208, (1991), Nucl. Phys. B 374, 567–614, (1992).
[60] Morf, RH. Phys. Rev. Lett., 80, 1505–1508, (1998).
[61] Rezayi, EH; Haldane, FDM. Phys. Rev. Lett., 84, 4685–4688, (2000).
[62] Shosuke Sasaki. ISRN Condensed Matter Physics Volume 2014 (2014), Article ID 468130, 16 pages, doi: 10.1155/2014/468130.
[63] Dean, CR; Young, AF; Cadden-Zimansky, P; Wang, L; Ren, H; Watanabe, K; Taniguchi, T; Kim, P; Hone, J; Shepard, KL. Nature Physics, 7, 693–696, (2011).
[64] Dong-Keun, K; Vladimir, I. Fal’ko & Alberto F. Morpurgo, arXiv:1305.4761v1 [cond-mat.mes-hall] (2013).
[65] Kirill, I; Bolotin, Fereshte Ghahari; Michael, D; Shulman, Horst, L. Stormer & Philip Kim, Nature 462, 196-199 (12 November 2009) | doi:10.1038/nature08582.
[66] Luhman, DR; Pan, W; Tsui, DC; Pfeiffer, LN; Baldwin, KW; West, KW. Phys. Rev. Lett., 101, 266804 [4 pages] (2008).
[67] Shabani, J; Yang Liu, M; Shayegan, LN; Pfeiffer, KW; West Baldwin, KW. arXiv:1306.5290v1 [cond-mat.mes-hall] (2013).
[68] Shabani, J; Gokmen, T; Shayegan, M. Phys. Rev. Lett., 103, 046805 [4 pages] (2009).
[69] Shosuke Sasaki, Journal of Modern Physics, 2015, 6, 584-600, http://dx.doi.org/10. 4236/jmp.2015.65064.
[70] Shosuke Sasaki. Journal of Modern Physics, 2015, 6, 955-971, doi: 10.4236/ jmp.2015.67100.
[71] Ahlers, FJ; Pesel, E; Pierz, K; Warnecke, P; Wegscheider, W. Conf. on Precision Electromagnetic Measurements Digest, (2008) 16-17. DOI 10.1109/CPEM. 2008. 4574630.
[72] Editors, RE; Prange, Girvin, SM. The Quantum Hall Effect (Springer-Verlag NewYork 1987).
[73] Chang, AM; Berglund, P; Tsui, DC; Stormer, HL; Hwang, JCM. Phys. Rev. Lett., 53(1984) 997.
[74] Ebert, G; von Klitzing, K; Maan, JC; Remenyi, G; Probst, C; Weimann, G; Schlapp, W. J. Phys., C, 17(1984) L 775.
[75] Clark, RG; Nicholas, RJ; Usher, A; Foxon, CT; Harris, JJ. Surface Science, 170(1986) 141.
[76] Shosuke Sasaki. in preparation.
[77] Kukushkin, IV; von Klitzing, K; Eberl, K. Phys. Rev. Lett., 82, (1999) 3665.
[78] Shosuke Sasaki. Surface Science, 532–535(2003) 567.
[79] Shosuke Sasaki. Proc. of Int. Conf. on ECOSS-22, Prague, Czech (2003), 16880.
[80] Shosuke Sasaki. in Proceedings of the 22nd European Conference on Surface Science, vol. 566–568, pp. 1040–1046, September 2004.,
[81] Shosuke Sasaki. Journal of Modern Physics, 2015, 6, 794-810. doi: 10.4236/ jmp. 2015.66085.
[82] Shosuke Sasaki. ISRN Condensed Matter Physics, Volume 2013, Article ID 489519, 19 pages. http://dx.doi.org/10.1155/2013/489519.
[83] Nicholas, RJ; Haug, RJ; Klitzing, KV. Weimann, G. Phys. Rev., B 37, 1294 (1988).
[84] Smith, AP; MacDonald, AH; Gumbs, G. Phys. Rev., B 45, 8829 (1992).
[85] Shosuke Sasaki. Phys. Rev. E, 53 (1996) 168.
[86] Peierls, RE. Quantum Theory of Solids (Oxford University, London, 1955).
[87] Bay, JW; Hart, Jr. HR; Interrante, LV; Jacobs, IS; Kasper, JS; Watkins, GD; Wee, SH; Bonner, JC. Phys. Rev. Lett., 35, (1975) 744.
[88] Jacobs, IS; Bay, JW; Hart, HR; Jr., L. V. Interrante, J. S. Kasper, G. D. Watkins, D. E. Prober, and J. C. Bonner, Phys. Rev., B14, (1976), 3036.
[89] Huizinga, S; Kommandeur, J; Sawatzky, GA; Thole, BT; Kopenga, K; de Jonge, WJM; Roos, D. Phys. Rev. B, 19, (1979), 4723.
[90] Hase, M; Terasaki, I; Uchinokura, K. Phys. Rev. Lett., 70, (1993), 3651.
[91] Luhman, DR; Pan, W; Tsui, DC; Pfeiffer, LN; Baldwin, KW; West, KW. Phys. Rev. Lett., 101, 266804 (2008) Phys. Rev. Lett. 101, 266804 (2008) [4 pages] http:// arxiv. org/pdf/0810.2274.pdf.
[92] Shosuke Sasaki. Journal of Physics, vol. 100, Article ID 042022, 4pages, 2008.
[93] Shosuke Sasaki. http://arxiv.org/abs/0803.0615.
[94] Shosuke Sasaki. Journal of Surface Science and Nanotechnology, vol. 8, pp. 121–124, 2010
[95] Shosuke Sasaki. http://arxiv.org/abs/0807.0288.
[96] Shosuke Sasaki. Journal of Modern Physics, 2013, 4, 1-7. http://dx.doi.org/10. 4236/jmp.2013.49A001.
[97] Zhang, SC; Hansson, TH; Kivelson, S. Phys. Rev. Lett., 62, (1989), 980.
[98] Kamilla, RK; Wu, XG; Jain, JK. Phys. Rev. Lett., 76, (1996), 1332.
[99] Blok, B; Wen, XG. Phys. Rev. B, 42, (1990), 8133.
[100] Jain, JK. A note contrasting two microscopic theories of the fractional quantum Hall effect, Indian J. Phys., 2014 88 (2014) 915-929.

Publish with Nova Science Publishers

We publish over 800 titles annually by leading researchers from around the world. Submit a Book Proposal Now!