The quantum Hall effect and its contexts
DOI:
https://doi.org/10.1590/S1678-31662013000100007Keywords:
Classical Hall effect, Quantum Hall effect, Quantum topologyAbstract
In this paper we address several conceptual and historical aspects of the quantum Hall effect. We argue that this effect offers a variety of perspectives for philosophical reflection, from the generation of theoretical entities to the epistemology of experimentation. The exposition attempts to maintain a certain sensitivity to the historical dynamics around the issue, considering at the same time its metrological implications for specific quantum areas. Given the vast scientific literature on the subject, a cut is made in order to rescue some meaningful profiles of the phenomena associated with this effect.Downloads
References
Ando, T. Theory of quantum transport in a two-dimensional electron system under magnetic fields. Journal of Physics Society, 37, p. 622-30, 1974.
Anderson, P. W. More is different. Science, 177, 4047, p. 393-6, 1972.
Anderson, P. W. Physics: the opening to complexity. Proceeding National Academy of Science USA, 92, p. 6653-4, 1995.
Arovas, D. et al. Fractional statistics and the quantum Hall effect. Physics Review Letters, 53, p. 722-3, 1984.
Avron, E. et al. A topological look at the quantum Hall effect. Physics Today, 56, 8, p. 38-42, 2003.
Bms News. Search and discovery: quantized Hall effect yields e2/h to a part per million. Physics Today, 19, p. 17-19, 1981.
Brüne C. et al. Spin polarization of the quantum spin Hall edge states. Nature Physics, 8, p. 485-90, 2012.
Chern, S. S. & Simons, J. Characteristic forms and geometric invariants. Annals of Mathematics, 99, 1, p. 48–69, 1974.
Dolev, M. et al. Observation of a quarter of an electron charge at the v = 5/2 quantum Hall state. Nature, 452, p. 829-34, 2008.
Dyakonov, M. I. Twenty years since the discovery of the fractional quantum Hall effect: current state of the theory. In: Vagner, I. D.; Wyder, P. & Maniv, T. (Ed.). Recent trends in theory of physical phenomena in high magnetic fields. Berlin: Springer, 2003. p. 75-88.
Ezawa, Z. F. Quantum Hall effects. 2 ed. Singapore: World Scientific, 2008.
Greiter, M., Quantum Hall quarks. Physica, E 1, p. 1-6, 1997.
Girvin, S. M. The quantum Hall effect: novel excitations and broken symmetries. Bloomington: Course 2, Dept. of Physics, Indiana University, 1999.
Goldhaber, A. S. Fractional charge definitions and conditions. Journal of Mathematical Physics, 44, 8, p. 3607-19, 2003.
Hall, E. H. On a new action of the magnet on electric currents. American Journal of Mathematics, 2, p. 287-92, 1879.
Hasan, M. & Kane, C. L. Topological insulators. Review of Modern Physics, 82, 4, p. 3045. 2010.
Jackson, J. D. Electrodinámica clásica. Madrid: Alhambra, 1980.
Jain, J. K. The composite fermion: a quantum particle and its quantum fluids. Physics Today, 53, 4, p. 39-45, 2000.
Laughlin R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Physics Review Letters, 50, 18, p. 1395-8, 1983.
Laughlin R. B. Nobel Lecture: Fractional quantization. Review of Modern Physics, 71, 4, p. 863-74, 1999.
Laughlin R. B. A different universe. Reinventing physics from the bottom down. Cambridge: Basic Books, 2005.
Maxwell, J. C. A treatise on electricity and magnetism. Oxford: Clarendon Press, 1873. 2 v.
Moore, J. The birth of topological insulators. Nature, 464, p. 194-8, 2010.
Mourik, V. et al. Signatures of Majorana Fermions in hybrid superconductor-semiconductor nanowire devices. Science, 336, 6084, p. 1003-7, 2012.
Murthy G. & Shankar, R. Hamiltonian theories of the fractional quantum Hall effect. Review of Modern Physics 75, 4, p. 1101-58, 2003.
Nayak, C. et al. Non-abelian anyons and topological quantum computation. Review of Modern Physics, 80, 3, p. 1083-159, 2008.
Panofsky, W. & Phillips, M. Classical electricity and magnetism. Nova York: Dover, 1962.
Qi X. L. & Zhang S. C. Topological insulators and superconductors. Review Modern Physics, 83, p. 1057-110, 2011.
Rodgers, P. New paths to the ultimate theory. Physics World, 14, 12, p. 5, 2001.
Stern, A. Anyons and the quantum Hall effect. A pedagogical review. Annals of Physics, 323, p. 204-49, 2008.
Stern, A. Non-abelian states of matter. Nature, 464, p. 187-93, 2010.
Stone, M. (Ed.). Quantum Hall effect. Singapore: World Scientific, 1992.
Stormer, H. L. Nobel lecture: the fractional quantum Hall effect. Review Modern Physics, 71, 4, p. 875-89, 1999.
Tsui, D. et al. Two-dimensional magnetotransport in the extreme quantum limit. Physics Review Letters, 48, 22, p. 1559, 1982.
Vagner, I. D.; Wyder, P. & Maniv, T. (Ed.). Recent trends in theory of physical phenomena in high magnetic fields. Berlin: Springer, 2003.
Von Klitzing, K. 25 years of quantum hall effect (QHE). A personal view on the discovery, physics and applications of this quantum effect. Séminaire Poincaré, 2, p. 1-16, 2004.
Von Klitzing, K. et. al. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Physics Review Letters, 45, 6, p. 494, 1980.
Weinberg, S. Dreams of a final theory. Nova York: Pantheon Books, 1993.
Wilczek, F. (Ed.). Fractional statistics and Anyon superconductivity. Singapore: World Scientific, 1990.
Wilczek, F. Some basic aspects of fractional quantum numbers. Fantastic Realities, 49, p. 359-83. 2006a.
Wilczek, F. From electronics to anyonics. Physics World, 19, 1, p. 22-3, 2006b.
Zhang S. & Hu, J. A four dimensional generalization of the quantum Hall effect. Science, 294, p. 823, 2001.
Downloads
Published
Issue
Section
License
Copyright (c) 2013 Scientiae Studia
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
A revista detém os direitos autorais de todos os textos nela publicados. Os autores estão autorizados a republicar seus textos mediante menção da publicação anterior na revista. A revista adota a Licença Creative Commons Attribution-NonCommercial-ShareAlike 4.
