Mott insulator: Difference between revisions
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{{Mergefrom|Mottness|date=May 2008}} |
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'''Mott insulators''' are a class of materials that are expected to [[electrical conductivity|conduct]] [[electricity]] under conventional [[electronic band structure|band theories]], but which in fact turn out to be [[electrical insulator|insulator]]s when measured (particularly at low temperatures). This effect is due to [[electron]]-electron interactions which are not considered in the formulation of conventional band theory. |
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==History== |
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Although the band theory of solids had been very successful in describing various electrical properties of materials, in 1937 [[Jan Hendrik de Boer]] and [[Evert Johannes Willem Verwey]] pointed out that a variety of [[transition metal oxide]]s that are predicted to be conductors by band theory (because they have an odd number of electrons per unit cell) are in fact insulators.<ref>{{cite journal | last=de Boer | first=J. H. | coauthors=Verwey, E. J. W. | title=Semi-conductors with partially and with completely filled <sub>3</sub>''d''-lattice bands | journal=Proceedings of the Physical Society of London | volume=49 | pages=59 | date=1937}}</ref> [[Nevill Mott]] and [[R. Peierls]] then (also in 1937) predicted that this anomaly can be explained by including interactions between electrons.<ref>{{cite journal | last=Mott | first=N. F. | coauthors=Peierls, R. | title=Discussion of the paper by de Boer and Verwey | journal=Proceedings of the Physical Society of London | volume=49 | pages=72 | date=1937 }}</ref> |
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In 1949, in particular, Mott proposed a model for [[nickel(II) oxide|NiO]] as an insulator, in which conduction can be understood based on the formula<ref>{{cite journal | last=Mott | first=N. F. | title=The basis of the electron theory of metals, with special reference to the transition metals | journal=Proceedings of the Physical Society of London Series A | volume=62 | pages=416 | date=1949 }}</ref> |
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:(Ni<sup>2+</sup>O<sup>2−</sup>)<sub>2</sub> <math>\rightarrow</math> Ni<sup>3+</sup>O<sup>2−</sup> + Ni<sup>1+</sup>O<sup>2−</sup>. |
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In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the [[Coulomb potential]] ''U'' between 3''d'' electrons and the transfer integral ''t'' of 3''d'' electrons between neighboring atoms (the transfer integral is a part of the [[Tight binding (physics)|tight-binding]] approximation). The total [[energy gap]] is then |
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:''E''<sub>gap</sub> = ''U'' − 2''zt'', |
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where ''z'' is the number of nearest-neighbor atoms. |
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In general, Mott insulators occur when the repulsive Coulomb potential ''U'' is large enough to create an energy gap. One of the simplest theories of Mott insulators is the 1963 [[Hubbard model]]. |
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==Applications== |
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Mott insulators are of growing interest in advanced [[physics]] research, and are not yet fully understood. They have applications in [[thin-film]] [[magnetic]] [[heterostructure]]s and [[high-temperature superconductivity]], for example.<ref>{{cite journal | last=Kohsaka | first = Y. | coauthors=Taylor, C.; Wahl, P.; ''et al.'' | title=How Cooper pairs vanish approaching the Mott insulator in Bi<sub>2</sub>Sr<sub>2</sub>CaCu<sub>2</sub>O<sub>8+''δ''</sub> | journal=Nature | volume=454 |pages=1072–1078 | date=August 28, 2008 | doi=10.1038/nature07243 }}</ref> |
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==See also== |
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*[[Hubbard model]] |
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*[[Tight binding (physics)|Tight-binding approximation]] |
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*[[Electronic band structure]] |
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*[[Mottness]] |
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==External links== |
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*[http://wyvern.phys.s.u-tokyo.ac.jp/f/lecture/srrc/SRRC_Mott.pdf lecture slides ] |
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==References== |
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{{reflist}} |
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Revision as of 21:43, 20 October 2008
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