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| {{Condensed matter physics|expanded=Electronic phases}}
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| '''Mott insulators''' are a class of materials that should [[electrical conductivity|conduct]] [[electricity]] under conventional [[electronic band structure|band theories]], but are [[electrical insulator|insulator]]s when measured (particularly at low temperatures). This effect is due to [[electron]]–electron interactions, which are not considered in conventional band theory.
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| The bandgap in a Mott insulator exists between bands of like character, such as 3d character, whereas the bandgap in [[charge transfer insulators]] exists between anion and cation states (see [http://wyvern.phys.s.u-tokyo.ac.jp/f/lecture/srrc/SRRC_Mott.pdf lecture slides ]), such as between O 2p and Ni 3d bands in [[Nickel(II)_oxide|NiO]].
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| <ref>{{ cite journal | journal = Physical Review Letters | volume = 62 | year = 1987 |pages = 221–224 | title = Character of Holes in Li<sub>x</sub>Ni<sub>1-x</sub>O<sub>2</sub> | author = P. Kuiper, G. Gruizinga, J. Ghijsen, G.A. Sawatzky, H. Verweij | pmid = 10039954 | issue = 2 | doi=10.1103/PhysRevLett.62.221|bibcode = 1989PhRvL..62..221K }}
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| </ref>
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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 predicted to be conductors by [[Electronic band structure|band theory]] (because they have an odd number of electrons per unit cell) are insulators.<ref>{{cite journal | doi=10.1088/0959-5309/49/4S/307 | 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 | volume=49 | issue=4S | pages=59 | year=1937}}</ref> [[Nevill Mott]] and [[Rudolf Peierls]] then (also in 1937) predicted that this anomaly can be explained by including interactions between electrons.<ref>{{cite journal | doi=10.1088/0959-5309/49/4S/308 | last=Mott | first=N. F. | coauthors=Peierls, R. | title=Discussion of the paper by de Boer and Verwey | journal=Proceedings of the Physical Society | volume=49 | issue=4S | pages=72 | year=1937 |bibcode = 1937PPS....49...72M }}</ref>
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| In 1949, in particular, Mott proposed a model for [[nickel(II) oxide|NiO]] as an insulator, where conduction is based on the formula<ref>{{cite journal | doi=10.1088/0370-1298/62/7/303 | 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 | series = Series A | volume=62 | issue=7 | pages=416 | year=1949 |bibcode = 1949PPSA...62..416M }}</ref>
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| :(Ni<sup>2+</sup>O<sup>2−</sup>)<sub>2</sub> → 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]]. The crossover from a metal to a Mott insulator as ''U'' is increased can be predicted within the so-called [[Dynamical Mean Field Theory]].
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| ==Mottness==
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| ''Mottism'' denotes the additional ingredient, aside from [[antiferromagnetic]] ordering, which is necessary to fully describe a Mott Insulator. In other words, we might write
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| :''antiferromagnetic order + mottism = Mott insulator''
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| Thus, mottism accounts for all of the properties of Mott insulators that cannot be attributed simply to antiferromagnetism.
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| There are a number of properties of Mott insulators, derived from both experimental and theoretical observations, which cannot be attributed to antiferromagnetic ordering and thus constitute mottism. These properties include
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| *Spectral weight transfer on the Mott scale <ref name="Phillips" /><ref name="Meinders" />
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| *Vanishing of the single particle [[Green's function (many-body theory)|Green function]] along a connected surface in momentum space in the [[Brillouin zone|first Brillouin zone]] <ref name="Stanescu" />
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| *''Two'' sign changes of the [[Hall effect|Hall coefficient]] as electron [[doping (semiconductors)|doping]] goes from <math>n=0</math> to <math>n=2</math> ([[Electronic band structure|band insulators]] have only one sign change at <math>n=1</math>)
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| *The presence of a charge <math>2e</math> (with <math>e<0</math> the charge of an electron) boson at low energies <ref name="Leigh" /><ref name="Choy" />
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| *A pseudogap away from half-filling (<math>n=1</math>) <ref name="Stanescu2" />
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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 | pmid=18756248 | issue=7208 |bibcode = 2008Natur.454.1072K }}</ref>
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| This kind of [[Insulator (electricity)|insulator]] can become a [[Electrical conductor|conductor]] if an external [[voltage]] is applied across the material. The effect is known as a [[Mott transition]] and can be used to build smaller [[field-effect transistor]]s, [[switch]]es and memory devices than possible with conventional materials.<ref>Newns, Dennis (2000). "Junction mott transition field effect transistor (JMTFET) and switch for logic and memory applications". http://www.google.com/patents/US6121642</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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| *[[Mott Criterion]]
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| *[[Dynamical Mean Field Theory]]
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| *[[Variable range hopping|(Mott) Variable range hopping]]
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| ==References==
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| * R.B. Laughlin, "A Critique of Two Metals," http://arxiv.org/abs/cond-mat/9709195
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| * Philip W. Anderson and G. Baskaran, "A Critique of 'A Critique of Two Metals,'" http://arxiv.org/abs/cond-mat/9711197
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| <references>
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| <ref name="Phillips">Philip Phillips, "Mottness," http://arxiv.org/abs/cond-mat/0702348</ref>
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| <ref name="Meinders">M.B.J. Meinders, H. Eskes, and G.A. Sawatzky, Phys. Rev. B '''48''' 3916 (1993)</ref>
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| <ref name="Stanescu">Tudor D. Stanescu, Philip Phillips, and Ting-Pong Choy, "Theory of the Luttinger surface in doped Mott insulators," Phys. Rev. B '''75''' 104503 (2007)</ref>
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| <ref name="Leigh">Robert G. Leigh, Philip Phillips, and Ting-Pong Choy, "Hidden Charge 2e Boson in Doped Mott Insulators: Field Theory of Mottness," to be published in Phys. Rev. Lett., http://arxiv.org/abs/cond-mat/0612130v3 (2007)</ref>
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| <ref name="Choy">Ting-Pong Choy, Robert G. Leigh, Philip Phillips, and Philip D. Powell, "Exact Integration of the High Energy Scale in Doped Mott Insulators," http://arxiv.org/abs/0707.1554</ref>
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| <ref name="Stanescu2">Tudor D. Stanescu and Philip Phillips, "Pseudogap in Doped Mott Insulators is the Near-neighbour Analogue of the Mott Gap," Phys. Rev. Lett. 91, 017002 (2003), http://arxiv.org/abs/cond-mat/0209118</ref>
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| </references>
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| {{reflist}}
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| [[Category:Quantum phases]]
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The writer is known by the name of Figures Lint. What I love performing is taking part in baseball but I haven't made a dime with it. Minnesota has usually been his house but his wife desires them to transfer. I am a meter reader but I plan on altering it.
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