View source for Physics:Mott insulator

 {{Short description|Materials classically predicted to be conductors, that are actually insulators
}}
{{Condensed matter physics|expanded=Electronic phases}}
'''Mott insulators''' are a class of materials that are expected to [[Physics:Electrical conductivity|conduct electricity]] according to conventional [[Physics:Electronic band structure|band theories]], but turn out to be insulators (particularly at low temperatures). These insulators fail to be correctly described by band theories of solids due to their strong [[Physics:Electron|electron]]–electron interactions, which are not considered in conventional band theory. A '''Mott transition''' is a transition from a metal to an insulator, driven by the strong interactions between electrons.<ref name=":0">{{Cite book|first=Patrik|last=Fazekas|url=http://worldcat.org/oclc/633481726|title=Lecture notes on electron correlation and magnetism|date=2008|publisher=World Scientific|isbn=978-981-02-2474-5|pages=147–150|oclc=633481726}}</ref> One of the simplest models that can capture Mott transition is the [[Physics:Hubbard model|Hubbard model]].

The band gap in a Mott insulator exists between bands of like character, such as 3d electron bands, whereas the band gap in [[Physics:Charge-transfer insulators|charge-transfer insulators]] exists between anion and cation states.

==History==
Although the [[Physics:Electronic band structure|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 oxides predicted to be conductors by [[Physics:Electronic band structure|band theory]] are insulators.<ref>{{cite journal | doi=10.1088/0959-5309/49/4S/307 | last=de Boer | first=J. H. |author2=Verwey, E. J. W. | title=Semi-conductors with partially and with completely filled 3''d''-lattice bands | journal=Proceedings of the Physical Society | volume=49 | issue=4S | pages=59 | year=1937| bibcode=1937PPS....49...59B }}</ref> With an odd number of electrons per unit cell, the [[Physics:Valence and conduction bands|valence band]] is only partially filled, so the [[Physics:Fermi level|Fermi level]] lies within the band. From the [[Physics:Electronic band structure|band theory]], this implies that such a material has to be a metal. This conclusion fails for several cases, e.g. [[Chemistry:Cobalt(II) oxide|CoO]], one of the strongest insulators known.<ref name=":0" />

Nevill Mott and [[Biography:Rudolf Peierls|Rudolf Peierls]] also in 1937 predicted the failing of band theory can be explained by including interactions between electrons.<ref>{{cite journal | doi=10.1088/0959-5309/49/4S/308 | last=Mott | first=N. F. |author2=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>

In 1949, in particular, Mott proposed a model for [[Chemistry: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=416–422 | year=1949 |bibcode = 1949PPSA...62..416M }}</ref>

:(Ni<sup>2+</sup>O<sup>2&minus;</sup>)<sub>2</sub> → Ni<sup>3+</sup>O<sup>2&minus;</sup> + Ni<sup>1+</sup>O<sup>2&minus;</sup>.

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 [[Physics:Tight binding|tight binding]] approximation). The total [[Physics:Energy gap|energy gap]] is then

:''E''<sub>gap</sub> = ''U'' &minus; 2''zt'',

where ''z'' is the number of nearest-neighbor atoms.

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 [[Physics:Hubbard model|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.

==Mottness==
''Mottism'' denotes the additional ingredient, aside from [[Physics:Antiferromagnetic|antiferromagnetic]] ordering, which is necessary to fully describe a Mott insulator. In other words, we might write: ''antiferromagnetic order + mottism = Mott insulator''.

Thus, mottism accounts for all of the properties of Mott insulators that cannot be attributed simply to antiferromagnetism.

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:

*Spectral weight transfer on the Mott scale<ref name="Phillips" /><ref name="Meinders" />
*Vanishing of the single particle [[Physics:Green's function (many-body theory)|Green function]] along a connected surface in momentum space in the [[Physics:Brillouin zone|first Brillouin zone]]<ref name="Stanescu" />
*''Two'' sign changes of the [[Physics:Hall effect|Hall coefficient]] as electron doping goes from <math>n=0</math> to <math>n=2</math> ([[Physics:Electronic band structure|band insulators]] have only one sign change at <math>n=1</math>)
*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" />
*A pseudogap away from half-filling (<math>n=1</math>)<ref name="Stanescu2" />

==Applications==

Mott insulators are of growing interest in advanced [[Physics:Physics|physics]] research, and are not yet fully understood. They have applications in thin-film [[Physics:Magnetic|magnetic]] heterostructures and the strong correlated phenomena in [[Physics:High-temperature superconductivity|high-temperature superconductivity]], for example.<ref>{{cite journal |  last=Kohsaka | first = Y. |author2=Taylor, C. |author3=Wahl, P. | s2cid = 205214473 | 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+''&delta;''</sub> | journal=Nature | volume=454 |pages=1072&ndash;1078 | date=August 28, 2008 | doi=10.1038/nature07243 |  pmid=18756248 |  issue=7208 |bibcode = 2008Natur.454.1072K |display-authors=0|arxiv=0808.3816 }}</ref><ref>{{Cite journal|last1=Markiewicz|first1=R. S.|last2=Hasan|first2=M. Z.|last3=Bansil|first3=A.|date=2008-03-25|title=Acoustic plasmons and doping evolution of Mott physics in resonant inelastic x-ray scattering from cuprate superconductors|journal=Physical Review B|volume=77|issue=9|pages=094518|doi=10.1103/PhysRevB.77.094518|bibcode=2008PhRvB..77i4518M}}</ref><ref>{{Cite journal|last1=Hasan|first1=M. Z.|last2=Isaacs|first2=E. D.|last3=Shen|first3=Z.-X.|last4=Miller|first4=L. L.|last5=Tsutsui|first5=K.|last6=Tohyama|first6=T.|last7=Maekawa|first7=S.|s2cid=2581764|date=2000-06-09|title=Electronic Structure of Mott Insulators Studied by Inelastic X-ray Scattering|url=https://www.science.org/doi/10.1126/science.288.5472.1811|journal=Science|language=en|volume=288|issue=5472|pages=1811–1814|doi=10.1126/science.288.5472.1811|issn=0036-8075|pmid=10846160|arxiv=cond-mat/0102489|bibcode=2000Sci...288.1811H}}</ref><ref>{{Cite journal|last1=Hasan|first1=M. Z.|last2=Montano|first2=P. A.|last3=Isaacs|first3=E. D.|last4=Shen|first4=Z.-X.|last5=Eisaki|first5=H.|last6=Sinha|first6=S. K.|last7=Islam|first7=Z.|last8=Motoyama|first8=N.|last9=Uchida|first9=S.|s2cid=30809135|date=2002-04-16|title=Momentum-Resolved Charge Excitations in a Prototype One-Dimensional Mott Insulator|journal=Physical Review Letters|volume=88|issue=17|pages=177403|doi=10.1103/PhysRevLett.88.177403|pmid=12005784|arxiv=cond-mat/0102485|bibcode=2002PhRvL..88q7403H}}</ref>

This kind of [[Physics:Insulator (electricity)|insulator]] can become a [[Physics:Electrical conductor|conductor]] by changing some parameters, which may be composition, pressure, strain, voltage, or magnetic field. The effect is known as a [[Physics:Mott transition|Mott transition]] and can be used to build smaller [[Engineering:Field-effect transistor|field-effect transistor]]s, [[Engineering:Switch|switch]]es and memory devices than possible with conventional materials.<ref>{{cite patent |inventor=Newns, Dennis |pubdate=2000 |title=Junction mott transition field effect transistor (JMTFET) and switch for logic and memory applications |status=patent |country=US |number=6121642}}</ref><ref>{{Cite journal|title = Correlated Electron Materials and Field Effect Transistors for Logic: A Review|journal = Critical Reviews in Solid State and Materials Sciences|date = 2013-01-01|issn = 1040-8436|pages = 286–317|volume = 38|issue = 4|doi = 10.1080/10408436.2012.719131|first1 = You|last1 = Zhou|first2 = Shriram|last2 = Ramanathan|s2cid = 93921400|arxiv = 1212.2684 |bibcode = 2013CRSSM..38..286Z }}</ref><ref>{{Cite journal|title = A heterojunction modulation-doped Mott transistor|journal = Applied Physics Letters|date = 2011-10-18|pages = 084503–084503–4|volume = 110|issue = 8|doi = 10.1063/1.3651612|first = Junwoo|display-authors=0|last = Son|s2cid = 27583830|arxiv = 1109.5299|bibcode = 2011JAP...110h4503S}}</ref>

==See also==
{{Div col}}
* {{annotated link|Physics:Dynamical mean-field theory}}
* {{annotated link|Physics:Electronic band structure}}
* {{annotated link|Physics:Hubbard model}}
* {{annotated link|Physics:Metal–insulator transition}}
* {{annotated link|Physics:Mott criterion}}
* {{annotated link|Physics:Tight binding}}
* {{annotated link|Physics:Variable-range hopping}} (Mott)
{{Div col end}}

==Notes==
{{Reflist|refs=
<ref name="Phillips">{{cite journal | last=Phillips | first=Philip | title=Mottness | journal=Annals of Physics | publisher=Elsevier BV | volume=321 | issue=7 | year=2006 | issn=0003-4916 | doi=10.1016/j.aop.2006.04.003 | pages=1634–1650|arxiv=cond-mat/0702348| bibcode=2006AnPhy.321.1634P }}</ref>
<ref name="Meinders">{{cite journal | last1=Meinders | first1=M. B. J. | last2=Eskes | first2=H. | last3=Sawatzky | first3=G. A. | title=Spectral-weight transfer: Breakdown of low-energy-scale sum rules in correlated systems | journal=Physical Review B | publisher=American Physical Society (APS) | volume=48 | issue=6 | date=1993-08-01 | issn=0163-1829 | doi=10.1103/physrevb.48.3916 | pages=3916–3926| pmid=10008840 | bibcode=1993PhRvB..48.3916M }}</ref>
<ref name="Stanescu">{{cite journal | last1=Stanescu | first1=Tudor D. | last2=Phillips | first2=Philip | last3=Choy | first3=Ting-Pong | title=Theory of the Luttinger surface in doped Mott insulators | journal=Physical Review B | publisher=American Physical Society (APS) | volume=75 | issue=10 | date=2007-03-06 | issn=1098-0121 | doi=10.1103/physrevb.75.104503 | page=104503|arxiv=cond-mat/0602280| bibcode=2007PhRvB..75j4503S | s2cid=119430461 }}</ref>
<ref name="Leigh">{{cite journal | last1=Leigh | first1=Robert G. | last2=Phillips | first2=Philip | last3=Choy | first3=Ting-Pong | title=Hidden Charge 2e Boson in Doped Mott Insulators | journal=Physical Review Letters | volume=99 | issue=4 | date=2007-07-25 | issn=0031-9007 | doi=10.1103/physrevlett.99.046404 | page=046404| pmid=17678382 |arxiv=cond-mat/0612130v3| bibcode=2007PhRvL..99d6404L | s2cid=37595030 }}</ref>
<ref name="Choy">{{cite journal | last1=Choy | first1=Ting-Pong | last2=Leigh | first2=Robert G. | last3=Phillips | first3=Philip | last4=Powell | first4=Philip D. | title=Exact integration of the high energy scale in doped Mott insulators | journal=Physical Review B | publisher=American Physical Society (APS) | volume=77 | issue=1 | date=2008-01-17 | issn=1098-0121 | doi=10.1103/physrevb.77.014512 | page=014512|arxiv=0707.1554| bibcode=2008PhRvB..77a4512C | s2cid=32553272 }}</ref>
<ref name="Stanescu2">{{cite journal | last1=Stanescu | first1=Tudor D. | last2=Phillips | first2=Philip | title=Pseudogap in Doped Mott Insulators is the Near-Neighbor Analogue of the Mott Gap | journal=Physical Review Letters | volume=91 | issue=1 | date=2003-07-02 | issn=0031-9007 | doi=10.1103/physrevlett.91.017002 | page=017002| pmid=12906566 |arxiv=cond-mat/0209118| bibcode=2003PhRvL..91a7002S | s2cid=5993172 }}</ref>
}}

==References==
*{{cite arXiv |eprint=cond-mat/9709195 |last1=Laughlin |first1=R. B. |title=A Critique of Two Metals |year=1997  }}
*{{cite arXiv|eprint=cond-mat/9711197 |last1=Anderson |first1=P. W. |last2=Baskaran |first2=G. |title=A Critique of ''A Critique of Two Metals'' |year=1997  }}
*{{cite journal |last1=Jördens |first1=Robert |last2=Strohmaier |first2=Niels |last3=Günter |first3=Kenneth |last4=Moritz |first4=Henning |last5=Esslinger |first5=Tilman |s2cid=4426395 |title=A Mott insulator of fermionic atoms in an optical lattice |journal=Nature |volume=455 |issue=7210 |pages=204–207 |doi=10.1038/nature07244 |pmid=18784720 |arxiv=0804.4009 |bibcode=2008Natur.455..204J |year=2008}}

[[Category:Correlated electrons]]
[[Category:Quantum phases]]

{{Sourceattribution|Mott insulator}}