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Mott insulator

December 26, 2022

Mott insulators are a class of materials that are expected to conduct electricity according to conventional 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 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.[1] One of the simplest models that can capture Mott transition is the 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 charge-transfer insulators exists between anion and cation states,[2] such as between O 2p and Ni 3d bands in NiO.[3]

History

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 oxides predicted to be conductors by band theory are insulators.[4] With an odd number of electrons per unit cell, the valence band is only partially filled, so the Fermi level lies within the band. From the band theory, this implies that such a material has to be a metal. This conclusion fails for several cases, e.g. CoO, one of the strongest insulators known.[1]

Nevill Mott and Rudolf Peierls also in 1937 predicted the failing of band theory can be explained by including interactions between electrons.[5]

In 1949, in particular, Mott proposed a model for NiO as an insulator, where conduction is based on the formula[6]

(Ni2+O2−)2 → Ni3+O2− + Ni1+O2−.

In this situation, the formation of an energy gap preventing conduction can be understood as the competition between the Coulomb potential U between 3d electrons and the transfer integral t of 3d electrons between neighboring atoms (the transfer integral is a part of the tight binding approximation). The total energy gap is then

Egap = U − 2zt,

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 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 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[7][8]
  • Vanishing of the single particle Green function along a connected surface in momentum space in the first Brillouin zone[9]
  • Two sign changes of the Hall coefficient as electron doping goes from   to   (band insulators have only one sign change at  )
  • The presence of a charge   (with   the charge of an electron) boson at low energies[10][11]
  • A pseudogap away from half-filling ( )[12]

Applications

Mott insulators are of growing interest in advanced physics research, and are not yet fully understood. They have applications in thin-film magnetic heterostructures and the strong correlated phenomena in high-temperature superconductivity, for example.[13][14][15][16]

This kind of insulator can become a conductor by changing some parameters, which may be composition, pressure, strain, voltage, or magnetic field. The effect is known as a Mott transition and can be used to build smaller field-effect transistors, switches and memory devices than possible with conventional materials.[17][18][19]

See also

Notes

  1. ^ a b Fazekas, Patrik (2008). Lecture notes on electron correlation and magnetism. World Scientific. pp. 147–150. ISBN 978-981-02-2474-5. OCLC 633481726.
  2. ^ lecture slides
  3. ^ P. Kuiper; G. Gruizinga; J. Ghijsen; G.A. Sawatzky; H. Verweij (1987). "Character of Holes in LixNi1−xO2". Physical Review Letters. 62 (2): 221–224. Bibcode:1989PhRvL..62..221K. doi:10.1103/PhysRevLett.62.221. PMID 10039954.
  4. ^ de Boer, J. H.; Verwey, E. J. W. (1937). "Semi-conductors with partially and with completely filled 3d-lattice bands". Proceedings of the Physical Society. 49 (4S): 59. Bibcode:1937PPS....49...59B. doi:10.1088/0959-5309/49/4S/307.
  5. ^ Mott, N. F.; Peierls, R. (1937). "Discussion of the paper by de Boer and Verwey". Proceedings of the Physical Society. 49 (4S): 72. Bibcode:1937PPS....49...72M. doi:10.1088/0959-5309/49/4S/308.
  6. ^ Mott, N. F. (1949). "The basis of the electron theory of metals, with special reference to the transition metals". Proceedings of the Physical Society. Series A. 62 (7): 416–422. Bibcode:1949PPSA...62..416M. doi:10.1088/0370-1298/62/7/303.
  7. ^ Phillips, Philip (2006). "Mottness". Annals of Physics. Elsevier BV. 321 (7): 1634–1650. arXiv:cond-mat/0702348. Bibcode:2006AnPhy.321.1634P. doi:10.1016/j.aop.2006.04.003. ISSN 0003-4916.
  8. ^ Meinders, M. B. J.; Eskes, H.; Sawatzky, G. A. (1993-08-01). "Spectral-weight transfer: Breakdown of low-energy-scale sum rules in correlated systems". Physical Review B. American Physical Society (APS). 48 (6): 3916–3926. Bibcode:1993PhRvB..48.3916M. doi:10.1103/physrevb.48.3916. ISSN 0163-1829. PMID 10008840.
  9. ^ Stanescu, Tudor D.; Phillips, Philip; Choy, Ting-Pong (2007-03-06). "Theory of the Luttinger surface in doped Mott insulators". Physical Review B. American Physical Society (APS). 75 (10): 104503. arXiv:cond-mat/0602280. Bibcode:2007PhRvB..75j4503S. doi:10.1103/physrevb.75.104503. ISSN 1098-0121. S2CID 119430461.
  10. ^ Leigh, Robert G.; Phillips, Philip; Choy, Ting-Pong (2007-07-25). "Hidden Charge 2e Boson in Doped Mott Insulators". Physical Review Letters. 99 (4): 046404. arXiv:cond-mat/0612130v3. Bibcode:2007PhRvL..99d6404L. doi:10.1103/physrevlett.99.046404. ISSN 0031-9007. PMID 17678382. S2CID 37595030.
  11. ^ Choy, Ting-Pong; Leigh, Robert G.; Phillips, Philip; Powell, Philip D. (2008-01-17). "Exact integration of the high energy scale in doped Mott insulators". Physical Review B. American Physical Society (APS). 77 (1): 014512. arXiv:0707.1554. Bibcode:2008PhRvB..77a4512C. doi:10.1103/physrevb.77.014512. ISSN 1098-0121. S2CID 32553272.
  12. ^ Stanescu, Tudor D.; Phillips, Philip (2003-07-02). "Pseudogap in Doped Mott Insulators is the Near-Neighbor Analogue of the Mott Gap". Physical Review Letters. 91 (1): 017002. arXiv:cond-mat/0209118. Bibcode:2003PhRvL..91a7002S. doi:10.1103/physrevlett.91.017002. ISSN 0031-9007. PMID 12906566. S2CID 5993172.
  13. ^ Kohsaka, Y.; Taylor, C.; Wahl, P.; et al. (August 28, 2008). "How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+δ". Nature. 454 (7208): 1072–1078. arXiv:0808.3816. Bibcode:2008Natur.454.1072K. doi:10.1038/nature07243. PMID 18756248. S2CID 205214473.
  14. ^ Markiewicz, R. S.; Hasan, M. Z.; Bansil, A. (2008-03-25). "Acoustic plasmons and doping evolution of Mott physics in resonant inelastic x-ray scattering from cuprate superconductors". Physical Review B. 77 (9): 094518. Bibcode:2008PhRvB..77i4518M. doi:10.1103/PhysRevB.77.094518.
  15. ^ Hasan, M. Z.; Isaacs, E. D.; Shen, Z.-X.; Miller, L. L.; Tsutsui, K.; Tohyama, T.; Maekawa, S. (2000-06-09). "Electronic Structure of Mott Insulators Studied by Inelastic X-ray Scattering". Science. 288 (5472): 1811–1814. arXiv:cond-mat/0102489. Bibcode:2000Sci...288.1811H. doi:10.1126/science.288.5472.1811. ISSN 0036-8075. PMID 10846160. S2CID 2581764.
  16. ^ Hasan, M. Z.; Montano, P. A.; Isaacs, E. D.; Shen, Z.-X.; Eisaki, H.; Sinha, S. K.; Islam, Z.; Motoyama, N.; Uchida, S. (2002-04-16). "Momentum-Resolved Charge Excitations in a Prototype One-Dimensional Mott Insulator". Physical Review Letters. 88 (17): 177403. arXiv:cond-mat/0102485. Bibcode:2002PhRvL..88q7403H. doi:10.1103/PhysRevLett.88.177403. PMID 12005784. S2CID 30809135.
  17. ^ Newns, Dennis (2000). "Junction mott transition field effect transistor (JMTFET) and switch for logic and memory applications". http://www.google.com/patents/US6121642
  18. ^ Zhou, You; Ramanathan, Shriram (2013-01-01). "Correlated Electron Materials and Field Effect Transistors for Logic: A Review". Critical Reviews in Solid State and Materials Sciences. 38 (4): 286–317. arXiv:1212.2684. Bibcode:2013CRSSM..38..286Z. doi:10.1080/10408436.2012.719131. ISSN 1040-8436. S2CID 93921400.
  19. ^ Son, Junwoo; et al. (2011-10-18). "A heterojunction modulation-doped Mott transistor". Applied Physics Letters. 110 (8): 084503–084503–4. arXiv:1109.5299. Bibcode:2011JAP...110h4503S. doi:10.1063/1.3651612. S2CID 27583830.

References

  • Laughlin, R. B. (1997). "A Critique of Two Metals". arXiv:cond-mat/9709195. Bibcode:1997cond.mat..9195L. {{cite journal}}: Cite journal requires |journal= (help)
  • Anderson, P. W.; Baskaran, G. (1997). "A Critique of A Critique of Two Metals". arXiv:cond-mat/9711197. Bibcode:1997cond.mat.11197A. {{cite journal}}: Cite journal requires |journal= (help)
  • Jördens, Robert; Strohmaier, Niels; Günter, Kenneth; Moritz, Henning; Esslinger, Tilman (2008). "A Mott insulator of fermionic atoms in an optical lattice". Nature. 455 (7210): 204–207. arXiv:0804.4009. Bibcode:2008Natur.455..204J. doi:10.1038/nature07244. PMID 18784720. S2CID 4426395.

December 26, 2022
mott, insulator, class, materials, that, expected, conduct, electricity, according, conventional, band, theories, turn, insulators, particularly, temperatures, these, insulators, fail, correctly, described, band, theories, solids, their, strong, electron, elec. Mott insulators are a class of materials that are expected to conduct electricity according to conventional 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 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 1 One of the simplest models that can capture Mott transition is the 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 charge transfer insulators exists between anion and cation states 2 such as between O 2p and Ni 3d bands in NiO 3 Contents 1 History 2 Mottness 3 Applications 4 See also 5 Notes 6 ReferencesHistory EditAlthough 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 oxides predicted to be conductors by band theory are insulators 4 With an odd number of electrons per unit cell the valence band is only partially filled so the Fermi level lies within the band From the band theory this implies that such a material has to be a metal This conclusion fails for several cases e g CoO one of the strongest insulators known 1 Nevill Mott and Rudolf Peierls also in 1937 predicted the failing of band theory can be explained by including interactions between electrons 5 In 1949 in particular Mott proposed a model for NiO as an insulator where conduction is based on the formula 6 Ni2 O2 2 Ni3 O2 Ni1 O2 In this situation the formation of an energy gap preventing conduction can be understood as the competition between the Coulomb potential U between 3d electrons and the transfer integral t of 3d electrons between neighboring atoms the transfer integral is a part of the tight binding approximation The total energy gap is then Egap U 2zt 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 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 EditMottism denotes the additional ingredient aside from 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 7 8 Vanishing of the single particle Green function along a connected surface in momentum space in the first Brillouin zone 9 Two sign changes of the Hall coefficient as electron doping goes from n 0 displaystyle n 0 to n 2 displaystyle n 2 band insulators have only one sign change at n 1 displaystyle n 1 The presence of a charge 2 e displaystyle 2e with e lt 0 displaystyle e lt 0 the charge of an electron boson at low energies 10 11 A pseudogap away from half filling n 1 displaystyle n 1 12 Applications EditMott insulators are of growing interest in advanced physics research and are not yet fully understood They have applications in thin film magnetic heterostructures and the strong correlated phenomena in high temperature superconductivity for example 13 14 15 16 This kind of insulator can become a conductor by changing some parameters which may be composition pressure strain voltage or magnetic field The effect is known as a Mott transition and can be used to build smaller field effect transistors switches and memory devices than possible with conventional materials 17 18 19 See also EditDynamical mean field theory Electronic band structure Describes the range of energies of an electron within the solid Hubbard model Metal insulator transition Change between conductive and non conductive state Mott criterion Tight binding Model of electronic band structures of solids Variable range hopping Mott Notes Edit a b Fazekas Patrik 2008 Lecture notes on electron correlation and magnetism World Scientific pp 147 150 ISBN 978 981 02 2474 5 OCLC 633481726 lecture slides P Kuiper G Gruizinga J Ghijsen G A Sawatzky H Verweij 1987 Character of Holes in LixNi1 xO2 Physical Review Letters 62 2 221 224 Bibcode 1989PhRvL 62 221K doi 10 1103 PhysRevLett 62 221 PMID 10039954 de Boer J H Verwey E J W 1937 Semi conductors with partially and with completely filled 3d lattice bands Proceedings of the Physical Society 49 4S 59 Bibcode 1937PPS 49 59B doi 10 1088 0959 5309 49 4S 307 Mott N F Peierls R 1937 Discussion of the paper by de Boer and Verwey Proceedings of the Physical Society 49 4S 72 Bibcode 1937PPS 49 72M doi 10 1088 0959 5309 49 4S 308 Mott N F 1949 The basis of the electron theory of metals with special reference to the transition metals Proceedings of the Physical Society Series A 62 7 416 422 Bibcode 1949PPSA 62 416M doi 10 1088 0370 1298 62 7 303 Phillips Philip 2006 Mottness Annals of Physics Elsevier BV 321 7 1634 1650 arXiv cond mat 0702348 Bibcode 2006AnPhy 321 1634P doi 10 1016 j aop 2006 04 003 ISSN 0003 4916 Meinders M B J Eskes H Sawatzky G A 1993 08 01 Spectral weight transfer Breakdown of low energy scale sum rules in correlated systems Physical Review B American Physical Society APS 48 6 3916 3926 Bibcode 1993PhRvB 48 3916M doi 10 1103 physrevb 48 3916 ISSN 0163 1829 PMID 10008840 Stanescu Tudor D Phillips Philip Choy Ting Pong 2007 03 06 Theory of the Luttinger surface in doped Mott insulators Physical Review B American Physical Society APS 75 10 104503 arXiv cond mat 0602280 Bibcode 2007PhRvB 75j4503S doi 10 1103 physrevb 75 104503 ISSN 1098 0121 S2CID 119430461 Leigh Robert G Phillips Philip Choy Ting Pong 2007 07 25 Hidden Charge 2e Boson in Doped Mott Insulators Physical Review Letters 99 4 046404 arXiv cond mat 0612130v3 Bibcode 2007PhRvL 99d6404L doi 10 1103 physrevlett 99 046404 ISSN 0031 9007 PMID 17678382 S2CID 37595030 Choy Ting Pong Leigh Robert G Phillips Philip Powell Philip D 2008 01 17 Exact integration of the high energy scale in doped Mott insulators Physical Review B American Physical Society APS 77 1 014512 arXiv 0707 1554 Bibcode 2008PhRvB 77a4512C doi 10 1103 physrevb 77 014512 ISSN 1098 0121 S2CID 32553272 Stanescu Tudor D Phillips Philip 2003 07 02 Pseudogap in Doped Mott Insulators is the Near Neighbor Analogue of the Mott Gap Physical Review Letters 91 1 017002 arXiv cond mat 0209118 Bibcode 2003PhRvL 91a7002S doi 10 1103 physrevlett 91 017002 ISSN 0031 9007 PMID 12906566 S2CID 5993172 Kohsaka Y Taylor C Wahl P et al August 28 2008 How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8 d Nature 454 7208 1072 1078 arXiv 0808 3816 Bibcode 2008Natur 454 1072K doi 10 1038 nature07243 PMID 18756248 S2CID 205214473 Markiewicz R S Hasan M Z Bansil A 2008 03 25 Acoustic plasmons and doping evolution of Mott physics in resonant inelastic x ray scattering from cuprate superconductors Physical Review B 77 9 094518 Bibcode 2008PhRvB 77i4518M doi 10 1103 PhysRevB 77 094518 Hasan M Z Isaacs E D Shen Z X Miller L L Tsutsui K Tohyama T Maekawa S 2000 06 09 Electronic Structure of Mott Insulators Studied by Inelastic X ray Scattering Science 288 5472 1811 1814 arXiv cond mat 0102489 Bibcode 2000Sci 288 1811H doi 10 1126 science 288 5472 1811 ISSN 0036 8075 PMID 10846160 S2CID 2581764 Hasan M Z Montano P A Isaacs E D Shen Z X Eisaki H Sinha S K Islam Z Motoyama N Uchida S 2002 04 16 Momentum Resolved Charge Excitations in a Prototype One Dimensional Mott Insulator Physical Review Letters 88 17 177403 arXiv cond mat 0102485 Bibcode 2002PhRvL 88q7403H doi 10 1103 PhysRevLett 88 177403 PMID 12005784 S2CID 30809135 Newns Dennis 2000 Junction mott transition field effect transistor JMTFET and switch for logic and memory applications http www google com patents US6121642 Zhou You Ramanathan Shriram 2013 01 01 Correlated Electron Materials and Field Effect Transistors for Logic A Review Critical Reviews in Solid State and Materials Sciences 38 4 286 317 arXiv 1212 2684 Bibcode 2013CRSSM 38 286Z doi 10 1080 10408436 2012 719131 ISSN 1040 8436 S2CID 93921400 Son Junwoo et al 2011 10 18 A heterojunction modulation doped Mott transistor Applied Physics Letters 110 8 084503 084503 4 arXiv 1109 5299 Bibcode 2011JAP 110h4503S doi 10 1063 1 3651612 S2CID 27583830 References EditLaughlin R B 1997 A Critique of Two Metals arXiv cond mat 9709195 Bibcode 1997cond mat 9195L a href Template Cite journal html title Template Cite journal cite journal a Cite journal requires journal help Anderson P W Baskaran G 1997 A Critique of A Critique of Two Metals arXiv cond mat 9711197 Bibcode 1997cond mat 11197A a href Template Cite journal html title Template Cite journal cite journal a Cite journal requires journal help Jordens Robert Strohmaier Niels Gunter Kenneth Moritz Henning Esslinger Tilman 2008 A Mott insulator of fermionic atoms in an optical lattice Nature 455 7210 204 207 arXiv 0804 4009 Bibcode 2008Natur 455 204J doi 10 1038 nature07244 PMID 18784720 S2CID 4426395 Retrieved from https en wikipedia org w index php title Mott insulator amp oldid 1100830784, wikipedia, wiki, book, books, library,

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