Primitive permutation group - Revision history

en>Teddyktchan at 12:02, 26 June 2014

2014-06-26T12:02:16Z

← Older revision		Revision as of 14:02, 26 June 2014
Line 1:		Line 1:
	~~{{Condensed matter physics\|expanded=Electronic phases}}~~		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.<br><br>my web blog [http://carnavalsite.com/demo-page-1/solid-advice-in-relation-to-yeast-infection/ std testing at home]
	'''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.~~

	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]].
	<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 }}
	~~</ref>~~

	~~==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 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>~~

	~~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>

	~~:(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>.~~

	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~~

	~~:''E''<sub>gap</sub> = ''U'' − 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 [[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 <ref name="Phillips" /><ref name="Meinders" />~~
	*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" />
	*''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>)
	*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]] 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>

	~~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>~~

	~~==See also==~~
	*[[Hubbard model]]
	*[[Tight binding (physics)\|Tight-~~binding approximation]]~~
	*[[Electronic band structure]]
	*[[Mott Criterion]]
	*[[Dynamical Mean Field Theory]]
	*[[Variable range hopping\|(Mott) Variable range hopping]]

	~~==References==~~
	* R.B. Laughlin, "A Critique of Two Metals," http://arxiv.org/abs/cond-~~mat~~/~~9709195~~
	* Philip W. Anderson and G. Baskaran, "A Critique of 'A Critique of Two Metals,'" http://arxiv.org/abs/cond-~~mat/9711197~~
	~~<references>~~
	~~<ref name="Phillips">Philip Phillips, "Mottness," http://arxiv.org/abs/cond~~-~~mat/0702348</ref>~~
	~~<ref name="Meinders">M.B.J. Meinders, H. Eskes, and G.A. Sawatzky, Phys. Rev. B '''48''' 3916 (1993)</ref>~~
	~~<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>~~
	~~<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>~~
	~~<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>~~
	<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>
	~~</references>~~
	~~{{reflist}}~~

	~~[[Category:Quantum phases]~~]

en>Jason Quinn: /* References */ used mathworld template

2013-06-30T06:09:32Z

References: used mathworld template

← Older revision		Revision as of 08:09, 30 June 2013
Line 1:		Line 1:
	~~Alyson Meagher~~ is the title ~~her mothers~~ and ~~fathers gave her but she doesn~~'~~t like when people use her complete~~ title. ~~North Carolina~~ is the ~~place he loves most but now he~~ is ~~contemplating other options~~. ~~Invoicing~~ is ~~what I do~~. ~~To perform lacross~~ is the ~~thing I adore most~~ of all.<br><br>~~Feel free~~ to ~~visit my web~~-~~site~~; ~~psychic solutions by lynne~~ ([http://www.~~edmposts~~.com/~~build~~-a-~~beautiful~~-~~organic~~-~~garden~~-~~using~~-~~these~~-~~ideas~~/ ~~www~~.~~edmposts~~.~~com~~])		{{Condensed matter physics\|expanded=Electronic phases}}
			'''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.

			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]].
			<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 }}
			</ref>

			==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 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>

			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>

			:(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>.

			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

			:''E''<sub>gap</sub> = ''U'' − 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 [[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 <ref name="Phillips" /><ref name="Meinders" />
			*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" />
			*''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>)
			*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]] 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>

			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>

			==See also==
			*[[Hubbard model]]
			*[[Tight binding (physics)\|Tight-binding approximation]]
			*[[Electronic band structure]]
			*[[Mott Criterion]]
			*[[Dynamical Mean Field Theory]]
			*[[Variable range hopping\|(Mott) Variable range hopping]]

			==References==
			* R.B. Laughlin, "A Critique of Two Metals," http://arxiv.org/abs/cond-mat/9709195
			* Philip W. Anderson and G. Baskaran, "A Critique of 'A Critique of Two Metals,'" http://arxiv.org/abs/cond-mat/9711197
			<references>
			<ref name="Phillips">Philip Phillips, "Mottness," http://arxiv.org/abs/cond-mat/0702348</ref>
			<ref name="Meinders">M.B.J. Meinders, H. Eskes, and G.A. Sawatzky, Phys. Rev. B '''48''' 3916 (1993)</ref>
			<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>
			<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>
			<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>
			<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>
			</references>
			{{reflist}}

			[[Category:Quantum phases]]

en>D.Lazard: Reverted good faith edits by Gareth Griffith-Jones (talk): The IP edit was correct and do not needs citation. (TW)

2012-07-03T06:32:44Z

Reverted good faith edits by Gareth Griffith-Jones (talk): The IP edit was correct and do not needs citation. (TW)

New page

Alyson Meagher is the title her mothers and fathers gave her but she doesn't like when people use her complete title. North Carolina is the place he loves most but now he is contemplating other options. Invoicing is what I do. To perform lacross is the thing I adore most of all.<br><br>Feel free to visit my web-site; psychic solutions by lynne ([http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ www.edmposts.com])