Conjunctive query - Revision history

en>Rjwilmsi: Filling in journal cites, using AWB (10395)

2014-08-21T18:54:44Z

Filling in journal cites, using AWB (10395)

← Older revision		Revision as of 20:54, 21 August 2014
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	~~'''The quantum spin Hall state''' is a state of matter proposed to exist in special~~, ~~two-dimensional, semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. The quantum spin Hall state of matter~~ is ~~the cousin of the integer [[Quantum Hall effect\|quantum Hall]] state,~~ and ~~both states can be realized on lattice that does not require the application of a large magnetic field~~. ~~The quantum spin Hall state does not break charge conservation symmetry~~ and ~~spin-<math>S_z</math> conservation symmetry~~		Hello, my title is Andrew and my spouse doesn't like it at all. My wife and I reside in Mississippi and I love every day residing right here. Credit authorising is exactly where my primary earnings comes from. One of the issues she enjoys most is canoeing and she's been doing it for fairly a whilst.<br><br>Feel free to visit my webpage :: good psychic ([http://www.publicpledge.com/blogs/post/7034 www.publicpledge.com])
	(in ~~order to have well defined Hall conductances). The first proposal for the existence of a quantum spin Hall state was developed by Kane and Mele<ref>C.L. Kane~~ and ~~E.J~~. Mele, Physical Review Letters 95, 226801 (2005).</ref> who adapted an earlier model for graphene by [[F. Duncan M. Haldane]]<ref>F.D.M. Haldane, Physical Review Letters 61, 2015 (1988).</ref> which exhibits an integer quantum Hall effect. The Kane and Mele model is two copies of the Haldane model such that the spin up electron exhibits a chiral integer quantum Hall Effect while the spin down electron exhibits an anti-chiral integer [[Quantum Hall effect\|quantum Hall]] effect.

	~~Overall the Kane-Mele model has a charge-Hall conductance of exactly zero but a spin-Hall conductance of~~ exactly <math>\sigma_{xy}^{spin}=2</math> (in units of <math>\frac{e}{4 \pi}</math>). Independently, a quantum spin Hall model was proposed by Bernevig and Zhang<ref>B.A. Bernevig and S.C. Zhang, Physical Review Letters 96, 106802 (2006)</ref> in an intricate strain architecture which engineers, due to spin-orbit coupling, a magnetic field pointing upwards for spin-up electrons and a magnetic field pointing downwards for spin-down electrons. The main ingredient is the existence of spin-orbit coupling, which can be understood as a momentum-dependent magnetic field coupling to the spin of the electron.

	~~Real experimental systems, however, are far~~ from the idealized picture presented above in which spin-up and spin-down electrons are not coupled. A very important achievement was the realization that the quantum spin Hall state remain to be non-trivial even after the introduction of spin-up spin-down scattering,<ref>C.L. Kane and E.J. Mele, Physical Review Letters 95, 146802 (2005)</ref> which destroy the quantum spin Hall effect. In a separate paper, Kane and Mele introduced a topological <math>Z_2</math> invariant who characterizes a state as
	~~trivial or non-trivial band insulator (regardless if the state~~
	~~exhibits or does not exhibit a quantum spin Hall effect)~~. ~~Further stability studies~~ of the ~~edge liquid through which conduction takes place in the quantum spin Hall state proved, both analytically and numerically that the non-trivial state~~ is ~~robust to both interactions and extra spin-orbit coupling terms that mix spin-up~~ and ~~spin-down electrons.~~
	~~Such a non-trivial state (exhibiting or not exhibiting a quantum spin Hall effect) is called a~~
	~~[[topological insulator]], which is an example of [[symmetry protected topological order]] protected by~~
	~~charge conservation symmetry and time reversal symmetry.~~
	(Note that the quantum spin Hall state is also a [[symmetry protected topological order\|symmetry protected topological]] state protected by charge conservation symmetry and spin-<math>S_z</math> conservation symmetry. We do not need time reversal symmetry to protect quantum spin Hall state.
	~~Topological insulator and quantum spin Hall state are different symmetry protected topological states.)~~

	~~==In HgTe quantum wells==~~
	~~Since graphene has extremely weak spin-orbit coupling, it is very unlikely to support a quantum spin Hall state at temperatures achievable with today~~'s ~~technologies. A very realistic theoretical proposal~~ for ~~the existence of the quantum spin Hall state has been put forward by Bernevig, Hughes and Zhang (BHZ) in Cadmium Telluride/Mercury Telluride/Cadmium Telluride (CdTe/HgTe/CdTe) quantum wells in which~~ a ~~thin (5-7 nanometers) sheet of HgTe is sandwiched between two sheets of CdTe,<ref name="Bern">B.A. Bernevig, T.L. Hughes and S.C. Zhang, Science 314, 1757 (2006)~~.<~~/ref~~> ~~and subsequently experimentally realized~~ <~~ref name="Konig"~~>~~Markus König, Steffen Wiedmann, Christoph Brüne, Andreas Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang Qi, and Shou-Cheng Zhang, Published online September 20, 2007; 10.1126~~/~~science.1148047 (Science Express Research Articles)~~
	</~~ref>~~
	~~(In fact, the proposed quantum wells do not exhibit the quantum spin Hall effect and should be regarded as~~
	~~[[topological insulators]]~~.)
	~~Different quantum wells of varying HgTe thickness can be built~~. When the sheet of HgTe in between the CdTe is thin, the system behaves like an ordinary insulator and does not conduct when the Fermi level resides in the band-gap. When the sheet of HgTe is varied and made thicker (this requires the fabrication of separate quantum wells), an interesting phenomenon happens. Due to the inverted band structure of HgTe, BHZ predicted that, at some critical HgTe thickness, a Lifshitz transition occurs in which the system closes the bulk band gap to become a semi-metal, and then re-opens it to become a quantum spin Hall insulator.

	In the gap closing and re-opening process, two edge states are brought out from the bulk and cross the bulk-gap. As such, when the Fermi level resides in the bulk gap, the conduction is dominated by the edge channels that cross the gap. The two-terminal conductance is <math>G_{xx}=2 \frac{e^2}{h}</math> in the quantum spin Hall state and zero in the normal insulating state. As the conduction is dominated by the edge channels, the value of the conductance should be insensitive to how wide the sample is. A magnetic field should destroy the quantum spin Hall state by breaking time-reversal invariance and allowing spin-up spin-down electron scattering processes at the edge. All these predictions <ref name="Bern"/~~> have been experimentally verified in an experiment <ref name="Konig"~~/~~> performed in the [[Laurens W~~. Molenkamp\|Molenkamp]] labs at [[University of Würzburg\|Universitat Würzburg]] in Germany. (In fact, a magnetic field in z-direction does not destroy the quantum spin Hall state which has conserved <math>S_z</math> spins. ~~The fact that the quantization of the two-terminal conductance~~
	~~is destroyed by magnetic field suggests that the quantum well is not a quantum spin Hall state, but a [[topological insulator]~~].)

	~~==References==~~
	~~<references/>~~

	~~==Further reading==~~
	* {{cite doi\|10.1146/annurev-conmatphys-062910-140538}}

	~~[[Category:Hall effect]]~~
	~~[[Category:Condensed matter physics]]~~
	~~[[Category:Quantum electronics]]~~
	~~[[Category:Spintronics]]~~

en>Beastinwith: Removed an inappropriate inline comment and tried to fix the sentence it was complaining about.

2014-01-03T17:29:52Z

Removed an inappropriate inline comment and tried to fix the sentence it was complaining about.

← Older revision		Revision as of 19:29, 3 January 2014
Line 1:		Line 1:
	~~Hi there~~. ~~My name is Sophia Meagher even though it~~ is not the ~~name on my birth certificate~~. ~~Her family members life~~ in ~~Ohio~~. ~~Credit authorising~~ is ~~how she makes~~ a ~~residing~~. ~~Playing badminton~~ is a ~~factor~~ that he is ~~totally addicted~~ to.<br><br>~~my site~~ - ~~tarot readings~~ (~~[http:~~//~~www~~.~~edmposts~~.~~com~~/~~build~~-a-~~beautiful~~-~~organic~~-~~garden~~-~~using~~-these-~~ideas~~/ ~~visit my homepage~~])		'''The quantum spin Hall state''' is a state of matter proposed to exist in special, two-dimensional, semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. The quantum spin Hall state of matter is the cousin of the integer [[Quantum Hall effect\|quantum Hall]] state, and both states can be realized on lattice that does not require the application of a large magnetic field. The quantum spin Hall state does not break charge conservation symmetry and spin-<math>S_z</math> conservation symmetry
			(in order to have well defined Hall conductances). The first proposal for the existence of a quantum spin Hall state was developed by Kane and Mele<ref>C.L. Kane and E.J. Mele, Physical Review Letters 95, 226801 (2005).</ref> who adapted an earlier model for graphene by [[F. Duncan M. Haldane]]<ref>F.D.M. Haldane, Physical Review Letters 61, 2015 (1988).</ref> which exhibits an integer quantum Hall effect. The Kane and Mele model is two copies of the Haldane model such that the spin up electron exhibits a chiral integer quantum Hall Effect while the spin down electron exhibits an anti-chiral integer [[Quantum Hall effect\|quantum Hall]] effect.

			Overall the Kane-Mele model has a charge-Hall conductance of exactly zero but a spin-Hall conductance of exactly <math>\sigma_{xy}^{spin}=2</math> (in units of <math>\frac{e}{4 \pi}</math>). Independently, a quantum spin Hall model was proposed by Bernevig and Zhang<ref>B.A. Bernevig and S.C. Zhang, Physical Review Letters 96, 106802 (2006)</ref> in an intricate strain architecture which engineers, due to spin-orbit coupling, a magnetic field pointing upwards for spin-up electrons and a magnetic field pointing downwards for spin-down electrons. The main ingredient is the existence of spin-orbit coupling, which can be understood as a momentum-dependent magnetic field coupling to the spin of the electron.

			Real experimental systems, however, are far from the idealized picture presented above in which spin-up and spin-down electrons are not coupled. A very important achievement was the realization that the quantum spin Hall state remain to be non-trivial even after the introduction of spin-up spin-down scattering,<ref>C.L. Kane and E.J. Mele, Physical Review Letters 95, 146802 (2005)</ref> which destroy the quantum spin Hall effect. In a separate paper, Kane and Mele introduced a topological <math>Z_2</math> invariant who characterizes a state as
			trivial or non-trivial band insulator (regardless if the state
			exhibits or does not exhibit a quantum spin Hall effect). Further stability studies of the edge liquid through which conduction takes place in the quantum spin Hall state proved, both analytically and numerically that the non-trivial state is robust to both interactions and extra spin-orbit coupling terms that mix spin-up and spin-down electrons.
			Such a non-trivial state (exhibiting or not exhibiting a quantum spin Hall effect) is called a
			[[topological insulator]], which is an example of [[symmetry protected topological order]] protected by
			charge conservation symmetry and time reversal symmetry.
			(Note that the quantum spin Hall state is also a [[symmetry protected topological order\|symmetry protected topological]] state protected by charge conservation symmetry and spin-<math>S_z</math> conservation symmetry. We do not need time reversal symmetry to protect quantum spin Hall state.
			Topological insulator and quantum spin Hall state are different symmetry protected topological states.)

			==In HgTe quantum wells==
			Since graphene has extremely weak spin-orbit coupling, it is very unlikely to support a quantum spin Hall state at temperatures achievable with today's technologies. A very realistic theoretical proposal for the existence of the quantum spin Hall state has been put forward by Bernevig, Hughes and Zhang (BHZ) in Cadmium Telluride/Mercury Telluride/Cadmium Telluride (CdTe/HgTe/CdTe) quantum wells in which a thin (5-7 nanometers) sheet of HgTe is sandwiched between two sheets of CdTe,<ref name="Bern">B.A. Bernevig, T.L. Hughes and S.C. Zhang, Science 314, 1757 (2006).</ref> and subsequently experimentally realized <ref name="Konig">Markus König, Steffen Wiedmann, Christoph Brüne, Andreas Roth, Hartmut Buhmann, Laurens W. Molenkamp, Xiao-Liang Qi, and Shou-Cheng Zhang, Published online September 20, 2007; 10.1126/science.1148047 (Science Express Research Articles)
			</ref>
			(In fact, the proposed quantum wells do not exhibit the quantum spin Hall effect and should be regarded as
			[[topological insulators]].)
			Different quantum wells of varying HgTe thickness can be built. When the sheet of HgTe in between the CdTe is thin, the system behaves like an ordinary insulator and does not conduct when the Fermi level resides in the band-gap. When the sheet of HgTe is varied and made thicker (this requires the fabrication of separate quantum wells), an interesting phenomenon happens. Due to the inverted band structure of HgTe, BHZ predicted that, at some critical HgTe thickness, a Lifshitz transition occurs in which the system closes the bulk band gap to become a semi-metal, and then re-opens it to become a quantum spin Hall insulator.

			In the gap closing and re-opening process, two edge states are brought out from the bulk and cross the bulk-gap. As such, when the Fermi level resides in the bulk gap, the conduction is dominated by the edge channels that cross the gap. The two-terminal conductance is <math>G_{xx}=2 \frac{e^2}{h}</math> in the quantum spin Hall state and zero in the normal insulating state. As the conduction is dominated by the edge channels, the value of the conductance should be insensitive to how wide the sample is. A magnetic field should destroy the quantum spin Hall state by breaking time-reversal invariance and allowing spin-up spin-down electron scattering processes at the edge. All these predictions <ref name="Bern"/> have been experimentally verified in an experiment <ref name="Konig"/> performed in the [[Laurens W. Molenkamp\|Molenkamp]] labs at [[University of Würzburg\|Universitat Würzburg]] in Germany. (In fact, a magnetic field in z-direction does not destroy the quantum spin Hall state which has conserved <math>S_z</math> spins. The fact that the quantization of the two-terminal conductance
			is destroyed by magnetic field suggests that the quantum well is not a quantum spin Hall state, but a [[topological insulator]].)

			==References==
			<references/>

			==Further reading==
			* {{cite doi\|10.1146/annurev-conmatphys-062910-140538}}

			[[Category:Hall effect]]
			[[Category:Condensed matter physics]]
			[[Category:Quantum electronics]]
			[[Category:Spintronics]]

en>Rjwilmsi: /* Formal properties of conjunctive queries */Format plain DOIs using AWB (8087)

2012-07-03T18:14:45Z

Formal properties of conjunctive queries: Format plain DOIs using AWB (8087)

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Hi there. My name is Sophia Meagher even though it is not the name on my birth certificate. Her family members life in Ohio. Credit authorising is how she makes a residing. Playing badminton is a factor that he is totally addicted to.<br><br>my site - tarot readings ([http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ visit my homepage])