Comments on: 188. Integer and fractional quantum Hall effect – what is it? http://www.nonequilibrium.net/188-integer-fractional-quantum-hall-effect/ Cosmology, turbulence, markets, non-equilibrium QFT and much more. No nonsense, just science Sat, 24 Jul 2010 18:49:02 +0000 http://wordpress.org/?v=2.9.1 hourly 1 By: Fractional quantum Hall effect in some multicomponent systems | NEQNET: Non-equilibrium Phenomena http://www.nonequilibrium.net/188-integer-fractional-quantum-hall-effect/comment-page-1/#comment-7692 Fractional quantum Hall effect in some multicomponent systems | NEQNET: Non-equilibrium Phenomena Fri, 27 Mar 2009 14:08:38 +0000 http://www.nonequilibrium.net/?p=1129#comment-7692 [...] Quantum Hall effect in the pioneering experimental work of 1980s was mainly concerned with thin layers of the so-called two dimensional electron gases (2DEGs), i.e. of electrons constrained to move in two spatial dimensions in specially prepared, high quality GaAs semiconductor heterostructures. Placing such a structure into the perpendicular magnetic field and driving current through it at very low temperatures , leads to a celebrated sequence of plateaus in the dependence of its transversal (Hall) resistance as a function of magnetic field. These plateaus occur at particular ratios between the number of electrons and the number of magnetic flux quanta that pierce the system in the direction perpendicular to the sample. This commensurability can be expressed as the filling factor in terms of integers (understood to have no common divisor), which is the single most important quantity that characterizes the quantum Hall state. The quantization is exact to impressive accuracy and is nowadays used as a standard for the unit of resistance. If , the effect can be explained in a straightforward way, by filling single-particle Landau levels (the integer quantum Hall effect, IQHE); if , the effect is highly non-trivial and presents a fascinating manifestation of fractional numbers in nature, hence the name fractional quantum Hall effect (FQHE). At places where transversal resistance is quantized, the longitudinal resistance (measured along the direction of current) drops to zero (in the limit of vanishing temperature). [...] [...] Quantum Hall effect in the pioneering experimental work of 1980s was mainly concerned with thin layers of the so-called two dimensional electron gases (2DEGs), i.e. of electrons constrained to move in two spatial dimensions in specially prepared, high quality GaAs semiconductor heterostructures. Placing such a structure into the perpendicular magnetic field and driving current through it at very low temperatures , leads to a celebrated sequence of plateaus in the dependence of its transversal (Hall) resistance as a function of magnetic field. These plateaus occur at particular ratios between the number of electrons and the number of magnetic flux quanta that pierce the system in the direction perpendicular to the sample. This commensurability can be expressed as the filling factor in terms of integers (understood to have no common divisor), which is the single most important quantity that characterizes the quantum Hall state. The quantization is exact to impressive accuracy and is nowadays used as a standard for the unit of resistance. If , the effect can be explained in a straightforward way, by filling single-particle Landau levels (the integer quantum Hall effect, IQHE); if , the effect is highly non-trivial and presents a fascinating manifestation of fractional numbers in nature, hence the name fractional quantum Hall effect (FQHE). At places where transversal resistance is quantized, the longitudinal resistance (measured along the direction of current) drops to zero (in the limit of vanishing temperature). [...]

]]> By: 228. Book review: D. Yoshioka. The quantum Hall effect http://www.nonequilibrium.net/188-integer-fractional-quantum-hall-effect/comment-page-1/#comment-5807 228. Book review: D. Yoshioka. The quantum Hall effect Wed, 04 Feb 2009 17:12:34 +0000 http://www.nonequilibrium.net/?p=1129#comment-5807 [...] a week ago we have briefly discussed the physics of the quantum Hall effect. Let me remind you the conclusions we came [...] [...] a week ago we have briefly discussed the physics of the quantum Hall effect. Let me remind you the conclusions we came [...]

]]> By: 198. Fractional quantum Hall effect - a few words about theory http://www.nonequilibrium.net/188-integer-fractional-quantum-hall-effect/comment-page-1/#comment-5656 198. Fractional quantum Hall effect - a few words about theory Sat, 24 Jan 2009 21:09:34 +0000 http://www.nonequilibrium.net/?p=1129#comment-5656 [...] As you remember, it is also characterized by the quantization of the the Hall resistivity [...] [...] As you remember, it is also characterized by the quantization of the the Hall resistivity [...]

]]> By: 191. Integer quantum Hall effect - theory http://www.nonequilibrium.net/188-integer-fractional-quantum-hall-effect/comment-page-1/#comment-5592 191. Integer quantum Hall effect - theory Tue, 20 Jan 2009 17:16:19 +0000 http://www.nonequilibrium.net/?p=1129#comment-5592 [...] you already have a first impression what physics of the quantum Hall effect is about, it is time to discuss theories that might have something to do with this physics. I’ll start [...] [...] you already have a first impression what physics of the quantum Hall effect is about, it is time to discuss theories that might have something to do with this physics. I’ll start [...]

]]> By: Dmitry http://www.nonequilibrium.net/188-integer-fractional-quantum-hall-effect/comment-page-1/#comment-5584 Dmitry Mon, 19 Jan 2009 21:26:59 +0000 http://www.nonequilibrium.net/?p=1129#comment-5584 Hi Keith, I would not call a material superconducting in the x-direction and not - in y-direction, especially taking into account that diagonal resistivity is an oscillating function of magnetic field (albeit its values are small compared to diagonal resistivity at [tex]H=0[/tex]). As for the particle zoo, let me turn to it in the tomorrow's post ;-) Cheers, Dmitry. Hi Keith,

I would not call a material superconducting in the x-direction and not – in y-direction, especially taking into account that diagonal resistivity is an oscillating function of magnetic field (albeit its values are small compared to diagonal resistivity at H=0).

As for the particle zoo, let me turn to it in the tomorrow’s post ;-)

Cheers,
Dmitry.

]]> By: Keith C http://www.nonequilibrium.net/188-integer-fractional-quantum-hall-effect/comment-page-1/#comment-5581 Keith C Mon, 19 Jan 2009 19:18:05 +0000 http://www.nonequilibrium.net/?p=1129#comment-5581 Hi Dmitry Thanks for your post. Since when we apply the electric field in the x-direction, we want the current in x-direction, and vanishing of rho_{xx} means that it is superconducting in the x-direction. So we can conductor current with loss when the conductor exhibits quantum hall effect, right? From the plot, to come up with a theory to explain it seems to me is as difficult as to explain the particle zoo. I guess the theory must be somehow related the BCS theory, right? Keith Hi Dmitry
Thanks for your post.
Since when we apply the electric field in the x-direction, we want the current in x-direction, and vanishing of rho_{xx} means that it is superconducting in the x-direction. So we can conductor current with loss when the conductor exhibits quantum hall effect, right?
From the plot, to come up with a theory to explain it seems to me is as difficult as to explain the particle zoo. I guess the theory must be somehow related the BCS theory, right?

Keith

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