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Hall effect

V H. H. J. z. y. x. Hall effect. x. Low Field Magnetoresistance, Hall effect in Drude Theory. V H. H. J. z. y. x. x. 2. 3. One measures the voltage drop along y and the current along x, not a resistance. z. y. x. V x. V H. H. J.

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Hall effect

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  1. VH H J z y x Hall effect x

  2. Low Field Magnetoresistance, Hall effect in Drude Theory VH H J z y x x 2

  3. 3

  4. One measures the voltage drop along y and the current along x, not a resistance z y x Vx VH H J Hall resistanceisproportional to magneticfieldsince the phenomenonis due to the Lorentz force and the conductoris linear and inverselyproportional to n since the Lorentz force goes with the velocity, not with J, and J=neV. 4

  5. Hall resistanceisproportional to magneticfieldin Drude theory, however….. Quantized Hall effect of the two-dimensional electron gas in GaAs- AlxGa1-xAs heterojunctionsatlowtemperatures to 50 mK. In the small-current and low-temperature limitsharpstepsconnecting the quantized Hall resistanceplateaus. The diagonalresistivityρxxdecreases with decreasingTat the Shubnikov—de Haaspeaks, aswellasat the dips, and isvanishingly small atmagneticfieldsabove 40 kG 5

  6. 2d electron gas in (x,y) plane in magneticfield H parallel to z axis z y x H We start with the Theory for spinless electrons Main alternative Choices of the gauge

  7. y kx

  8. Free electron density of states at B=0 (continuous model)

  9. The energylevels do notdepend on kx, so theirdegeneracyis just the number of kxpoints: itisfound by imposingthat y0cannotexceed sample size. y kx r(w) with H r(w) without H E E

  10.  Лев Васи́льевич Шу́бников

  11. Including spin

  12. m Ht H Groundstate energy – 2DEG

  13. Note! All electrons contribute , not only the open LL

  14. K. v. Klitzing Used the depletionlayer of a GaAs MOSFET as a 2d electron gas

  15. K. v. Klitzing discovery: 1980 Nobel prize: 1985 Oscillations of longitudina resistivity =Shubnikov-deHaas, minima close to 0. Plateaux in Hall resistivity r=h/(ne2) with integer n correspond to the minima (From Datta page 25)

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