The Quantized hall Effect

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2009-02

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Addis Ababa University

Abstract

The study of the Hall Effect in the two-dimensional electron Systems (2DES) showed new quantum effects. The Experimental or theoretical works show that at high magnetic fields and low temperatures, instead of increasing linearly with increasing magnetic field as in CHE, the Hall resistivity exhibits a series of step up increasing plateaus. In these same intervals of magnetic fields, the longitudinal resistivity vanishes. For each plateau, the Hall resistivity is given by the Plank’s constant h divided by the square of the electron charge e multiplied by an integer i , which represents the number of completely filled Landau levels. In the extreme (high magnetic fields and low temperatures) case, the Lowest Landau Levels (LLL) is partially filled it results in FQHE where i = the fraction number. Bits of magnetic field can get attached to each electron, creating other objects. Such particles have properties very different from those of the electrons. They sometimes seem to be unaware to huge magnetic fields and move in straight lines, although any bare electron would orbit on a very tight circle. All of these strange phenomena occur in two dimensional electron systems at low temperatures exposed to a high magnetic field only electrons and a magnetic field. We see a brief, high light on classical Hall Effect and overview on description of the integer and fractional quantized Hall effects, and the basic conditions associated with their occurrence. The way in which these conditions are satisfied, the integer quantized Hall Effect can be understood in terms of non interacting electrons, using flux quantization. The fractional quantized Hall Effect depends fundamentally on electron-electron interactions. Which lead to peculiar highly correlated elementary quasi particle excitations. We shall overview and briefly discuss such phenomena

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Quantized hall Effect

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http://10.90.10.223:4000/handle/123456789/4480

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Physics