How this hall resistance is useful in measuring the physical parameters like density and mobility of charge carriers?
read these papers ! i hope these will help u to understand about applications of quantum hall effect
http://www.sciencedirect.com/science/article/pii/S1631070511000910
https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CDEQFjAB&url=http%3A%2F%2Fwww.bourbaphy.fr%2Fklitzing.pdf&ei=_O5hU5_bEYaTrgee54CgCA&usg=AFQjCNGNtJd0qKKGuJ11fobva85p_ySkPA&sig2=qljYwIYzTjlhKiQ51K3wZQ&bvm=bv.65788261,bs.1,d.c2E
Thanks for your suggestion.. Are we getting two or three dimensional picture of electron gas in this experiment.? If is it so how we are capturing that image.?
Briefly, quantum Hall measurements yield the value of the ratio h (the constant of Planck) and the square of the electron charge, e^2, with high accuracy. This is mainly due to the exact quantisation of Hall resistance in the integer quantum Hall regime (Robert Laughlin uses a gauge argument proving this fact [See R. Laughlin, Phys. Rev. B23, 5632 (1981)] -- impurities play a significant role, in fixing the chemical potential inside the gap in the regions of quantum Hall plateaus), but very importantly from the practical perspective due to the fact that in two spatial dimensions Hall resistance R_{xy} is the same as the Hall resistivity ρ_{xy}, as a consequence of which accurate measurement of h/e^2 does not require an accurate measurement of the sample geometry. Knowledge of an accurate value of h/e^2 is important, since with the aid of the Josephson effect one can determine a very accurate value for the ratio e/h. Combining these two very accurate results, one obtains very accurate values for both h and e.
It happens that our knowledge regarding the values of the natural constants arises from a fitting procedure, relying on a set of very accurate independent experimental observations (detailed description of the adopted fitting procedure is in public domain, written in the past mostly by E. Richard Cohen and Pierre Giacomo). Following a new fitting exercise, subsequent to the discovery of the Integer Quantum Hall effect (thus using the very accurate values for h and e), the uncertainties in the values of all natural constants diminished. For instance, the 4th significant digit of the conversion factor between the Rydberg constant and electron volt (eV) changed as a result.
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