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The value of h/e2 from quantum Hall effect

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Author(s): Keshav N. Shrivastava

Journal: Maejo International Journal of Science and Technology
ISSN 1905-7873

Volume: 4;
Issue: 01;
Start page: 20;
Date: 2010;
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Keywords: Hall effect | constant h/e2 | spin | charge

ABSTRACT
The quantum Hall effect and the emergence of the value of h/e2 is found to be understood within five steps. Here h is the Planck's constant and e is the charge of the electron. The Hall resistivity is found to become a function of spin. For positive spin, one value is found but for negative sign in the spin, another value occurs. In this way, there is never only one value of the resistivity but doubling of values. The value of h/e2 is a special case of the more general dependence of resistivity on the spin. We investigate the effect of Landau levels. For extreme quantum limit, n=0, the effective charge of the electron becomes (1/2)ge. The fractional charge arises for a finite value of the angular momentum. There is a formation of spin clusters. As the field increases, there is a phase transition from spin ½ to spin 3/2 so that g value becomes 4 and various values of n in Landau levels, g(n+1/2), form plateaus in the Hall resistivity. For finite values of the orbital angular momenta, many fractional charges emerge. The fractional as well as the integral values of the charge are in full agreement with the experimental data. The generalised constant is h/[(1/2)ge]e which under special conditions becomes h/e2, the ratio of Planck's constant to the square of the electron charge. The flux is usually quantised in units of o =hc/e. When the angular momentum is properly taken into account, hc/e is replaced by hc/(1/2)ge. Thus, we predict a new superfluid which has (1/2)ge in place of the charge, e.
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