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- W1641808532 abstract "We assume that in a semiconductor if the electric field is applied along the x-direction and a magnetic field along the z-direction, then there is a Hall voltage along the y direction. The Hall resistivity is given by $$ {rho _H}(x,y) = - {{{B_z}} over {nec}} $$(1)where n is the concentration of electrons, e the charge and c is the velocity of light. It may be observed that all of the three dimensions are equally important at this stage. Since the magnetic field is directed along the z-direction, the current is along x direction and the electric voltage is along y direction, the electrons are confined in the x — y plane and hence may exhibit two-dimensional behaviour. It was found by v. Klitzing et al1,2 that the above resistance is quantized as $$ rho (x,y) = {h over {v{e^2}}} $$(2)where v is an integer. It can be interpretted as a Landau level filling factor for electrons in two-dimensions. For v = 1, the quantity $$frac{h}{{{e^2}}} = 25812.8{text{ ohms}}$$(3)is called “one Klitzing”. Later on, it was found by Tsui, Stormer and Gossard3 that v need not be an integer. While measuring the transverse resistivity as a function of field, a plateau was found at v = 1/3. Later studies discovered many different values of the fraction, v." @default.
- W1641808532 created "2016-06-24" @default.
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- W1641808532 date "2001-01-01" @default.
- W1641808532 modified "2023-09-23" @default.
- W1641808532 title "Theory of Quantum Hall Effect: Effective Fractional Charge" @default.
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- W1641808532 doi "https://doi.org/10.1007/978-1-4615-1339-1_23" @default.
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