Describe the variation of Hall resistance Pxy and longitudinal resistance px with magnetic field in integer quantum Hall effect and fractional quantum Hall effect. Can these phenomena be explained using free electron theory?
In the Integer Quantum Hall Effect (IQHE), the Hall resistance, RxyR_{xy}, exhibits plateaus as the magnetic field, BB, increases. These plateaus occur at quantized values of RxyR_{xy}, where the Hall resistance is given by Rxy=h/(e2ν)R_{xy} = h/(e^2 \nu), with ν\nu ________ _______ _______ _____ _____ _________ _____ ________ _________.
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