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We show that any critical transition region between two adjacent Hall plateaus in either integer or fractional quantum Hall effect is characterized by a universal "semicircle" relationship between the longitudinal and transverse conductivities σₓₓ, σxy, provided the sample is homogeneous and isotropic on a large scale. This is demonstrated both for the phase-coherent quantum transport as well as for the incoherent transport.
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Ruzin et al. (1995) studied this question.
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