Universal relation between longitudinal and transverse conductivities in quantum Hall effect

TL;DR

This paper reveals a universal semi-circle law linking longitudinal and transverse conductivities during quantum Hall transitions, applicable to both coherent and incoherent transport regimes, assuming sample homogeneity and isotropy.

Contribution

It establishes a universal semi-circle relationship for quantum Hall transitions, extending across integer and fractional effects, for both phase-coherent and incoherent transport.

Findings

Universal semi-circle law between conductivities

Applicable to both integer and fractional quantum Hall effects

Valid for coherent and incoherent transport regimes

Abstract

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 semi-circle relationship between the longitudinal and transverse conductivities, provided the sample is homogeneous and isotropic on a large scale. This conclusion is demonstrated both for the phase-coherent quantum transport as well as for the incoherent transport.