Critical exponent in the fractional quantum Hall effect

Abstract

We report the observation of a universal critical exponent in the fractional quantum Hall effect (FQHE) from a study of the temperature ( T) dependent electron transport in between Landau level filling factors v = 2 5 and v = 1 3 , over a T range from 1.2 K to 22 mK. in an AlGaAs-GaAs heterostructure. Specifically, the maximum value of dp xy dB and the width of p xx show the same power law dependence on T, i.e. ~ T − K . The critical exponent K=0.43 ± 0.02.This power law dependence is the same as that obtained in the integral quantum Hall effect (IQHE) [Wei et al., Phys. Rev. Lett. 61 (1988) 1294], in analogy to which our result indicates the existence of a divergent correlation length for the wavefunction of the quasi-particles in the FQHE for 1 3 < v < 2 5 . The localization to delocalization transition can be characterized by a universal critical exponent, k, in both the IQHE and the FQHE.