Critical exponents of the plateau-to-plateau transitions in the fractional quantum Hall regime

Scaling in disordered, quantum Hall systems has been studied extensively with the emergence of a single extended state (Ec), characterized by a power-law divergence of the localization length [ξ∝(E-E_c)^-ν] in the zero temperature limit [1]. Experimentally, scaling has been investigated mostly by measuring the plateau-to-plateau transitions between integer quantum Hall states [2,3]. Improvements in epitaxially-grown GaAs quantum wells have led to ultra-high-quality 2D electron systems [4] which show a plethora of fractional quantum Hall states enabling us to investigate the scaling behavior in the fractional filling regime. We obtain the critical exponents by studying the temperature dependence of the longitudinal resistivity in a series of GaAs quantum wells with varying well widths ranging from 20 to 70 nm. While recent calculations in the fractional quantum Hall regime suggest identical critical exponents in the integer and fractional states [5], we report differing exponents as we transition between the fractional states.

1.    A. M. M. Pruisken, Phys. Rev. Lett. 61, 1297 (1988).

2.    H. P. Wei et al., Phys. Rev. Lett. 61, 1294 (1988).

3.    L. Engel et al. Surface science 229, 13 (1990). 

4.    Yoon Jang Chung et al., Nature Materials 20, 632 (2021).

5.    Songyang Pu et al., Phys. Rev. Lett. 128, 116801 (2022).