Non-universal localization transition in the quantum Hall effect probed through broken-symmetry states of graphene

The quantum Hall effect hosts quantum phase transitions in which the localization length, that is the size of disorder-induced bulk localized states, is governed by universal scaling from percolation theory. However, this universal character is not systematically observed in experiments, including very recent ones in extremely clean devices. Here we explore this non-universality by systematically measuring the localization length in broken-symmetry quantum Hall states of graphene. Depending on the nature and gap size of these states, we observe differences of up to a tenfold in the minimum localization length, accompanied by clear deviations from universal scaling. Our results, as well as the previously observed non-universality, are fully captured by a simple picture based on the co-existence of localized states from two successive sub-Landau levels.