Abstract: Composite fermion wavefunctions describe a one to one correspondence between the low energy properties of the FQH and the IQH phases which has been tested extensively in experiments and through numerical studies [1]. Here we consider the FQH state in the presence of a weak disorder potential. The full many-body problem is numerically difficult [2,3] but the effective Hamiltonian of a single quasiparticle can numerically be calculated in a weak disorder regime; and here we find a one to one correspondence between the FQH and the IQH systems [4]. If this correspondence extends to the many quasiparticle cases as well, we expect the FQH transitions to be similar to the IQH plateau transitions. Unfortunately, the many-quasiparticle problem in the FQH system is numerically intractable even within the variational space. So we turn to experiments and show results from a recent set of experiments on graphene and GaAs devices that show similar critical behaviour at both FQH and IQH transitions [5,6].
[1] Jain Phys. Rev. Lett. 63, 199–202 (1989)
[2] Sheng et al. Phys. Rev. Lett. 90, 256802 (2003)
[3] Krishna et al Phys. Rev. B 99, 041111(R) (2019)
[4] Pu et al Phys. Rev. Lett., vol. 128, 116801 (2022)
[5] Madathil et al Phys. Rev. Lett 130, 226503 (2023)
[6] Kaur et al, in preparation