Quasiparticles Charge in Hole-States of the FQHE

Current and energy flow in fractional hole-states of the first Landau level; namely, with filling $\nu $in the range 1/2\textless $\nu $\textless 1, is much more complicated than in the particle-states (Laughlin's, 1/2\textgreater $\nu $\textgreater 0). In the hole-states topological counter-propagating charge and/or neutral edge-modes coexist, moving charge and energy downstream as well as upstream. While their thermal conductance [1] and the proliferation of upstream neutral modes were recently reported [2,3], their partitioned quasiparticle charge was studied only in $\nu =$2/3 [3]. Studying the main hole-states $\nu \quad =$2/3, 3/5, and 4/7, we found a universal behavior. The `apparent partitioned charge' (by a QPC) was always $e^{\ast }=\nu e$, as deduced from shot-noise measurements. The surprising part was that the Fano factor was not due to charge partitioning; but was directly related to the fragmentation of upstream neutral modes to particle-hole pairs. The fragmentation led to current fluctuations with the observed, quantized, Fano factor [3]. [1] M. Banerjee et al., To be published. [2] H. Inoue et al., Nat. Comm. 5, 4067 (2014). [3] R. Sabo et al., arXiv:1603.06908.