A Toy Model for the 2/3 Fractional Quantum Hall edge channel

We present a minimal model capturing the intriguing physics of the fractional quantum Hall state at filling factor $\nu=2/3$. Inserting fictive reservoirs \textemdash either Landauer Reservoirs (LRs) or Energy Preservings Reservoirs (EPRs) \textemdash along the counter-propagating modes to mimic edge channel mixing, the conductance is shown rapidly converging towards the Kane-Fisher-Polchinski conductance fixed point $2/3 \times (e^2/h$) for both EPRs and LRs. However, LRs give equal charge and thermal relaxation lengths while EPRs show infinite thermal relaxation length. The Hall bar current noise is found varying linearly with current at large bias, leading to an apparent (or Fake) Fano factor $\simeq 0.19.../\sqrt{N+1}$ for N LRs, or exponentially vanishing for EPRs. Withal, inserting a Quantum Point Contact in the middle of the Hall bar reveals the recently observed $0.5e^{2}/h$ conductance plateau. Finally, the 2010 Bid et al. first reported observation of neutral modes can be explained by an upstream diffusive heat flow and delta-T noise, without introducing any specific collective neutral mode.
Comment: 19 pages, 5 figures