Quantization of the Hall conductance from density quantization alone

We consider a phenomenological model of the two-dimensional electron gas (2DEG) in the presence of a high magnetic field and a ground plane. The model is based on two physically plausible assumptions: (1) that except at certain "magic" densities the uniform density state of the 2DEG is thermodynamically unstable to phase separation and (2) that the surface tension between two regions of different "magic" densities is positive. As a consequence of these assumptions, and in the presence of a ground plane near the 2DEG (the actual experimental geometry), the 2DEG at arbitrary density is found to partially phase separate into regions of quantized density. We show that in this model it is possible to obtain precisely quantized plateaus in the Hall conductance at fractional multiples of e2/h as a consequence of density quantization alone, with no need for fractionally charged quasiparticles. Some possible experimental consequences of this alternative explanation are discussed.