Collapse of spin splitting in the quantum Hall effect

It is known experimentally that at not very large filling factors {ν} the quantum Hall conductivity peaks corresponding to the same Landau level number N and two different spin orientations are well separated. These peaks occur at half-integer filling factors {ν}=2N+1/2 and {ν}=2N+3/2 so that the distance {δ}{ν} between them is unity. As {ν} increases {δ}{ν} shrinks. Near certain N=Nc two peaks merge into a single peak at {ν}=2N+1. We argue that this collapse of the spin splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron g factor. We use the mean-field approach to show that in the limit of zero Zeeman energy {δ}{ν} experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for Nc in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures Nc=0.9dn5/6{n}ᵢ^{{{-}}1/3}$, where d is the spacer width, n is the density of the two-dimensional electron gas, and ${n}ᵢ$ is the two-dimensional density of randomly situated remote donors.