Collapse of spill splitting in the quantum Hall effect

It is known experimentally that at not very large filling factors nu 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 nu = 2N + 1/2 and nu = 2N + 3/2 so that the distance delta nu between them is unity. As nu increases delta nu shrinks. Near certain N = N-c two peaks merge into a single peak at nu = 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-held approach to show that in the limit of zero Zeeman energy delta nu experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for N-c in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures N-c = 0.9dn(5/6)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.