COLLAPSE OF SPILL SPLITTING IN THE QUANTUM HALL-EFFECT

It is known experimentally that at not very large filling factors nu t he quantum Hall conductivity peaks corresponding to the same Landau le vel number N and two different spin orientations are well separated. T hese 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 en ergy delta nu experiences a second-order phase transition as a functio n 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-mobil ity 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.