Collapse of spin splitting in the quantum Hall effect

It is known experimentally that at not very large filling factors 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 =2N+1/2 and =2N+3/2 so that the distance between them is unity. As increases shrinks. Near certain N=Nc two peaks merge into a single peak at =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 experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for Nc in terms of a samples parameters. For example, we predict that for high-mobility heterostructures Nc=0.9dn5/6ni-1/3, where d is the spacer width, n is the density of the two-dimensional electron gas, and ni is the two-dimensional density of randomly situated remote donors.