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 δν between them is unity. As ν increases δν shrinks. Near certain N=${\mathit{N}}_{\mathit{c}}$ 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 δν experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for ${\mathit{N}}_{\mathit{c}}$ in terms of a sample’s parameters. For example, we predict that for high-mobility heterostructures ${\mathit{N}}_{\mathit{c}}$=0.9${\mathit{dn}}^{5/6}$${\mathit{n}}_{\mathit{i}}^{\mathrm{-}1/3}$, where d is the spacer width, n is the density of the two-dimensional electron gas, and ${\mathit{n}}_{\mathit{i}}$ is the two-dimensional density of randomly situated remote donors.

• Received 20 June 1995

DOI:https://doi.org/10.1103/PhysRevB.52.17366