P -wave pairing and ferromagnetism in the metal-insulator transition in two dimensions

Based on recent experimental evidence for a spin-polarized ground state in the insulating phase of the two-dimensional electron system, we propose that ferromagnetic spin fluctuations lead to an attractive interaction in the triplet channel and cause p-wave pairing in the conducting phase. We use the Landau-Fermi liquid phenomenology to explain how the enhanced spin susceptibility near the critical density yields an attractive potential, in a similar mechanism to superfluidity in ${}^{3}\mathrm{He}.$ As the density is decreased, the p-wave order parameter undergoes a transition from a unitary to a nonunitary state, in which it coexists with ferromagnetism for a range of densities. As the density is further reduced, the pairing amplitude vanishes and the system is described by a ferromagnetic insulator. Thus, we find two quantum critical points as a function of density associated with the polarization of the paired state and ferromagnetism. We explain the magnetotransport measurements in parallel and perpendicular magnetic fields and propose a shot-noise experiment to measure the pair charge.