Nuclear spin induced scattering between quantum Hall edges with opposite spin polarization

We consider the nuclear spin induced scattering between two quantum Hall edge state channels with opposite spin polarization. Nonequilibrium spin polarization of nuclear spins is calculated, and dependence on temperature, voltage and magnetic field is analyzed. Nuclear spin relaxation due to spin diffusion caused by magnetic dipole-dipole interactions is considered. A renormalization group (RG) analysis of the hyperfine interaction is performed and a RG flow is obtained for the filling factor $ u=1/q$ case, $q$ being an odd integer. The RG flow appears to be different from that for edge states of a 2D topological insulator. Our results are relevant to recent experiments on nuclear spin related transport in the quantum Hall system and may provide a way to obtain dynamic nuclear polarization.