Nuclear-spin relaxation and spin-wave collective modes in a disordered two-dimensional electron gas

The spin-polarization of nuclei near a two-dimensional electron gas (2D EG) may be relaxed by spin-flip excitations of the electron system. The spectrum of low-energy electronic spin-flip excitations depends on the disorder broadening of Landau levels and on the interaction enhancement of the Landau-level spin splitting. Disorder vertex corrections to the spin-flip response function capture the fact that the nuclear relaxation rate depends on local rather than thermodynamic Landau-level broadening, while interaction vertex corrections can strongly enhance the relaxation rate. We illustrate these effects by summing the disorder and interaction ladder diagrams for the spin-flip response function in the strong-magnetic-field limit. Our approach is also able to describe the effect of disorder on the spin-wave collective modes of a spin-polarized 2D EG.