We calculate the Overhauser frequency shifts in semiconductor nanostructures resulting from the hyperfine interaction between nonequilibrium electronic spins and nuclear spins. The frequency shifts depend on the electronic local density of states and spin polarization as well as the electronic and nuclear spin relaxation mechanisms. Unlike previous calculations, our method accounts for the electron confinement in low dimensional semiconductor nanostructures, resulting in both nuclear spin polarizations and Overhauser shifts that are strongly dependent on position. Our results explain previously puzzling measurements of Overhauser shifts in an Al$_x$Ga$_{1-x}$As parabolic quantum well by showing the connection between the electron spin lifetime and the frequency shifts.
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