Nuclear spin diffusion in semiconductor nanostructures: Effects of inhomogeneous hyperfine interactions

We study the effect of contact hyperfine interaction on the nuclear spin diffusion coefficients in semiconductor quantum dots. The diffusion coefficients are calculated with both the method of moment and density matrix. We show that nuclear spin diffusion is strongly suppressed by the nonuniform hyperfine coupling resulting from the confined electron wavefunction. Our results agree with the observed suppression of nuclear spin diffusion in these structures in recent experiments, and clarify the degree of validity of the method of moment in an inhomogeneous system.