  Intrinsic and extrinsic spin Hall effects are considered together on an equal
theoretical footing for the Rashba spin-orbit coupling in two-dimensional (2D)
electron and hole systems, using the diagrammatic method for calculating the
spin Hall conductivity. Our analytic theory for the 2D holes shows the expected
lowest-order additive result for the spin Hall conductivity. But, the 2D
electrons manifest a very surprising result, exhibiting a non-analyticity in
the Rashba coupling strength $\alpha$ where the strictly extrinsic spin Hall
conductivity (for $\alpha = 0$) cannot be recovered from the $\alpha \to 0$
limit of the combined theory. The theoretical results are discussed in the
context of existing experimental results.
