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We calculate an effect of spinless impurities on the spin Hall effect of theLuttinger model representing p-type semiconductors. The self-energy in the Bornapproximation becomes diagonal in the helicity basis and its value isindependent of the wavenumber or helicity. The vertex correction in the ladderapproximation vanishes identically, in sharp contrast with the Rashba model.This implies that in the clean limit the spin Hall conductivity reproduces thevalue of the intrinsic spin Hall conductivity calculated in earlier papers.Comment: 4 pages, minor corrections, to appear in Phys. Rev.

physical review. b, condensed matter and materials physics

Absence of vertex correction for the spin Hall effect in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>-type semiconductors

Absence of vertex correction for the spin Hall effect inp-type semiconductors