Theory of spin-Hall transport of heavy holes in semiconductor quantum wells

Based on a proper definition of the spin current, we investigate the spin-Hall effect of heavy holes in narrow quantum wells in the presence of Rashba spin orbit coupling by using a spin-density matrix approach. In contrast to previous results obtained on the basis of the conventional definition of the spin current, we arrive at the conclusion that an electric-field-induced steady-state spin-Hall current does not exist in both pure and disordered infinite samples. Only an ac field can induce a spin-Hall effect in such systems. Recently, the same conclusions were derived for the Rashba model, in which the spin splitting of electron states is linear in k.