Rashba spin-splitting in wurtzite based two dimensional holes systems

We present a theoretical study of the Rashba-like spin-orbit coupling in two dimensional hole systems formed in wurtizite semiconductor heterostructures.~ Using an 8X8 band Kane model within the envelope function approximation we derive exact analytical expressions for the Rashba-like Hamiltonians of the heavy and light holes.~ The linear and cubic dependence in the wave vector of such Hamiltonians will be discussed. Simple analytical expressions for the spin-orbit coupling parameters can be also extracted from our model. A variational approach has been used in order to estimate the hole spin-splitting energies in typical group III nitrides semiconductor quantum wells. These results could be of relevance for the design and implementation of novel (hole) transport spintronic devices.