Abstract
We propose a topological quantum phase transition for quantum states with different Berry phases in hole-doped III-V semiconductor quantum wells with bulk and structure inversion asymmetry. The Berry phase of the occupied Bloch states can be characteristic of topological metallic states. It is found that the adjustment of the thickness of the quantum well may cause a transition of the Berry phase in a two-dimensional hole gas. Correspondingly, the jump of the spin Hall conductivity accompanies the change of the Berry phase. This property is robust against the impurity potentials in the system. Experimental detection of this topological quantum phase transition is discussed.