  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 thickness of the quantum well may cause a transition of Berry
phase in two-dimensional hole gas. Correspondingly, the jump of 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.
