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We propose a topological quantum phase transition for quantum states withdifferent Berry phases in hole-doped III-V semiconductor quantum wells withbulk and structure inversion asymmetry. The Berry phase of the occupied Blochstates can be characteristic of topological metallic states. It is found thatthe adjustment of thickness of the quantum well may cause a transition of Berryphase in two-dimensional hole gas. Correspondingly, the jump of spin Hallconductivity accompanies the change of the Berry phase. This property is robustagainst the impurity potentials in the system. Experimental detection of thistopological quantum phase transition is discussed.

Topological quantum phase transition and the Berry phase near the Fermi surface in hole-doped quantum wells