  We show that the Quantum Spin Hall Effect, a state of matter with topological
properties distinct from conventional insulators, can be realized in HgTe/CdTe
semiconductor quantum wells. By varying the thickness of the quantum well, the
electronic state changes from a normal to an "inverted" type at a critical
thickness $d_c$. We show that this transition is a topological quantum phase
transition between a conventional insulating phase and a phase exhibiting the
QSH effect with a single pair of helical edge states. We also discuss the
methods for experimental detection of the QSH effect.
