  We describe how the three-dimensional quantum spin Hall phase arises from the
insulator phase by changing an external parameter. In 3D systems without
inversion symmetry, a gapless phase should appear between the two phases with a
bulk gap. The gapless points are monopoles and antimonopoles (in k space),
whose topological nature is the source of this gapless phase. In general, when
the external parameter is changed from the ordinary insulator phase, two
monopole-antimonopole pairs are created and the system becomes gapless. The
gap-closing points (monopoles and antimonopoles) then move in the k space as
the parameter is changed further. They eventually annihilate in pairs, with
changing partners from the pair creations, and the system opens a gap again,
entering into the quantum spin Hall phase.
