  We study a topological phase transition between a normal insulator and a
quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal
and two-fold rotation symmetries. Contrary to the case of ordinary
time-reversal invariant systems where a direct transition between two
insulators is generally predicted, we find that the topological phase
transition in systems with an additional two-fold rotation symmetry is mediated
by an emergent stable two-dimensional Weyl semimetal phase between two
insulators. Here the central role is played by the so-called space-time
inversion symmetry, the combination of time-reversal and two-fold rotation
symmetries, which guarantees the quantization of the Berry phase around a 2D
Weyl point even in the presence of strong spin-orbit coupling.
Pair-creation/pair-annihilation of Weyl points accompanying partner exchange
between different pairs induces a jump of a 2D $Z_{2}$ topological invariant
leading to a topological phase transition. According to our theory, the
topological phase transition in HgTe/CdTe quantum well structure is mediated by
a stable 2D Weyl semimetal phase since the quantum well, lacking inversion
symmetry intrinsically, has two-fold rotation about the growth direction.
Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior
within a small but finite interval in the thickness of HgTe layers between a
normal insulator and a quantum spin Hall insulator. We also propose that
few-layer black phosphorus under perpendicular electric field is another
candidate system to observe the unconventional topological phase transition
mechanism accompanied by emerging 2D Weyl semimetal phase protected by
space-time inversion symmetry.
