  Quantum anomalous Hall (QAH) effect generates quantized electric charge Hall
conductance without external magnetic field. It requires both nontrivial band
topology and time-reversal symmetry (TRS) breaking. In most cases, one could
break the TRS of time-reversal invariant topological materials to yield QAH
effect, which is essentially a topological phase transition. Conventional
topological phase transition induced by external field/stimulus needs a route
along which the bandgap closes and re-opens. Hence, the phase transition occurs
only when the magnitude of field/stimulus is larger than a critical value. In
this work we propose that using gapless surface states, the transition can
happen at arbitrarily weak (but finite) external field strength. This can be
regarded as an unconventional topological phase transition, where the bandgap
closing is guaranteed by bulk-edge correspondence and symmetries, while the
bandgap reopening is induced by external fields. We demonstrate this concept on
the 2D surface states of 3D topological insulators like $\rm Bi_2Se_3$, which
become 2D QAH insulators once a circularly polarized light is turned on,
according to van Vleck's effective Hamiltonian in Floquet time crystal theory.
The sign of quantized Chern number can be controlled via the chirality of the
light. This provides a convenient and dynamical approach to trigger topological
phase transitions and create QAH insulators.
