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 Vlecks 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.
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