  Surface states of a topological insulator demonstrate interesting quantum
phenomena, such as the quantum anomalous Hall (QAH) effect and the quantum
magnetoelectric effect. Fermi energy tuning plays a role in inducing phase
transitions and developing future device functions. Here, we report on
controlling the topological phases in a dual-gate field-effect transistor of a
semi-magnetic topological insulator heterostructure. The heterostructure
consists of magnetized one-surface and non-magnetic other-surface. By tuning
the Fermi energy to the energy gap of the magnetized surface, the Hall
conductivity $\sigma_{xy}$ becomes close to the half-integer quantized Hall
conductivity $e^2/2h$, exemplifying parity anomaly. The dual-gate control
enables the band structure alignment to the two quantum Hall states with
$\sigma_{xy} = e^2/h$ and 0 under a strong magnetic field. These states are
topologically equivalent to the QAH and axion insulator states, respectively.
Precise and independent control of the band alignment of the top and bottom
surfaces successively induces various topological phase transitions among the
QAH, axion insulator, and parity anomaly states in magnetic topological
insulators.
