Quantum phase transitions in ultrathin films of three-dimensional topological insulators in the presence of an electrostatic potential and a Zeeman field

We investigate transport properties of the surface states of three-dimensional topological insulator thin films in the presence of an electrostatic potential $\ensuremath{\gamma}$ and a spin-splitting Zeeman field $g$. It is shown that there exist a quantum pseudospin Hall phase, a quantum anomalous Hall phase, and a common insulator phase in this system. By tuning $g$ and $\ensuremath{\gamma}$, three quantum phase transitions between them can occur accompanied with energy-band closing, each of which is characterized by a change of the quantized pseudospin Chern numbers.