Quantum Hall effect in thin films of three-dimensional topological insulators

We show that a thin film of a three-dimensional topological insulator (3DTI) with an exchange field is a realization of the famous Haldane model for quantum Hall effect (QHE) without Landau levels. The exchange field plays the role of staggered fluxes on the honeycomb lattice, and the hybridization gap of the surface states is equivalent to alternating onsite energies on the $AB$ sublattices. A peculiar phase diagram for the QHE is predicted in 3DTI thin films under an applied magnetic field, which is quite different from those either in traditional QHE systems or in graphene.