Phase Transitions in Topological Bilayer Chern Insulator Model

We investigate a bilayer system where the individual layers obey a Chern Insulator model Hamiltonian coupled together with an interlayer contact interaction between the layers. Due to the interplay between the topology and the interlayer interaction, it is natural to expect the emergence of a coherent excitonic insulating phase. Using Hartree-Fock self-consistent mean field simulations, we report on the phase transitions that occur as a result of varying the interaction strength, the potential difference between the top and bottom layers, and the topology of the layers (each of which can be varied independently). We find a rich phase diagram that supports both metallic and insulating behavior as well as the expected excitonic behavior. We also observe reentrant behavior in the metallic phase.