Gate tuning from exciton superfluid to quantum anomalous Hall in van der Waals heterobilayer

Van der Waals heterostructures of two-dimensional (2D) materials provide a powerful approach toward engineering various quantum phases of matter. Examples include topological matter such as quantum spin Hall (QSH) insulator and correlated matter such as exciton superfluid. It can be of great interest to realize these vastly different quantum phases matter on a common platform; however, their distinct origins tend to restrict them to material systems of incompatible characters. Here, we show that heterobilayers of 2D valley semiconductors can be tuned through interlayer bias between an exciton superfluid, a quantum anomalous Hall insulator, and a QSH insulator. The tunability between these distinct phases results from the competition of Coulomb interaction with the interlayer quantum tunneling that has a chiral form in valley semiconductors. Our findings point to exciting opportunities for harnessing both protected topological edge channels and bulk superfluidity in an electrically configurable platform.