  Van der Waals heterostructures of 2D materials provide a powerful approach
towards engineering various quantum phases of matters. Examples include
topological matters such as quantum spin Hall (QSH) insulator, and correlated
matters such as exciton superfluid. It can be of great interest to realize
these vastly different quantum matters on a common platform, however, their
distinct origins tend to restrict them to material systems of incompatible
characters. Here we show that heterobilayers of two-dimensional valley
semiconductors can be tuned through interlayer bias between an exciton
superfluid (ES), a quantum anomalous Hall (QAH) insulator, and a QSH insulator.
The tunability between these distinct phases results from the competition of
Coulomb interaction with the interlayer quantum tunnelling 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.
