  Throughout the years, strongly correlated coherent states of excitons have
been the subject of intense theoretical and experimental studies. This topic
has recently boomed due to new emerging quantum materials such as van der Waals
(vdW) bound atomically thin layers of transition metal dichalcogenides (TMDs).
We analyze the collective properties of charged interlayer excitons observed
recently in bilayer TMD heterostructures. We predict new strongly correlated
phases - crystal and Wigner crystal - that can be selectively realized with TMD
bilayers of properly chosen electron-hole effective masses by just varying
their interlayer separation distance. Our results open up new avenues for
nonlinear coherent control, charge transport and spinoptronics applications
with quantum vdW heterostuctures.
