Excitonic quantum criticality in a transition metal dichalcogenide heterostructure

Interlayer exciton condensation has been experimentally demonstrated in semiconducting two-dimensional transition metal dichalcogenide based heterostructures. Here we consider the problem in the presence of electron doping and show that the ensuing metallic state has an inter-band (excitonic) charge density wave instability, which crucially can be controlled via a perpendicular displacement field. Focusing on MoX₂/WX₂ heterobilayers, we calculate the displacement field required to tune across the charge density wave quantum phase transition and study superconductivity near the phase transition.