The Possibility of Novel Superconductity with High-Order Excitonic Complexes*

Two-dimensional monolayers and bilayers of transition metal dichalcogenides (TMDs) allow for numerous higher-order excitonic species, including not only single excitons (an electron-hole bound pair), but also trions (an exciton bound to an extra charge), biexcitons (two excitons bound together), indirect excitons (an electron and hole in adjacent layers of a bilayer), charged biexitons (a biexciton bound to an extra charge), and "quaternions" (an exciton bound to two extra charges). This last complex is a boson that carries net charge, and therefore a Bose-Einstein condensate of them would also be a superconductor. In this talk I will review this menagerie of excitonic states, when they are predicted to appear, and the experimental evidence we have for them, with a focus on the evidence for doubly charged excitons which could provide a non-BCS mechanism for superconductivity.