Three-dimensional electron-hole superfluidity in a superlattice close to room temperature

Although there is strong theoretical and experimental evidence for electron-hole superfluidity in separated sheets of electrons and holes at low $T$, extending superfluidity to high $T$ is limited by strong two-dimensional fluctuations and Kosterlitz-Thouless effects. We show this limitation can be overcome using a superlattice of alternating electron- and hole-doped semiconductor monolayers. The superfluid transition in a three-dimensional superlattice is not topological, and for strong electron-hole pair coupling, the transition temperature ${T}_{c}$ can be at room temperature. As a quantitative illustration, we show ${T}_{c}$ can reach $270\phantom{\rule{4pt}{0ex}}\mathrm{K}$ for a superfluid in a realistic superlattice of transition metal dichalcogenide monolayers.