Phase Diagram of High-Temperature Electron-Hole Quantum Droplet in Two-Dimensional Semiconductors

Quantum liquids, systems exhibiting effects of quantum mechanics and quantum statistics at macroscopic levels, represent one of the most exciting research frontiers of modern physical science and engineering. Notable examples include Bose-Einstein condensation (BEC), superconductivity, quantum entanglement, and a quantum liquid. However, quantum liquids are usually only stable at cryogenic temperatures, significantly limiting fundamental studies and device development. Here we demonstrate the formation of stable electron-hole liquid (EHL) with the quantum statistic nature at temperatures as high as 700 K in monolayer MoS₂ and elucidate that the high-temperature EHL exists as droplets in sizes of around 100-160 nm. We also develop a thermodynamic model of high-temperature EHL and, based on the model, compile an exciton phase diagram, revealing that the ionized photocarrier drives the gas-liquid transition, which is subsequently validated with experimental results. The high-temperature EHL provides a model system to enable opportunities for studies in the pursuit of other high-temperature quantum liquids. The results can also allow for the development of quantum liquid devices with practical applications in quantum information processing, optoelectronics, and optical interconnections.