Quadrupolar Exciton and Excitonic Bose-Einstein Condensation in Layered Ga₂Ge₂X₂ (X = S, Se)

In many-particle physics, excitonic Bose-Einstein condensation (BEC) reveals a long-sought macroscopic quantum coherent phase, which is scarce. In single-phase multilayer Ga₂Ge₂X₂ (X = S, Se), we prove that a new kind of spatially indirect exciton, the quadrupolar exciton, can be optically generated, which is in stark contrast to the previous findings based exclusively on the artificial van der Waals layers of transition metal dichalcogenides (TMDCs). In particular, we verify the bright-dark exciton transition due to the fermion exchange interaction, indicative of excitonic BEC constituted by quadrupolar dark excitons with ultralong lifetimes. In light of long lifetimes, small effective mass, and large binding energy, theoretical critical temperature for the BEC in Ga₂Ge₂S₂/Ga₂Ge₂Se₂ achieves as high as 395.3/386.7 K and 98.8/96.7 K for the Berezinskii-Kosterlitz-Thouless (BKT) superfluid phase. In this work, results open new possibilities for the study of excitonic physics and correlated quantum phase.