Excitonic Tonks-Girardeau and charge-density-wave phases in monolayer semiconductors

Excitons in two-dimensional semiconductors provide a novel platform for fundamental studies of many-body interactions. In particular, dipolar interactions between spatially indirect excitons may give rise to strongly correlated phases of matter that so far have been out of reach of experiments in ultracold gases. Here, we show that excitonic few-body systems in atomically thin transition-metal dichalcogenides confined to a one-dimensional geometry undergo a crossover from a Tonks-Girardeau to a charge-density-wave regime. To this end, we take into account realistic system parameters and predict the effective exciton-exciton interaction potential. We find that the pair correlation function of excitons contains key signatures of the many-body crossover already at small exciton numbers and show that photoluminescence spectra provide readily accessible experimental fingerprints of these strongly correlated quantum many-body states. We then study the system within the Luttinger Liquid theory that agrees remarkably well with few-body exact calculations in predicting spatial correlation functions and blueshifting of the photoluminescence spectra for an increasing number of excitons. Finally, we predict the excitation spectrum of the system for all densities in the many-body limit and study the temporal-spatial pair-correlation functions of emitted photons. Our findings showcase TMDs as an alternative platform for many-body dipolar physics in low-dimensions that may outperform most alternative experimental settings in different tasks and that may complement studies using ultracold molecules that have yet to reach the required densities and control to realize their full potential.