under pressure*

Spontaneous condensation of excitons is a long sought phenomenon analogous to the condensation of Cooper pairs in a superconductor. It is expected to occur in a semiconductor at thermodynamic equilibrium if the binding energy of the excitons overcomes the band gap, giving rise to a new phase: the 'excitonic insulator' (EI). Transition metal dichalcogenides are excellent candidates for the EI realization because of reduced Coulomb screening, and indeed a structural phase transition was observed in few-layer systems. However, previous work could not disentangle to which extent the origin of the transition was in the formation of bound excitons or in the softening of a phonon. Here we focus on bulk MoS₂ and predict from first principles that at high pressure it is prone to the condensation of genuine excitons of finite momentum, whereas the phonon dispersion remains regular [arXiv:2011.02380]. We show that the self-consistent electronic charge density of the EI sustains an out-of-plane permanent electric dipole moment with an in-plane antiferroelectric texture: At the onset of the EI phase, those optical phonons that share the exciton momentum provide a Raman fingerprint for the EI formation, which was observed experimentally.