Ab initio study of exciton insulator phase: Emergent $\textit{p}$-wave spin textures from spontaneous excitonic condensation

An excitonic insulator$^{1,2}$ (EI) is a correlated many-body state of electron-hole pairs, potentially leading to high-temperature condensate and superfluidity$^{3-7}$. Despite ever-growing experiments suggesting possible EI states in various materials, direct proofs remain elusive and debated. Here we address the problem by introducing an ab initio methodology, enabling the parameter-free determination of electron-hole pairing order parameter and single-particle excitations within a Bardeen-Cooper-Schrieffer (BCS)-type formalism. Our calculations on monolayer 1T'-MoS$_{2}$$^{8,9}$ reveals that it is an unconventional EI with a transition temperature ~900K, breaking spontaneously the crystal's inversion, rotation, and mirror symmetries, while maintaining odd parity and unitarity. We identify several telltale spectroscopic signatures emergent in this EI phase that distinguish it from the band insulator (BI) phase, exemplified with a giant $\textbf{k}$-dependent $\textit{p}$-wave spin texture.