Fractional phase slips across the charge-density-wave domain walls in 1-T TiSe2
The microscopic origin of the charge density wave (CDW) in 1\textit{T}-TiSe$_2$ remains controversial, with competing scenarios based on phonon-driven lattice instability and electronically driven excitonic correlations. Here, we combine low-temperature scanning tunneling microscopy with two-dimensional lock-in phase analysis to directly resolve the local CDW phase in real space and track its evolution across individual domain walls. In homogeneous regions, the CDW phase remains uniform; by contrast, across domain walls we uncover a robust and reproducible $2\pi/3$ phase shift that occurs collectively in all three symmetry-related CDW components. This nontrivial and correlated phase-slip configuration places stringent constraints on the order-parameter manifold and challenges the simplest purely phonon-driven commensurate lock-in picture, which would instead predict a $\pi$ phase shift. A minimal free-energy model incorporating both electron-phonon and electron-hole interactions reproduces the observed phase behavior and indicates that electronic interactions play an important role in shaping the local phase structure of the CDW order. These results establish domain walls as direct real-space probes of the microscopic interactions underlying multicomponent order and provide a general phase-resolved framework for constraining competing ordering mechanisms in correlated materials.