Revisiting the charge-density-wave superlattice of 1$T$-TiSe$_2$

Abstract: A number of intriguing phenomena, including exciton condensation, orbital ordering, and emergence of chirality, have been proposed to accompany charge-density-wave (CDW) formation in the layered transition metal dichalcogenide 1$T$-TiSe$_2$. Explaining these effects relies on knowledge of the atomic displacement pattern underlying the CDW, yet structural proposals based on spatially-averaging bulk crystal diffraction and surface-dependent scanning tunneling microscopy have remained inconsistent. Here, we revisit the CDW superlattice structure with selected-area electron diffraction, a bulk-sensitive probe capable of capturing sub-micrometer spatial variations while maintaining high momentum resolution. We resolved two distinct, spatially separated CDW phases characterized by different interlayer ordering. In both phases, previously reported atomic displacement patterns fail to account for the observed extinction rules. Instead, our analysis reveals a new superlattice structure, which features a large number of nearly degenerate CDW domains. These findings not only provide a new basis for understanding the gyrotropic electronic order and metastability in 1$T$-TiSe$_2$, they also underscore the importance of bulk-sensitive mesoscopic techniques in investigating materials that host unconventional superlattices.