Stripe and short range order in the charge density wave of 1T-Cu$_x$TiSe$_2$
We study the impact of Cu intercalation on the charge density wave (CDW) in 1T-Cu$_{\text{x}}$TiSe$_{\text{2}}$ by scanning tunneling microscopy and spectroscopy. Cu atoms, identified through density functional theory modeling, are found to intercalate randomly on the octahedral site in the van der Waals gap and to dope delocalized electrons near the Fermi level. While the CDW modulation period does not depend on Cu content, we observe the formation of charge stripe domains at low Cu content (x$<$0.02) and a breaking up of the commensurate order into 2$\times$2 domains at higher Cu content. The latter shrink with increasing Cu concentration and tend to be phase-shifted. These findings invalidate a proposed excitonic pairing as the primary CDW formation mechanism in this material.