Search

Charge density waves (CDWs) are understood in great details in one dimension, but they remain largely enigmatic in two dimensional systems. In particular, numerous aspects of the associated energy gap and the formation mechanism are not fully understood. Two long standing riddles are the amplitude and position of the CDW gap with respect to the Fermi level ($E_F$) and the frequent absence of CDW contrast inversion (CI) between opposite bias scanning tunneling microscopy (STM) images. Here, we find compelling evidence that these two issues are intimately related. Combining density functional theory and STM to analyse the CDW pattern and modulation amplitude in 1$T$-TiSe$_2$, we find that CI takes place at an unexpected negative sample bias because the CDW gap opens away from $E_F$, deep inside the valence band. This bias becomes increasingly negative as the CDW gap shifts to higher binding energy with electron doping. This study shows the importance of CI in STM images to identify periodic modulations with a CDW and to gain valuable insight into the CDW gap, whose measurement is notoriously controversial., Comment: Main text 8 pages, 4 figures + Supplemental Material 7 pages, 6 figures

The charge density wave (CDW) in solids is a collective ground state combining lattice distortions and charge ordering. It is defined by a complex order parameter with an amplitude and a phase. The amplitude and wavelength of the charge modulation are readily accessible to experiment. However, accurate measurements of the corresponding phase are significantly more challenging. Here we combine reciprocal and real space information to map the full complex order parameter based on topographic scanning tunneling microscopy (STM) images. Our technique overcomes limitations of Fourier space based techniques to achieve distinct amplitude and phase images with high spatial resolution. Applying this analysis to transition metal dichalcogenides provides striking evidence that their CDWs consist of three individual unidirectional charge modulations whose ordering vectors are connected by the fundamental rotational symmetry of the crystalline lattice. Spatial variations in the relative phases of these three modulations account for the different CDW contrasts often observed in STM topographic images. Phase images further reveal topological defects and discommensurations, a singularity predicted by theory for a nearly commensurate CDW. Such precise real space mapping of the complex order parameter provides a powerful tool for a deeper understanding of the CDW ground state whose formation mechanisms remain largely unclear.

We report a detailed study of the microscopic effects of Cu intercalation on the charge density wave (CDW) in 1T-CuxTiSe2. Scanning tunneling microscopy and spectroscopy reveal a unique, Cu-driven spatial texturing of the charge-ordered phase, with the appearance of energy-dependent CDW patches and sharp π-phase shift domain walls (πDWs). The energy and doping dependencies of the patchwork are directly linked to the inhomogeneous potential landscape due to the Cu intercalants. They imply a CDW gap with unusual features, including a large amplitude, the opening below the Fermi level, and a shift to higher binding energy with electron doping. Unlike the patchwork, the πDWs occur independently of the intercalated Cu distribution. They remain atomically sharp throughout the investigated phase diagram and occur in both superconducting and nonsuperconducting specimens. These results provide unique atomic-scale insight into the CDW ground state, questioning the existence of incommensurate CDW domain walls and contributing to understanding its formation mechanism and interplay with superconductivity.

We study the impact of Cu intercalation on the charge density wave (CDW) in $1T\text{\ensuremath{-}}{\mathrm{Cu}}_{x}{\mathrm{TiSe}}_{2}$ 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 ($xl0.02$) and a breaking up of the commensurate order into $2\ifmmode\times\else\texttimes\fi{}2$ 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.