The capability to isolate one to few unit-cell thin layers from the bulk matrix of layered compounds 1 opens fascinating prospects to engineer novel electronic phases. However, a comprehensive study of the thickness dependence and of potential extrinsic effects are paramount to harness the electronic properties of such atomic foils. One striking example is the charge density wave (CDW) transition temperature in layered dichalcogenides whose thickness dependence remains unclear in the ultrathin limit 2-5 .Here we present a detailed study of the thickness and temperature dependences of the CDW in VSe 2 by scanning tunnelling microscopy (STM). We show that mapping the real-space CDW periodicity over a broad thickness range unique to STM provides essential insight 6 . We introduce a robust derivation of the local order parameter and transition temperature based on the real space charge modulation amplitude. Both quantities exhibit a striking non-monotonic thickness dependence that we explain in terms of a 3D to 2D dimensional crossover in the FS topology. This finding highlights thickness as a true tuning parameter of the electronic ground state and reconciles seemingly contradicting thickness dependencies determined in independent transport studies.Following the ground-breaking exfoliation of graphite into one atom thin carbon sheets, an increasing number of layered compounds can now be isolated from their bulk matrix in the form of one to few unit-cell thin layers. These sheets often feature unique 7-9 or enhanced 2,10 properties in comparison to their parent bulk compounds. They depend on material thickness and can be further tuned through doping, electrostatic gating and assembly of distinct layers into complex heterostructures. Transition metal dichalcogenides (TMDs) are of particular interest in this context. They can be readily exfoliated into thin flakes down to the single unitcell limit 11 and offer a unique playground for studying the thickness dependence of their electronic properties. For example, in MoS 2 , photo active transitions become available in the

Ideal monolayers of common semiconducting transition-metal dichalcogenides (TMDCs) such as MoS, WS, MoSe, and WSe possess many similar electronic properties. As it is the case for all semiconductors, however, the physical response of these systems is strongly determined by defects in a way specific to each individual compound. Here we investigate the ability of exfoliated monolayers of these TMDCs to support high-quality, well-balanced ambipolar conduction, which has been demonstrated for WS, MoSe, and WSe, but not for MoS. Using ionic-liquid gated transistors, we show that, contrary to WS, MoSe, and WSe, hole transport in exfoliated MoS monolayers is systematically anomalous, exhibiting a maximum in conductivity at negative gate voltage ( V ) followed by a suppression of up to 100 times upon further increasing V. To understand the origin of this difference, we have performed a series of experiments including the comparison of hole transport in MoS monolayers and thicker multilayers, in exfoliated and CVD-grown monolayers, as well as gate-dependent optical measurements (Raman and photoluminescence) and scanning tunneling imaging and spectroscopy. In agreement with existing ab initio calculations, the results of all these experiments are consistently explained in terms of defects associated with chalcogen vacancies that only in MoS monolayers, but not in thicker MoS multilayers nor in monolayers of the other common semiconducting TMDCs, create in-gap states near the top of the valence band that act as strong hole traps. Our results demonstrate the importance of studying systematically how defects determine the properties of 2D semiconducting materials and of developing methods to control them.

We acknowledge the support of the Hungarian National Research Fund OTKA NN76727, CNK80991, T72954, K107228, the New Hungary Development Plan TA ḾOP-4.2.1/B-09/1/KMR-2010-0002, and the Swiss NSF and its NCCR MaNEP. E .K. acknowledges support of the Bolyai Jańos Scholarship of the Hungarian Academy of Sciences.

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 earlier 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 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 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.The spatially averaged intensity of the CDW order parameter is usually accessed by scattering techniques sensitive to the local lattice distortions, or electron spectroscopy and transport measurements sensitive to changes in the band structure due to the opening of the CDW gap.Detecting the phase has been traditionally limited to dynamic experiments (for good reviews see e.g. refs 1, 2). More recently, different strategies have been followed to access phase

Contrast inversion (CI) between opposite polarity scanning tunneling microscopy (STM) images, although seen as a hallmark of the charge density wave (CDW) ground state, is only rarely observed. Combining density functional theory and STM on pristine 1T-TiSe2, we show that CI takes place at increasingly negative sample bias as the CDW gap shifts to higher binding energy with electron doping. There is a point where the gap is shifted so far below the Fermi level (EF) that CI disappears altogether. Contrast inversion thus gives a different insight into the CDW gap, whose measurement by scanning tunneling spectroscopy is notoriously controversial. It provides unique evidence that the CDW gap is not bound to EF and that it can develop deep inside the valence band, an explicit constraint on any model description of the CDW phase transition.The charge density wave (CDW) ground state is an atomic length scale periodic distortion, combining lattice and charge degrees of freedom [1]. The precise mechanism driving this quantum phase transition remains largely unknown. Fermi surface nesting, electron-electron or electron-phonon interactions, and coupling of electrons to other degrees of freedom in the host crystal are among the main mechanisms discussed over the years [2,3].Below the CDW phase transition, atoms rearrange into periodic lattice distortions. Concomitantly, charge is redistributed in real space to form alternating regions of charge accumulation and charge depletion. In the classic Peierls mechanism, mostly states in the vicinity of the Fermi level (EF) are involved in the CDW formation and a gap opens at EF. Scanning tunneling microscopy (STM), owing to its high spatial topographic resolution, is an ideal probe to characterize the real space charge ordering. In the Peierls scenario, STM images of the CDW at negative bias will show enhanced intensity over charge accumulation regions, whereas images of the same area at positive bias will show enhanced intensity over charge depleted regions. This is known as contrast inversion (CI) of the CDW STM contrast between positive and negative sample bias images.