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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

International audience; The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study, from first-principles, the anharmonic properties of solids. The free energy as a function of average atomic positions (centroids) can be used to study quantum or thermal lattice instability. In particular the centroids are order parameters in second-order structural phase transitions such as, e.g., charge-density-waves or ferroelectric instabilities. According to Landau's theory, the knowledge of the second derivative of the free energy (i.e. the curvature) with respect to the centroids in a high-symmetry configuration allows the identification of the phase-transition and of the instability modes. In this work we derive the exact analytic formula for the second derivative of the free energy in the self-consistent harmonic approximation for a generic atomic configuration. The analytic derivative is expressed in terms of the atomic displacements and forces in a form that can be evaluated by a stochastic technique using importance sampling. Our approach is particularly suitable for applications based on first-principles density-functional-theory calculations, where the forces on atoms can be obtained with a negligible computational effort compared to total energy determination. Finally we propose a dynamical extension of the theory to calculate spectral properties of strongly anharmonic phonons, as probed by inelastic scattering processes. We illustrate our method with a numerical application on a toy model that mimics the ferroelectric transition in rock-salt crystals such as SnTe or GeTe.

Using angle-resolved photoemission, we report the first observation of an incomplete charge-density-wave (CDW) gap opening for the quasi-two-dimensional material Mo4O11. Our data indicate that the gap opening occurs over a range of 0.5 (A)ngstrom(-1) in the Brillouin zone. The maximum gap opening (Delta(max)) we observe is 60 +/- 10 meV, which leads to a ratio of 2 Delta(max)/kT(CDW) = 14 +/- 6 (T-CDW = transition temperature), well above the weak coupling value of 3.5. Our data suggest that both 1-dimensional and 2-dimensional electronic states may be involved in the gap opening.

To get insight into the influence of different growth conditions of 1T-TiSe2 onto its charge density wave (CDW) phase transition, we have performed angle-resolved photoelectron spectroscopy (ARPES) on TiSe2 in its CDW phase at low temperatures comparing the results with resistivity measurements. Though the local resistivity maxima become less pronounced with increasing growth temperatures, we do not find this trend in ARPES. While shape and intensity of the emission near EF change drastically, the backfolded valence bands are not affected. The question of the significance of the peaking resistivity as a characteristical ‘fingerprint’ of the CDW phase transition arises.

Motivated by the recent synthesis of single layer TiSe2,we used state-of-the-art density functional theory calculations, to investigate the structural and electronic properties of zigzag and armchairedged nanoribbons (NRs) of this material. Our analysis reveals that, differing from ribbons of other ultra-thin materials such as graphene, TiSe2 NRs have some distinctive properties. The electronic band gap of the NRs decreases exponentially with the width and vanishes for ribbons wider than 20 Å. For ultranarrow zigzag-edged NRs we find odd-even oscillations in the band gap width, although their band structures show similar features. Moreover, our detailed magnetic-ground-state analysis reveals that zigzag and arm chair edged ribbons have non-magnetic ground states. Passivating the dangling bonds with hydrogen at the edges of the structures influences the band dispersion. Our results shed light on the characteristic properties of T phase NRs of similar crystal structures., Flemish Science Foundation (FWO-Vl); Methusalem foundation of the Flemish government; FWO Pegasus Long Marie Curie Fellowship; FWO Pegasus Short Marie Curie Fellowship; TUBITAK (114F397)

International audience; We present angle-resolved photoemission experiments on 1T-TiSe(2) at temperatures ranging from 13K to 288 K. The data evidence a dramatic renormalization of the conduction band below 100 K, whose origin can be related to the new potential responsible for the charge density wave phase at low temperature in this system. The renormalization translates into a substantial effective mass reduction of the dominant charge carriers and this observation is thus in opposition to the common belief that strong interactions produce heavier quasiparticles through an increased effective mass

The charge density wave phase transition of 1T-TiSe2 is studied by angle-resolved photoemission over a wide temperature range. An important chemical potential shift which strongly evolves with temperature is evidenced. In the framework of the exciton condensate phase, the detailed temperature dependence of the associated order parameter is extracted. Having a mean-field-like behaviour at low temperature, it exhibits a non-zero value above the transition, interpreted as the signature of strong excitonic fluctuations, reminiscent of the pseudo-gap phase of high temperature superconductors. Integrated intensity around the Fermi level is found to display a trend similar to the measured resistivity and is discussed within the model., 8 pages, 6 figures

International audience; Recently we found strong evidence in favor of a BCS-like condensation of excitons in 1T-TiSe2 [Cercellier , Phys. Rev. Lett. 99, 146403 (2007)]. Theoretical photoemission intensity maps have been generated by the spectral function calculated within the exciton condensate phase model and set against experimental angle-resolved photoemission spectroscopy data. The scope of this paper is to present the detailed calculations in the framework of this model. They represent an extension of the original excitonic insulator phase model of Jerome [Phys. Rev. 158, 462 (1967)] to three dimensional and anisotropic band dispersions. A detailed analysis of its properties and comparison with experiment is presented. Finally, the disagreement with density-functional theory is discussed.

International audience; We present recent results obtained using angle-resolved photoemission spectroscopy performed on 1T-TiSe2. Emphasis is put on the peculiarity of the bandstructure of TiSe2 compared to other transition metal dichalcogenides, which suggests that this system is an excellent candidate for the realization of the excitonic insulator phase. This exotic phase is discussed in relation to the BCS theory, and its spectroscopic signature is computed via a model adapted to the particular bandstructure of 1T-TiSe2. A comparison between photoemission intensity maps calculated with the spectral function derived for this model and experimental results is shown, giving strong support for the exciton condensate phase as the origin of the charge density wave transition observed in 1T-TiSe2. The temperature-dependent order parameter characterizing the exciton condensate phase is discussed, both on a theoretical and an experimental basis, as well as the chemical potential shift occurring in this system. Finally, the transport properties of 1T-TiSe2 are analyzed in the light of the photoemission results.