We report high-resolution inelastic x-ray measurements of the soft phonon mode in the chargedensity-wave compound TiSe2. We observe a complete softening of a transverse optic phonon at the L point, i.e. q = (0.5, 0, 0.5), at T ≈ TCDW . Renormalized phonon energies are observed over a large wavevector range (0.3, 0, 0.5) ≤ q ≤ (0.5, 0, 0.5). Detailed ab-initio calculations for the electronic and lattice dynamical properties of TiSe2 are in quantitative agreement with experimental frequencies for the phonon branch involving the soft mode. The observed broad range of renormalized phonon frequencies is directly related to a broad peak in the electronic susceptibility stabilizing the chargedensity-wave ordered state. Our analysis demonstrates that a conventional electron-phonon coupling mechanism can explain a structural instability and the charge-density-wave order in TiSe2 although other mechanisms might further boost the transition temperature.PACS numbers: 71.45. Lr, 63.20.kd, 63.20.dd, 63.20.dk The origin of charge-density-wave (CDW ) order, i.e., a periodic modulation of the electronic density, is a long-standing problem relevant to a number of important issues in condensed matter physics, such as the role of stripes in cuprates [1] and charge fluctuations in the colossal magnetoresistive manganites [2]. Chan and Heine derived the criterion for a stable CDW phase with a modulation wavevector q as [3]where η q is the electron-phonon coupling (EPC) matrix element associated with a mode at an unrenormalized energy of ω bare , χ q is the dielectric response of the conduction electrons, and U q and V q are their Coulomb and exchange interactions. Static CDW order typically is taken as a result of a divergent electronic susceptibility χ q due to nesting, i.e. parallel sheets of the Fermi surface (FS) separated by twice the Fermi wavevector 2k f . Electron-phonon coupling (EPC) is required to stabilize the structural distortion and, hence, an acoustic phonon mode at the CDW wavevector q CDW = 2k f softens to zero energy at the transition temperature T CDW [3,4]. However, when electronic probes reported only small and not well nested Fermi surfaces this scenario has been discarded for the prototypical CDW compound TiSe 2 [5][6][7].Alternative scenarios such as indirect or band-type Jahn-Teller effects [6][7][8] and, most prominently, exciton formation [5,9,10] are discussed in the theoretical as well as experimental literature. More recently, van Wezel et al. have invoked a model including exciton formation as well as EPC [11] and have shown that it can explain data from angle-resolved photoemission spectroscopy (ARPES) [12], formerly taken as evidence of an excitonic insulating phase in TiSe 2 [9]. Determining the origin of CDW formation in TiSe 2 is all the more important with respect to the nature of superconductivity, which emerges both as function of pressure [13] and Cu intercalation [14]. In particular, pressure induced superconductivity is expected to be closely linked to the nature of the parent CDW state.I...

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature Tcdw. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at Tcdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states.