Superconductivity and hybrid soft modes in TiSe$_2$
  The competition between superconductivity and other ground states of solids is one of the challenging topics in condensed matter physics. Apart from high-temperature superconductors [1,2] this interplay also plays a central role in the layered transition-metal dichalcogenides, where superconductivity is stabilized by suppressing charge-density-wave order to zero temperature by intercalation [3] or applied pressure [4-7]. 1T-TiSe$_2$ forms a prime example, featuring superconducting domes on intercalation as well as under applied pressure. Here, we present high energy-resolution inelastic x-ray scattering measurements of the CDW soft phonon mode in intercalated Cu$_x$TiSe$_2$ and pressurized 1T-TiSe$_2$ along with detailed ab-initio calculations for the lattice dynamical properties and phonon-mediated superconductivity. We find that the intercalation-induced superconductivity can be explained by a solely phonon-mediated pairing mechanism, while this is not possible for the superconducting phase under pressure. We argue that a hybridization of phonon and exciton modes in the pairing mechanism is necessary to explain the full observed temperature-pressure-intercalation phase diagram. These results indicate that 1T-TiSe$_2$ under pressure is close to the elusive state of the excitonic insulator. 
M. Maschek, S. Rosenkranz, R. Hott, R. Heid, D. Zocco, A. H. Said, A.   Alatas, G. Karapetrov, Shan Zhu, Jasper van Wezel an...
cond-mat.supr-con