Exciton-phonon-driven charge density wave inTiSe2

In charge ordered materials such as the transition-metal dichalcogenides, the strong coupling between the lattice modes and the charges offers an excellent opportunity for novel phases and unconventional forms of superconductivity to arise. One such material, ${\text{TiSe}}_{2}$, has recently been found to superconduct under pressure [A. F. Kusmartseva, B. Sipos, H. Berger, L. Forr\'o, and E. Tuti\ifmmode \check{s}\else \v{s}\fi{}, Phys. Rev. Lett. 103, 236401 (2009)]. This finding cannot be explained simply as conventional superconductivity arising from an imbalance of charge carriers. To understand the nature of the fluctuations driving this superconducting phase, it is necessary to elucidate the driving mechanism of the charge ordered state from which it arises. Here we analyze the normal state of ${\text{TiSe}}_{2}$ starting from a tight-binding model to fit its band structure. The results of this procedure suggest that ${\text{TiSe}}_{2}$ is best viewed as a system of weakly linked quasi-one-dimensional chains. Building on these findings we propose a simplified quasi-one-dimensional model in which the interaction between the structural and excitonic charge fluctuations can be studied. The balance between competition and cooperation of these degrees of freedom is seen to have a large effect on the nature of the observed charge density wave transition. It is found that neither type of excitation can be held solely responsible for the transition and that it is rather the combined influence of both excitons and phonons that must underlie the observed properties of the charge density wave phase of ${\text{TiSe}}_{2}$. A qualitative description of experimental results based on the picture of hybrid exciton-phonon modes driving the transition is given and new experiments are proposed which may give quantitative insight into the extent to which each mode is involved.