There is an excellent review paper by K. Rossnagel on the origin of charge density waves (CDWs) in the transition metal dichalcogenide compounds (such as 2H-NbSe, 1T-TiSe, 2H-TaSe, etc.) . A lot of the work on these materials was undertaken in the 70s and 80s, but there has been a recent revival of interest because of the nature of superconductivity in a few of these compounds.
By “nature”, I mean that the phase diagrams in these materials bear a striking resemblance to the phase diagram in the cuprates, except that the anti-ferromagnetism is replaced by a CDW phase. Shown below is the phase diagram for 1T-TiSe under pressure and with copper intercalation (taken from this paper).
Strangely, with copper intercalation, the Hall resistance is negative, while it is positive under pressure. This is interesting because like the cuprates, superconductivity can be brought about with either electrons or holes as majority carriers. A similar phase diagram is also observed for another TMD 1T-TaS (see here for instance). 1T-TaS has also been shown to exhibit Mott physics at low temperature in the parent compound.
It is suspected that the origin of the CDWs in 1T-TiSe and 1T-TaS are at least in part electronically driven (see Rossnagel’s review article and references therein). This makes the observation of the superconductivity in these compounds all the more interesting — as the superconductivity may also be primarily electronically driven. I have also blogged previously about another set of CDW materials (the rare earth tritellurides) that exhibit cuprate-like phase diagrams including an antiferromagnetic phase, and also about the interplay between CDWs and superconductivity in NbSe.
It seems to me that there are some really quite fundamental open questions in the study of these compounds, which is in part why I keep re-visiting this topic myself.