Nematic and stripe orders within the charge density wave state of doped TiSe₂

In this work, we present a theory to reconcile conflicting experimental claims regarding the charge density wave (CDW) state in TiSe₂, including whether there is a single or multiple CDW transitions and the occasional observation of rotation symmetry breaking. Using a k.p model coupled to the CDW order parameter, we show how commonplace conduction band doping x must cause a transition from the C₃-symmetric 3Q state to a C₃-breaking 1Q stripe state at a critical doping x_1Q. In addition, for sufficient ellipticity of the conduction bands, as displayed by the realistic band structure of TiSe2, a new nematic 3Q state also emerges in a region with x < x_1Q driven by a van Hove singularity. We then show how both stripe and nematic states emerge from a minimal interacting tight-binding model, for both positive and negative initial gaps. Our theory clarifies a long-standing puzzle and its predictions can be verified with a variety of probes including transport, photoemission and tunneling.