We present a model for the combined nematic and `smectic or stripe-like orders seen in recent scanning tunneling microscopy (STM) experiments in cuprates. We model the stripe order as an electronic charge density wave with associated Peierls distorti
on -- a `Pomeranchuk wave. Disorder restricts this primary order to nanoscale domains, while secondary coupling to strain generates nematic order with considerably longer range.
A general constructive procedure is presented for analyzing magnetic instabilities in two-dimensional materials, in terms of [predominantly] double nesting, and applied to Hartree-Fock HF+RPA and Gutzwiller approximation GA+RPA calculations of the Hu
bbard model. Applied to the cuprates, it is found that competing magnetic interactions are present only for hole doping, between half filling and the Van Hove singularity. While HF+RPA instabilities are present at all dopings (for sufficiently large Hubbard U), in a Gutzwiller approximation they are restricted to a doping range close to the range of relevance for the physical cuprates. The same model would hold for charge instabilities, except that the interaction is more likely to be q-dependent.
