Signatures of Competing Orders in Ab Initio Calculations

Question

Some materials have various competing and/or synergistic orders, such as charge density waves and superconducting pairing.

Are there signatures of such an interplay between orders that can be seen in the results of ab initio calculations?

Answer 1

In the specific case of charge density wave and superconductivity, both are phenomena that can be calculated using density functional theory:

1. Charge density wave. It usually manifests as an imaginary phonon in the reference structure that drives the charge density wave formation.
2. Superconductivity. Phonon-mediated superconductivity can be calculated almost routinely in the context of density functional theory, the basic quantity being the electron-phonon matrix element.

A nice example of this interplay occurs in TiSe$_2$, and density functional theory is capable of describing both phenomena as explained in this paper.

I do not really have a good general answer, but I would say that the usual approach in a first principles context (e.g. DFT) would be to separately evaluate the energy of the system in the competing phases and then compare the results.