Phonon branch-resolved harmonic sampling

I would like to do a phonon band-resolved harmonic sampling, following the recipes from the paper by West and Estreicher (harmonic sampling). In fact, the method presented in the paper is already implemented in some codes devoted to the lattice dynamics (TDEP, fhi-vibes) at finite temperature.

The methodology is described in details in TDEP manual. Thus, I would just point to the equations (2)-(6) in the mentioned manual.

In this approach eigenvectors and eigenvalues of the dynamical matrix computed at the Gamma-point are used. In other words, we got data from the commensurate q-points.

In my case, I would like to do displacements using particular phonon branch. Which means that I should take only those eigenvectors and eigenstates of the dynamical matrix, which are related to the same phonon branch. Consequently, is there anyone who knows a method to assign phonon branch label to the specific eigenvector, eigenvalue? Any hints on how to do that are highly appreciated.

Since I already spend some time trying to figure it out on my own I would share what I have found at the moment. First of all, I looked if phonopy has anything related to this problem. It turned out that in phonopy during the plotting of the phonon dispersion there is a function, which estimates which q-points to connect (estimate_band_connection in the phonopy/phonon) and it works simply based on the scalar product between different eigenvectors at neighboring qpoints. I am not sure that this method is completely reliable, i.e. what do to with band-crossing (use symmetry representation of phonons of this branches?). In addition to that I have found out this paper (How to resolve a phonon-associated property into contributions of basic phonon modes), but this methodology seems to be similar to the one used in Phonopy and I am also not sure if this is what I need.

Sincerely, Nikita Rybin PhD student at the FHI, Berlin

• +1 Welcome to our site!
– Camps
Commented Jun 3, 2022 at 12:27
• +1 and welcome again to our community! Have you figured out anything more about this over the last 6+ months? Please update us! Commented Dec 10, 2022 at 16:34
• Hello! Perhaps, the most general formalism, which would allow to perform such analysis is based on the Berry phase theory. There are a bunch of papers doing this, for example, journals.aps.org/prb/abstract/10.1103/PhysRevB.101.081403, and nature.com/articles/s41467-021-21293-2. Authors of the latter paper wrote that the code they developed can be shared. I haven't tried it, since in my case the link to the paper I mentioned in the text of the question worked. Commented Dec 12, 2022 at 10:58
• @NikitaRybin nice. It looks like you've figured things out? Can you write a self-answer? It would be very helpful for future users that visit the site! Commented Feb 6, 2023 at 20:43