When the atoms of a crystal move along the path of a circularly polarized phonon mode, they form closed loops and therefore carry angular momentum. Below, we show animations of two typical phonon modes of graphene that involves circular motions.
Phonon angular momentum (PAM) therefore refers to orbital motion of an atom in a lattice about its equilibrium position, and it can be likened to an electron's orbital about the atomic center. In 2014, Niu et al. first introduced the concept of phonon angular momentum in their PRL paper.
"Angular momentum of phonons and the Einstein-de Haas effect", PRL, 112, 085503 (2014)
For detail formulation of the PAM, please refer to this post.
The script pham_band.py reads the phonon frequencies and phonon polarization
vectors from phonopy output band.yaml, then calculate the PAM according to
the formula in the 2014 PRL paper, finally superimpose the phonon angular
momentum on the phonon dispersion.
The phonon related data for ZnO were retrieved from phonopy examples.
- First, generate the phonon band data using
phonopy
cd examples/ZnO
phonopy --nac band.conf- Secondly, execute the script
# horizontal 1x3 layout
pham_band.py --layout h -i band.yaml -t 0
# or vertical 3x1 layout
pham_band.py --layout v -i band.yaml -t 0The resulting images follow:
