Each mode's symmetry is denoted as dI, it has a degeneracy d, and transforms as an irrep I of the Skyrmion's symmetry group. We use the notation of Cotton. Character tables may be found here.
The zero modes are translations, rotations and isorotations. These decompose as 2E1u + 1A2u, 2E1g + 1A2g and 2E2u + 1A2g respectively. Note that, for the toroidal configuration, a rotation about the z-axis is equivalent to a isorotation about the white/black axis.
| Freq. | Symmetry | Description/Notes | Visualization |
|---|---|---|---|
| 0.37 | 2E2g | The torus splits into two individual Skyrmions. |
|
| 0.99 | 2E1u | Two halves of the torus isorotate in different directions, around the white/black axis. This may also be interpreted as two individual Skyrmions breathing out of phase. |
|
| 1.03 | 1A1g | The breathing mode. |
|
| 1.08 | 1A2u | The equator of the color wheel moves up and down. |
|
Notes
Hover over an image (or if you're on a tablet/phone: tap on an image) to make it come to life. The hover-over text tells you the Cartesian realization of the element of the irrep you are looking at.