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 3T1u, 3T1g and 3T2g respectively.
| Freq. | Symmetry | Description/Notes | Visualization |
|---|---|---|---|
| 0.32 | 5Hg | Two opposite faces pull away from the center of the Skyrmion. |
|
| 0.38 | 5Hu | The energy density concentrates around an edge. Asymptotically this becomes the edge of a B=4 Skyrmion. The opposite side of the Skyrmion becomes a B=3 torus. |
|
| 0.47 | 3T2u | Two nearby faces pull away from the center. The remaining energy density forms a long hat on the opposite side of the Skyrmion. Asymptotically, it is pulling out 3 tori and leaving a 1-Skyrmion behind. |
|
| 0.54 | 4Gu | The dodecahedron contains five cubes. Here, a single cube is deformed while retaining tetrahedral symmetry. |
|
| 0.73 | 1Ag | The breathing mode. |
|
| 0.76 | 3T1u | A dipole breathing mode. |
|
| 0.84 | 4Gg | This is the mode described by Singer and Sutcliffe. Asymptotically, six individual Skyrmions travel along the Cartesian axes towards one at the origin. They form the dodecahedron then become a cube. Our deformation is not large enough to reach the cubic structure. The dodecahedron contains five cubes and so there are naively five of these modes. However, they are linearly dependent as the sum of all five modes is trivial. |
|
| 0.91 | 5Hg | Similar to the 0.32 mode, but physically due to breathing. |
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| 0.94 | 4Gu | A non-trivial out-of-phase isorotation which retains the tetrahedral symmetry of one of the dodecahedron's cubes. |
|
| 1.01 | 4Gg | Another non-trivial out-of-phase isorotation which retains the tetrahedral symmetry of one of the dodecahedron's cubes, but in a different way than the 0.94 4Gu mode. |
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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.