# The B = 5 Skyrmion's vibrational modes

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 1B2 + 2E, 1A2 + 2E and 1A2 + 2E respectively.

We have found it is helpful to view the B=5 Skyrmion from above when describing these modes, and hence have plotted the viewpoint from above as well as our standard angle.

Note: it is also helpful to interpret the top and bottom edges of the B=5 Skyrmion as single Skyrmions and the central equator as a torus. We will refer to these concepts throughout the descriptions.

Freq. Symmetry Description/Notes Visualization
0.10 2E
The top edge shears away from the rest of the Skyrmion, which moves to preserve the center of mass. The bottom edge remains stationary.
0.23 1B1
The top and bottom edges twist in opposite directions.
0.42 1A1
The entire Skyrmion elongates. Asymptotically, it becomes a chain of five individual Skyrmions.
0.43 1B2
The Skyrmion splits in half, four of its holes lying in the incision plane.
0.45 2E
A B=2 torus emerges from the top of the Skyrmion. Asymptotically, the Skyrmion splits into B=2 and B=3 clusters.
0.49 1B2
The top edge detaches from the rest, leaving a B=4 core. In the other direction, the bottom edge detaches instead.
0.51 2E
A B=1 Skyrmion detaches from the equatorial torus, along the x-axis.
0.57 1A1
The Skyrmion elongates while also pushing outwards. The asymptotic configuration looks like a riding saddle with D2d symmetry.
0.61 1B1
The equator, interpreted as a B=2 Skyrmion, performs 1+1 90 degree scattering.
0.77 1A2
The top and bottom halves of the Skyrmion twist in different directions.
0.8 2E
One of the four long faces (containing two holes) inflates while the opposite one deflates. The remaining two remain unchanged.
0.81 1A1
The top and bottom edges break away from the equator, which deforms into a square-like object.
0.84 1B1
The top half isorotates clockwise around the black/white axis while the bottom half isorotates in the other direction.
0.89 1B2
The top half inflates while the bottom half deflates.
0.95 1B2
Similar to the 0.43 mode, but physically due to breathing.
0.95 2E
Similar to the 0.45 mode, but physically due to breathing.
1.00 1A1
The breathing mode.
1.04 1A2
The top and bottom half isorotate in the same direction, but the equator remains unchanged. This is similar to the 0.84 mode but in phase.
1.09 1A1
Similar to the 0.57 mode, but physically due to breathing.

## 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.