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 + 2E1, 1A2 + 2E5 and 1A2 + 2E2 respectively.
The B = 8h Skyrmion has a torus on it's top and bottom. It is often useful to describe the vibrations in terms of deformations of these tori.
| Freq. | Symmetry | Description/Notes | Visualization |
|---|---|---|---|
| 0.13 | 2E3 | The top and bottom tori slide back and forth, out of phase, yielding a shear mode. |
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| 0.21 | 2E5 | The top and bottom tori rotate around an axis perpendicular to their symmetry axis, out of phase. |
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| 0.24 | 2E4 | The Skyrmion begins to split in half, along the x-axis and then the y-axis. |
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| 0.28 | 2E2 | Two opposite vertices of the equatorial hexagon move upwards while the edges which lie between them move downwards. |
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| 0.33 | 1B1 | The top and bottom tori rotate, out of phase. |
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| 0.40 | 2E1 | A single Skyrmion lying on a vertex of the equatorial hexagon pulls away from the center. The remaining Skyrmion deforms to compensate for this motion. |
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| 0.45 | 1A1 | The top and bottom tori move away from the center at the same time. |
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| 0.45 | 1B2 | The top and bottom tori move away from, and then towards the center, out of phase. |
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| 0.45 | 2E2 | The top and bottom tori split into individual Skyrmions, out of phase. |
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| 0.49 | 2E3 | The tori move from side to side in phase, while the equator moves in the opposite direction to keep the center of mass constant. |
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| 0.5 | 2E2 | The top and bottom tori split into individual Skyrmions, in phase. The equator deforms significantly to accommodate the splitting. |
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| 0.57 | 2E1 | Two sides of the hexagonal equator breathe, out of phase. |
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| 0.69 | 1B2 | The top and bottom tori breathe, out of phase. |
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| 0.70 | 1A1 | The entire Skyrmion breathes. |
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| 0.75 | 2E5 | Two opposite quarters of the Skyrmion inflate, pushing the torus closest to them away. |
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| 0.76 | 2E1 | One half of the Skyrmion inflates, pushing both tori away from the center. |
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| 0.87 | 2E5 | Two holes which lie on an axis stay stationary. The neighboring holes move towards one and away from the other. |
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| 0.88 | 2E4 | The top and bottom tori split into individual Skyrmions, out of phase. Unlike the 0.50 mode, the equator does not deform. |
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| 0.89 | 1A1 | The top and bottom tori breathe, in phase. |
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| 0.89 | 2E4 | The equator inflates along one axis and deflates along the perpendicular one. |
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| 0.90 | 2E1 | Similar to the 0.40 mode but physically due to isorotation. |
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| 0.96 | 2E2 | Two neighboring faces move towards, then away, from one another. |
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| 1.01 | 2E4 | Similar to the 0.24 mode but physically due to isorotation. |
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| 1.02 | 2E5 | Similar to the 0.21 mode but physically due to isorotation. |
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| 1.03 | 2E3 | A tri-axially symmetric breathing motion. |
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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.