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 + 2E3 and 1A2 + 2E2 respectively.
Notes: it is helpful to think of the B=6 Skyrmion as three tori, stacked upon each other. The Cartesian realizations are orientated as if the C4 axis is aligned with the z-axis.
| Freq. | Symmetry | Description/Notes | Visualization |
|---|---|---|---|
| 0.25 | 1A1 | The outer tori move away from the central torus. |
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| 0.28 | 1B1 | The outer tori rotate in opposite directions. |
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| 0.33 | 2E1 | The outer tori rotate, deforming the Skyrmion like a hinge. |
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| 0.40 | 2E3 | The outer tori shear, out of phase. |
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| 0.41 | 2E2 | The outer tori split into two B=1 Skyrmions in the plane perpendicular to their common symmetry axis. The bottom mirrors the motion of the top, but rotated by 45 degrees. In both cases, the B=1's move towards a vertex of the core. |
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| 0.46 | 2E2 | A similar motion as the 0.41 mode, but the B=1's move towards a hole of the core. |
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| 0.47 | 1B2 | One of the outer tori pull away, leaving a B=4 core. |
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| 0.50 | 2E1 | The center torus pulls away from the Skyrmion while the outer tori deform to maintain the center of mass. |
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| 0.52 | 2E2 | Viewing the B=6 Skyrmion as two overlapping B=4 cubes, the cubes perform the B=4, 0.52 mode out of phase. |
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| 0.76 | 1A1 | The breathing mode. |
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| 0.77 | 2E1 | Two of the eight central holes grow while another two shrink. |
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| 0.80 | 2E3 | Viewing the B=6 Skyrmion as two overlapping B=4 cubes, the cubes perform the B=4, 0.62 mode out of phase. |
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| 0.87 | 1B2 | One half of the Skyrmion deflates as the other inflates. The central torus oscillates between the two outer tori, yielding a Newton's cradle motion of tori.
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| 0.90 | 2E2 | Similar to the 0.46 mode, but physically due to breathing. |
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| 0.95 | 1A1 | The Skyrmion elongates then flattens, maintaining D4h symmetry. |
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| 0.95 | 2E3 | One face inflates while the diagonally opposite face deflates. |
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| 1.01 | 2E1 | Viewing the B=6 Skyrmion as two overlapping B=4 cubes, the cubes perform the B=4, 0.94 mode out of phase. |
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| 1.08 | 2E2 | Similar to the 0.41 mode, but physically due to isorotation |
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| 1.11 | 2E3 | Viewing the B=6 Skyrmion as two overlapping B=4 cubes, the cubes perform the B=4, 1.14 mode in phase. |
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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.