A Smörgåsbord of Skyrmions: index, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
12a ε1.0954 ± 0.0001
b0.9999
r2.7878
VD(2092.9,12829.9,12831.4)
UD(473.5,438.6,448.4)
0.80%symD4h [R. Battye, N. S. Manton and P. Sutcliffe, Proc. Roy. Soc. Lond. A463, 261-279 (2007)]
A slice of the infinite twisted chain. Three cubes with the middle cube twisted by 90 degrees around the axis that joins the cubes.
12b ε1.0958 ± 0.0001
b0.9999
r2.3685
VD(3141.7,8327.0,8335.2)
UD(430.4,444.3,444.4)
9.80%symD5d
Two 7a-Skyrmions sharing a face. Can be thought of as a stack of tori. From top to bottom: a 2-, 3-, 2-, 3- and 2- torus are stacked on top of one another.
12c ε1.0961 ± 0.0001
b0.9999
r2.3890
VD(3115.0,8505.6,8513.9)
UD(429.3,448.0,448.0)
0.08%symD5h
Two 7a-Skyrmions sharing a face. Can be thought of as a stack of tori. From top to bottom: a 2-, 3-, 2-, 3- and 2- torus are stacked on top of one another. Their orientations are different than in the 12b-Skyrmion.
12d ε1.0962 ± 0.0001
b0.9999
r2.2408
VD(4970.4,4974.9,7682.2)
UD(453.0,446.2,446.3)
16.6%symC3v [R. Battye and P. Sutcliffe, Phys. Rev. C73, 055205 (2006)]
Out-of-phase graphene. Each hole on the top layer of the Skyrmion aligns with a vertex on the bottom layer, and vice versa.
12e ε1.0962 ± 0.0001
b0.9999
r2.4221
VD(3024.0,8506.5,9219.4)
UD(460.4,440.9,439.9)
30.5%symC1h
A cube attached to symmetric graphene.
12f ε1.0971 ± 0.0001
b0.9999
r2.5824
VD(2656.1,10496.7,10576.4)
UD(439.8,447.4,455.2)
5.85%symC1h
The 7a-Skyrmion weakly attached to the 5a-Skyrmion. The pentagonal symmetry of the 7a and the square symmetry of the 5a mean that there can be a maximum of one reflection symmetry.
12g ε1.0973 ± 0.0001
b0.9999
r2.4629
VD(2912.5,9283.8,9329.1)
UD(455.0,440.3,436.7)
1.30%sym∅
The 7a-Skyrmion attached to a cube, using a single Skyrmion.
12h ε1.0974 ± 0.0001
b0.9999
r2.2712
VD(5092.5,5094.5,7785.3)
UD(464.4,452.7,452.8)
0.97%symD3h [R. Battye, N. S. Manton and P. Sutcliffe, Proc. Roy. Soc. Lond. A463, 261-279 (2007)]
Three cubes arranged in a triangle with alternating faces up.
12i ε1.0976 ± 0.0001
b0.9999
r2.5269
VD(3646.3,8720.9,10310.3)
UD(487.7,439.8,444.3)
4.94%symC2v [R. Battye, N. S. Manton and P. Sutcliffe, Proc. Roy. Soc. Lond. A463, 261-279 (2007)]
Three cubes in a bent chain with alternating faces up.
12j ε1.0976 ± 0.0001
b0.9999
r2.4079
VD(3124.8,8315.0,9100.7)
UD(472.9,431.4,436.2)
0.58%symC1h
A cube attached weakly to symmetric graphene. Similar to the 12e-Skyrmion.
12k ε1.0978 ± 0.0001
b0.9999
r2.3114
VD(3512.4,7016.8,8425.8)
UD(436.3,440.0,452.4)
6.32%symC2
Asymmetric graphene.
12l ε1.0980 ± 0.0001
b0.9999
r2.2808
VD(3684.3,6633.0,8117.6)
UD(433.8,450.1,442.0)
16.1%sym∅
Asymmetric graphene. The visible central hole is surrounded by five holes, while on the other side it is surrounded by six holes.
12m ε1.0981 ± 0.0001
b0.9999
r2.5255
VD(3046.0,9372.7,10293.6)
UD(437.9,454.7,458.6)
1.16%symC1h
The 6a-Skyrmion attached to a distorted 6a-Skyrmion.
12n ε1.0981 ± 0.0001
b0.9999
r2.2882
VD(3676.7,6686.2,8195.5)
UD(451.3,443.8,434.2)
0.17%sym∅
Almost-symmetric graphene.
12o ε1.0982 ± 0.0001
b0.9999
r2.2571
VD(4020.6,6023.6,8018.9)
UD(431.1,452.7,444.7)
0.44%symD2h
Can be thought of as symmetric graphene or two clusters attached in a symmetric way; though it’s not obvious what the clusters are.
12p ε1.0983 ± 0.0001
b0.9999
r2.2369
VD(4955.2,5017.4,7673.3)
UD(452.3,444.0,442.9)
0.06%symC2v
Symmetric graphene.
12q ε1.0985 ± 0.0001
b0.9999
r2.2669
VD(4130.7,6072.2,7964.0)
UD(483.5,434.4,429.8)
1.49%symD2h
Can be thought of as symmetric graphene or two 6a-Skyrmions attached in a symmetric way.
12r ε1.0985 ± 0.0001
b0.9999
r2.6469
VD(2749.9,10793.4,11456.6)
UD(447.9,459.1,456.5)
0.58%symC1h
Similar to the 12m-Skyrmion.
12s ε1.0985 ± 0.0001
b0.9999
r2.2914
VD(3580.9,6831.3,8164.8)
UD(442.1,447.2,446.5)
0.52%symC1h
The larger cluster looks like an 8b-Skyrmion with D6d symmetry. This configuration is unstable alone, but stabilizes when attached to the cluster on the right.
12t ε1.0988 ± 0.0001
b0.9999
r2.6807
VD(2749.0,11102.0,11773.9)
UD(458.2,454.8,455.9)
0.03%symC1h
Two weakly bound 6a-Skyrmions.
12u ε1.0990 ± 0.0001
b0.9999
r2.3255
VD(4953.4,5674.3,8453.6)
UD(503.9,438.3,428.8)
0.03%symC2v
Three cubes arranged in an approximate triangle. The two tightly bound cubes have the same orientation, unlike the symmetric triangular configuration 12h.
12v ε1.0995 ± 0.0001
b0.9999
r2.2139
VD(4590.6,5212.7,7337.7)
UD(463.5,450.3,433.0)
0.03%symD2d
Symmetric graphene with a well-defined edge. A slice of the infinite two-layer graphene solution.
12w ε1.0995 ± 0.0001
b0.9999
r2.5117
VD(3495.3,8747.8,10211.9)
UD(479.4,449.4,439.8)
0.69%symC1h
A cube, tetrahedron, and 5a-Skyrmion bound together into a bent chain.
12x ε1.0999 ± 0.0001
b0.9999
r2.3283
VD(4080.8,6621.1,8579.5)
UD(433.0,464.1,455.9)
0.66%symC1h
The tetrahedron weakly bound to symmetric graphene.
12y ε1.1001 ± 0.0001
b0.9999
r2.6114
VD(2979.3,10197.2,11177.6)
UD(464.0,452.2,450.0)
0.06%symC1h
A bent chain. A natural extension of the 11g-Skyrmion.
12z ε1.1002 ± 0.0001
b0.9999
r2.4169
VD(3676.9,8489.2,8598.3)
UD(462.8,441.6,433.1)
0.06%symC2v
A D6d symmetric 8b-Skyrmion weakly bound to the cube.
12aa ε1.1002 ± 0.0001
b0.9999
r2.4595
VD(3586.2,8722.6,9151.0)
UD(445.1,456.2,469.9)
0.03%sym∅
Two weakly bound 6a-Skyrmions.
12ab ε1.1003 ± 0.0001
b0.9999
r2.4875
VD(3498.8,8539.9,9931.3)
UD(449.2,453.7,464.7)
0.08%symC2v
Two weakly bound 6a-Skyrmions.