In quadratic band touching fermionic systems, vortex cores support color-degenerate competing orders from SO(5) mass algebra splitting zero modes, while skyrmions allow additional Kekule or s-wave orders.
It should be notated that the exchange of two layers and valleys are accompanied by the inversions of momentum axes ky→− ky and kx→− kx, respectively
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Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
In quadratic band touching fermionic systems, vortex cores support color-degenerate competing orders from SO(5) mass algebra splitting zero modes, while skyrmions allow additional Kekule or s-wave orders.