What's the index (or topological charge) of this vector field image?

Question

I am doing some research in a condensed matter system, and found this Berry curvature / vector field configuration that is unusual. I cannot find another example of something similar, either from physics or math examples. To me it looks like a i=+2 that had another half turn added to one side.

research level topology vector fields weyl semimetal

mike stone · Answer

It could make sense for a nematic liquid crystal, where $uparrow$ and $downarrow$ correspond to the same state. Otherwise the configuration is discontinuous and does not have a winding number. Where did you get this particular configuration?

Answered by mike stone on February 12, 2021

What's the index (or topological charge) of this vector field image?

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