Broken piece in headband

If they are still under warranty, pursue that option. If you want to try a repair super glue probably wouldn't hold, but there's a version for pvc that might. PVC is commonly used in headphone manufacture, but that might not be the case here. Plastics and the adhesives that work on them vary, for example the plastic that many adhesive come in is pretty darn hard to glue with anything... point being PVC adhesive won't work with vinyl and so on. Liquid exopy might or might not hold and would probably be unsightly (you'd be the judge of whether that matters) molding epoxy putty around that break, if it doesn't impair function might suit you. For the prettiest repair that will hold under stress you need to identify the plastic and use a solvent adhesive made for it. Say, PVC gorilla glue for pvc. If going by trial and error you can test in a small hidden spot to see what works before making a mess with the wrong adhesive. 3M scotch weld is a good choice if you don't know what plastic it is but it is pricey. I'd tell you where to buy a replacement but couldn't find any.