Is there a schematic symbol for a supercapacitor?
A supercapacitor or Electric double-layer capacitor (EDLC) is functionally no different from a polarized capacitor, at the schematic level-of-abstraction. Hence, there is no standard symbol for it (yet), as distinct from the polarized capacitor symbol. 

As with other schematic symbols, if there is a pressing need to indicate that a particular part on a design is a supercapacitor, that would be an annotation to the symbol.