I'm sure a lot of people have chosen this gemstone but it's a favorite of mine from trips to the American south west.

Turquoise is an intelligent type gem like Peridot and Pearl.
She has two gems, one on each temple but she is not a fusion.
Her "weapon" is her ability to shoot energy from her index finger (think of little kids playing cops and robbers).
When in a fighting stance her weapon materializes as glasses which improve her accuracy.
She is a refugee gem from the Gem Homeworld who immigrated to Earth.

She is only loosely affiliated with the Crystal Gems. She announced her arrival and was given a set of guidelines for settling on Earth, mostly to do no harm.