this article at Physical Review Focus, based on a paper yet to be published at Physical Review Letters.
I would suggest reading that first, then read Jones' article re same: here.
Jones links to a wonderful explanation of Topological Insulators by Condensate experimentalist and proprietor of Uncertain Principles, Chad Orzel. Read that too, then let's talk.
Interesting stuff, but Jones' title may give the false impression that we'll soon have anti-gravity and levitating cars as in Star Wars. We won't, not anytime soon. "Anti-Gravity" already exists, but it exists everywhere: we call it Dark Energy, and we haven't a clue as to what it is.
To date, the only known "levitators" are Maharishi Maheesh Yogi and David Blaine. :-)