> The CNT layer has a nanostructured surface which tends to trap incoming gas molecules. These traps make the air molecules collide with the surface multiple times on average before leaving, resulting in a higher thermal accommodation coefficient for the CNT-air side compared to the mylar-air side. This difference between the surface properties results in a higher departing velocity for the air molecules on the CNT (bottom) side compared to the mylar (top) side. The net momentum transfer from these gas-surface interactions results in an upward recoil force that levitates the sample.
The light heats up the sample and the sample's construction mean the bottom heats air up faster than the top. This generates the lift. I wouldn't say that it's air currents or a difference in temperature between the top and the bottom. They even mention that it still levitates when the light shines from above.