It is exceedingly interesting whether a lighter-than-air solid material can be created. Not an air-balloon, but a normal solid material. A bar of such material will not drop down when unhanded, but, on the contrary, will fly up. And it will be fly up until it fades from view.
The principle of creating such a material is simple enough in the abstract. It should be a porous material with no air in its pores. It is known that vacuum has no weight at all and has a much greater lift than any of light gases. Why has not such a material been created so far?

The problem is that the lift of the air-free cavities must be greater that the summarized weight of the cavity walls. This means that the walls must be extremely thin. But they are exposed to a high atmospheric pressure, so the walls must be made from a very strong material. Do you remember a well-known school experiment, when even an insignificant pressure reduction inside an empty tin causes its collapse by atmospheric pressure? And in our case we mean high vacuum.

This is the sticking point for inventors. However, even though no lighter-than-air material exists, a considerable progress has been made in this field. NASA has reported creation of aerogel, which is noted in the Guinness Book of World Records as a solid with the lowest density.
Interesting is the method of making the aerogel. A mixture of liquid glass and fast- evaporating liquid is heated in a closed chamber. The liquid starts boiling and escapes from the chamber. Silicon dioxide forms a light openwork structure – solid smoke – that is 99.8% cavities. Now it only remains to evacuate air from the cavities and a lighter-than-air material is created! 
 

Source: http://www.jpl.com.