In one of them, Dr. Geim managed to levitate a frog in a magnetic field, for which he won an Ig Nobel — a parody award for “improbable research” — in 2000. On another occasion they produced a “gecko tape” that mimicked the way geckos and Spider-Man can walk on the ceiling.

The work on graphene arose from the pair’s desire to investigate the electrical properties of graphite. To do that, they needed very thin pieces, which they first tried to produce by filing down graphite crystals, with no luck. Then a technician showed them how graphite was cleaned before being observed in a scanning tunneling microscope by peeling layers off with Scotch tape.

Image Konstantin Novoselov, left, and Andre Geim. Credit... University of Manchester, via Associated Press

The scientists placed a flake of graphite on some tape and then by folding the tape over it again and again, gradually cleaved it thinner and thinner until it was only one atom thick.

The Scotch tape technique is still used, although the Manchester researchers have switched to a different tape. Dr. Geim once described the process as “very nonboffinlike” — using British slang for a research scientist — and an example of how you could do great experiments even if you did not have the resources of Harvard or Cambridge behind you. “You can still do something amazing,” he said.

The first two papers on graphene were published in Science and online in 2004. Three more appeared in 2005. Since then, the Swedish Academy said, “research in this area has literally exploded,” producing a growing number of papers about graphene, its amazing properties and its promise.

If scaled up to the thickness of plastic refrigerator wrap, a sheet of graphene stretched over a coffee cup could support the weight of a truck bearing down on a pencil point, according to tests conducted by two Columbia University researchers, Jeffrey Kysar and James Hone.