Dr. Geim says his main contribution was not the tape, but his way of spotting the single-layer graphene among the thicker flakes. The highest of high-tech microscopes can spot the bumps of a single atom, but using them to measure the thickness of each flake is impossibly slow. A one-atom-thick sheet is generally invisible, but Dr. Geim found that a sheet that thin does change the color of the silicon oxide layer atop the wafer, much as a sheen of oil on water generates a rainbow of colors.

Now, at a glance under a simple light microscope, researchers can tell whether a graphite flake is more than 100 layers thick (yellow), 30 to 40 layers thick (blue), about 10 layers thick (pink) or just a single-layer (pale, almost invisible, pink).

Image Dr. Andre Geim Credit... University of Manchester

Dr. Geim said he thought the earlier researchers — and indeed, anyone who has written with a pencil — was likely to have produced graphene but simply could not see it.

After researchers had an easy way to make graphene, they started playing with all types of experiments. Techniques borrowed from silicon technology allow them to cut graphene into specific shapes, constructing transistors and other electronic devices. They face years of challenges. The ragged edges can affect the devices’ properties, though they also offer the possibility of tuning the electronics by attaching various atoms at the edges.

Scientists have also explored more esoteric aspects of graphene, including a prediction from more than half a century ago. Because of how the electrons flowing in graphene interact with the honeycomb chicken-wire structure, they behave as if they have no mass, always traveling at the same speed regardless of their energy, like particles of light. Dr. Beenakker at Leiden has proposed taking advantage of graphene’s unusual behavior in a new type of electronics that he calls “valleytronics.”

Independently, Dr. Geim and Dr. Kim at Columbia demonstrated a phenomenon known as the quantum Hall effect, where the electrical resistance perpendicular to the current and an applied magnetic field jumps between certain discrete values. The quantum Hall effect is usually seen just at very low temperatures in semiconductors, but it occurs in graphene at room temperature. A more recent paper by Dr. Geim and his collaborators describes a suspended graphene sheet as not flat, but wavy.