The discovery of graphene, a honeycomb sheet of carbon, was so important it earned a Nobel Prize, yet graphene isn't an exotic material. You can make it yourself!
Graphene From a Pencil
When you draw with a pencil, you are depositing graphite onto paper. Graphite consists, essentially, of stacked and bonded layers of graphene. If you draw a thick pencil layer onto paper, you can use an eraser to remove the extra sheets to obtain single graphene sheets.
Graphene from Graphite
Take a crystal of graphite (pencil lead works) and a piece of tape. Stick the tape to the graphite to pull away a bit of graphite. Use more tape to pull away graphite from the bit stuck on the first piece of tape. You can pull away layers to obtain single sheets of graphene.
Graphene from Silicon
Silicon is very, very flat. If you draw graphite onto a sheet of silicon, a single sheet of graphite can be deposited on the silicon. If you have an ordinary light microscope, you can see the difference between the graphite layers and the single sheets of graphene.