Graphene introduced a new paradigm in materials science. Not only does it have pretty incredible electronic properties, it’s technically a 2-Dimensional crystal, previously thought to have been impossible to exist. I think the sellotape idea was a kind of “why not give this a try” and it happened to work. The sticky tape prevents the Graphene from being suspended freely in air, making it stable to view under an electron microscope. I’ve been to conferences in which Andre Geim (the discoverer of single layer Graphene) has given talks, and he’s super clever!
One cool property of Graphene (other than 1 square metre of single layer Graphene held at the edges could theoretically hold the weight of an average Cat!) is its ability to have ballistic transport of electrons, which means that as Graphene conducts electrons, the electrons don’t knock into anything, making it super low resistance.