Two-dimensional materials cannot exist

What actually happened

The theoretical objection, associated with Landau and Peierls, was serious and long-standing: thermal fluctuations should destroy long-range order in a strictly 2D crystal. The conclusion drawn from it, that such materials could not be made, turned out to be a misreading of a result about idealized flat sheets. Real graphene ripples slightly in the third dimension, which stabilizes it.

The method is the famous part. Geim's lab ran "Friday night experiments," speculative projects with no expectation of success, and the winning technique was pressing sticky tape onto graphite, peeling it off, and repeating until single-atom layers remained. It is essentially free, and the resulting material is around 200 times stronger than steel, conducts heat and electricity superbly, and is transparent. The Nobel followed six years later, one of the fastest turnarounds in the prize's history. Graphene opened an entire field of 2D materials that the textbook said should not be there.