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Nobel Prize in Physics For Discovery of Graphene
bugsbunnyak writes "The 2010 Nobel Prize in Physics has been awarded for the discovery of graphene to Andre Geim and Konstantin Novoselov. Graphene is a novel one-atom-thick lattice state of carbon which has demonstrated unique quantum mechanical properties. These properties derive in part from the 2-dimensional nature of the material: quantum interactions are constrained to the effectively planar dimension of the lattice. Graphene holds promise for physical applications including touch screens, light cells, and potentially solar panels. Geim becomes the first scientist to achieve a Nobel prize despite earlier winning the highly-coveted Ig Nobel in 2000 for his studies of diamagnetic levitation — also known as The Flying Frog." Slashdot originally mentioned the frog almost exactly 10 years ago.
At the University of Maryland they have levitated graphene flakes. Although this was not diamagnetic levitation. The story was discussed in an earlier /. post.
HOPG (Highly Ordered Pyrolytic Graphite), a form of highly crystalline graphite, from which graphene is obtained in the lab, can also be diamagnetically levitated :)
Currents are only induced by time-changing magnetic fields, not by a constant gradient. The field strength they used for the frog was 16 T, I think. That's on the order of field strength they use for MRI. When MRIs use rapidly-changing fields, there are noticeable, but not particularly painful, neural effects. I've personally been near 5+ T static fields, and it's entirely uninteresting.
Although real-world objects cannot actually span only two dimensions (if you ignore possible theories about strings), the interaction of certain particles can be constrained to 2 spatial degrees of freedom (well plus the time dimension, but ignoring that for now). Two degrees of freedom can be basically lay-man-transliterated as 2-dimensional nature since many people don't really understand 2 degrees of freedom, but they can relate to 2 dimensions (like a sheet of paper to use your analogy).
In this case, the electrons that "move" in the (2d grid-like) lattice of carbon atoms are effectively constrained to 2 spatial degrees of freedom (can represent the position as x & y of the 2d grid of atoms) and will exhibit similar properties as being constrain to a 2 dimensional object even though the lattice of carbon atoms occupies 3 spatial dimensions since the electrons (of a certain energy) only have 2 actual degrees of freedom.
FWIW Quantum physics is usually weird and non-intuitive when you chop down the number of degrees of freedom of an object, although it can be sometimes be understood by using an analogy about reducing the number of dimensions.
It is a macro-scale (more or less) object that exhibits quantum properties in two dimensions, because the atoms are bound to their neighbors in a flat sheet. When the distances are less than the wavelength of the particles you're studying, they act in some ways as if that direction doesn't exist - i.e. it is not a "degree of freedom" in the system, a typical physics definition of a dimension.