Back in February, 2007, I mentioned that I thought that making and measuring nanostructures directly out of strongly correlated materials was a promising research direction. I still think so, in part because of the experiences my lab and others have had in the mean time. As I've mentioned before, strongly correlated materials are those where we can no longer get away with our (often miraculously good) simple single-particle description of electronic structure that ignores the electron-electron interaction. Examples of correlated materials include the high temperature superconductors and various transition metal oxides. In the high Tc case, single-particle band structure says that the undoped parent compound should be a metal, when it's found instead to be an antiferromagnetic insulator. Strongly correlated materials often display a rich variety of interesting electronic states as well as phase transitions between them.
Why nanostructures? Three main reasons. First, when some strongly correlated materials go through electronic (and structural, sometimes) transitions, they display inhomogeneities. For example, when vanadium dioxide goes through its metal-insulator transition (from below) near 341 K, metallic domains nucleate and grow, eventually encompassing the whole material. Nanostructures can allow you to access such materials on the scale of individual domains, as was done here and here in VO2, and here in a colossal magnetoresistance oxide.
Second, nanospaced electrodes allow you to use electric field as an interesting perturbation, and to tell the difference between effects driven by voltage (or energy) and those actually driven by field. For example, in this paper (very influential and highly cited), the authors found that a charge-ordered oxide could be kicked out of an insulating state and into a low resistance state when around 1000 V was applied across a 1mm crystal of the material. That's cool, and prompted much work, but as an experimentalist one always wonders whether the 106 V/m electric field is responsible (which would be particularly interesting), or whether the energy available to the electrons is actually doing some kind of chemistry or damage to the material. In a nanostructured system, one could get the same electric field by applying 100 mV across electrodes separated by 100 nm, getting big fields without big available energies. We've done work along these lines in Fe3O4, and have had quite a bit of fun with it.
Third, nanospaced electrodes are a way of driving systems far from equilibrium and potentially measuring them under those conditions. When an ordinary electron is injected into a correlated material, it can be thought of as a superposition of the "natural" low-energy excitations of the correlated system. For example, in a Luttinger liquid, the injected carrier "fractionalizes" into a spinon (spin-1, chargeless mode) and a holon (charged, spinless mode). Truly nano-spaced measurements may be a means of catching this process in action, though it won't be easy!
I still think that this is a fun and exciting area, and interest appears to be growing.