I haven't written too much about my own research on this blog, mostly because I figure that people who really care about it can read my group homepage or my papers. However, there is one area out there that I think has real promise, and I'd like to get other folks thinking about it, at least in general terms.
Electronic transport measurements in nanoscale systems can be considered a kind of spectroscopy. In particular, when a chunk of conducting material is sufficiently small and relatively weakly coupled to leads (call them a "source" and a "drain", after transistor terminology), conduction can be dominated by one or a few specific quantum states of that material. There has been great work done by many groups over the past 15 years or so, looking at these individual electronic states in a bunch of systems, including metal nanoparticles, patches of doped semiconductor, and semiconductor nanowires and nanocrystals. As neat as these systems are, they're all comparatively simple from the electron-electron interaction point of view. With a few exceptions (like Kondo-based physics), you can pretty much work in a single-particle picture. That is, adding one more electron to these systems doesn't drastically change the spectrum of electronic states - the spectrum itself is mostly unchanged except for the population of the states, one of which has increased by 1.
Many interesting materials exist where strong electronic correlations are more important. For example, the high-Tc superconductors in their normal state are often "bad metals" that are not well described by a picture of weakly interacting electrons. There are similar phases in the heavy fermion compounds. Even magnetite (Fe3O4), a comparatively simple compound, has strong correlation effects: it's not really a metal or a semiconductor; it has a room temperature resistivity in the milliOhm-cm range (say 1000 times higher than Cu or Au), and that resistivity increases with decreasing temperature, but not in a simple way as in a semiconductor.
I think it would be very revealing for transport spectroscopy experiments to be performed on nanostructures made from these strongly correlated materials. This won't be easy for many practical reasons (e.g., stoichiometry can be tough to control in nanomaterials; noone knows how to make many of these systems in nanostructured forms yet), but I'm convinced that there is much to learn in such experiments.