For years now, there has been a fairly heated debate about the nature of an apparent metal-insulator transition (as a function of carrier density) seen in various 2d electronic and hole systems. The basic observation, originally made in some Si MOSFETs of impressively high interface quality made in Russia, is that as the 2d carrier density is reduced, the temperature dependence of the sheet resistance changes qualitatively, from a metallic dependence (lower T = lower resistance) at high carrier concentration to an insulating dependence (lower T = higher resistance) at low concentration, with a separatrix in between with nearly T-independent resistance at some critical carrier density. A famous 1979 paper by the "Gang of Four" (Anderson, Abrahams, Licciardello, and Ramakrishnan) on the scaling theory of localization had previously argued that 2d systems of noninteracting carriers all become insulating at T=0 for arbitrarily weak disorder.So, there has been a long-simmering controversy about why some 2d systems (electrons or holes) seem to show a really metallic temperature dependence of their conductance at low temperatures. This dependence, where the conductivity apparently increases by, say, a factor of 2 from \(T =\) 4.2K down to 0.1 K, takes place over a temperature range where the scattering of electrons by lattice vibrations (the mechanism responsible for the increase in conductivity of ordinary metals as they are cooled from room temperature down to cryogenic temperatures) is supposed to be all finished. I mentioned this as an ongoing controversy in '06 and again in '12. What is going on here?
There is a new preprint from Bruce Kane and colleagues at Maryland that clarifies things considerably, in my view. Kane, probably best known for proposing a quantum computing scheme involving individual phosphorus donors in Si, is a very clever experimentalist. He has developed a method of creating field-effect transistors,where the conducting channel is the hydrogen-terminated surface of a Si wafer, and the gate dielectric is vacuum (!). Using these devices, his group has been able to look at the apparent metallicity in both electrons and holes in the same system. They find that the improvement in conduction at low temperatures has to do with the screening of charged impurities by the conducting system (and for the experts: in Si the electrons are able to do this better than the holes because there are 6 conduction band valleys, while there is no valley degeneracy for the holes). This doesn't directly get to the "fundamental" question about whether the true, zero-temperature ground state is insulating in a real, interacting system, but it does go a long way toward demonstrating why the conductivity still has a metallic change with temperature even though phonons should be out of the picture.