| Clean two dimensional electronic systems at very high and very low densities are Fermi liquids and Wigner crystals, respectively. It is known that if there is a direct phase transition between Wigner crystals and Fermi liquids, it must be first order. However, by a variational calculation we have shown that such a density-driven first order phase transition is impossible in two dimensions because of the long range Coulomb interaction. We conclude there must be intermediate phases between the Fermi liquid and Wigner crystal that are mesoscopic mixtures of the two phases at mean field level. The presence of such inhomogeneous phases can underlie the explanation of the highly anomalous transport phenomena in clean 2D heterojunctions. Another quasi-two-dimensional system with a high degree of inhomogeneity, as seen by Scanning Tunneling Microscopy (STM), is the cuprate superconductor Bi2Sr2CaCu 2O8+delta (BSCCO). We have developed a method to extract the local parameters of the effective Hamiltonian from the STM data. We apply our method to STM data in BSCCO and find that while the variation in the superconducting gap function is very large, the variation in the electrochemical potential is remarkably small. |
