NMR Studies of Novel Electronic Phases in Low Dimensional Molecular Solids at High Pressure and Low Temperature*

Molecular superconductors are known for anisotropic electronic band structure, correlations, and a sensitivity to mechanical or chemical pressure which acts to control the relative strength of the respective kinetic and potential energies. Modest pressures, of order 1 GPa are commonly used to continuously tune from a Mott insulating ground state to a superconducting state, and NMR has been particularly successful in identifying the orders involved, and the nature of the excitations in the various phases encountered. The family of quasi-two dimensional systems $\kappa$-(BEDT-TTF)$_2$X ({\it e.g.}, X=Cu(NCS)$_2$, Cu[N(CN)$_2$]Cl) includes a line of first order phase transitions separating the Mott and superconducting phases, with the superconducting state exhibiting signatures for line nodes associated with an order parameter sign-change over the Fermi surface. The pressure/temperature phase diagram of the quasi-one dimensional materials (TMTSF)$_2$X, X=PF$_6$, ClO$_4$,...) includes more phases, as a consequence of effective 1/4-filling and a substantial density wave susceptibility. The SC ground state is singlet, and there is evidence for a sign-change of the order parameter over the Fermi surface. The high-conductivity normal state exhibits properties associated with two-dimensional spin fluctuations, with signatures in the relaxation rate, as well as transport that are reminiscent of behaviors observed in other correlated superconductors.