Quantum phases in frustrated strongly correlated two-dimensional systems

The strong Coulomb repulsion between charge carriers in a system with one electron per site can lead to a full localization of the electrons. The resulting state is called a Mott insulating state. The interplay between the physics of Mott insulators and of unconventional superconductors has been a focus in condensed matter physics for a long time. Although it has frequently been argued that the proximity to a Mott insulating phase is responsible for the emergence of unconventional superconductivity, little progress has been made in obtaining a convincing microscopic theory. Due to the strong electron-electron (e-e) interaction involved in Mott insulators, mean field theory is not a reliable tool. Thus other nonperturbative methods, including the Resonating Valence Bond (RVB) variational theory, have been developed. Recently experimental results showing that a spin liquid state, which is a Mott insulator without long range magnetic order, can undergo a pressure induced transition into an unconventional superconducting state has helped to sharpen this question. This experimental observation demonstrates that the onset of unconventional superconductivity doesn't require magnetic ordering. The RVB picture serves perfectly in this context since it starts with a nonmagnetic state. The major goal of this thesis is to investigate the unconventional electronic and magnetic properties of a superconductor close to a Mott insulating phase. Particular emphasis is given to frustrated systems where the role of quantum frustration is known to be strong and where the Mott insulator is not magnetically ordered. Specifically we study models relevant to two frustrated quantum spin systems.; One material of interest is kappa - (ET)2 Cu 2 (CN)3, an organic superconductor. Its spin-liquid ground state can be tuned by pressure into an unconventional superconducting state. We propose a new variational wavefunction by introducing nonlocal correlation effects into the usual partially projected Gutzwiller wavefunction. We successfully find a superconducting state of d-wave pairing symmetry sandwiched between a metallic state and a spin liquid state around some critical onsite repulsion U. We also find strong "Fermi surface" renormalization when superconductivity starts to emerge.; The other material of interest is SrCu2 ( BO3)2 whose ground state is known to be a singlet dimer state. We derive a multiband BCS wavefunction and apply onto it the full Gutzwiller projection. We show that the obtained trial wavefunction can give the exact ground state energy to the undoped system. We then find that the physical properties are dramatically different for the electron and hole doped cases. We find, for the hole doped case, a plaquette d-wave pairing pattern and enhanced superconductivity due to this pairing inhomogeneity; while for the electron doped case, we find a strange metallic state.