TECHNICAL SUMMARY This award supports theoretical research and education to study experimentally observed magnetic phenomena in quasi-one-dimensional (TMTSF)2X (X = PF6, ClO4, etc.), (Per)2M(mnt)2 (M=Pt, Au) and quasi-two-dimensional (ET)-, (DMET)-, and (BETS)-based organic superconductors and conductors. The main distinctive feature of these materials is that they demonstrate unique physical properties in a magnetic field. Among them are the Lebed magic angles and other Fermi liquid and non-Fermi-liquid angular oscillations, magnetic field-induced spin-density-wave phases and associated three-dimensional quantum Hall effect. The PI will investigate the following topics: (1) The unique features of the 3D quantum Hall Effect in the field induced spin density wave and charge density wave phases, including experimentally observed fractional quantum magnetic oscillations of the 3D quantum Hall effect in (TMTSF)2ClO4; (2) The unusual properties of a novel "super-crystalline" phase proposed by the PI. The PI aims to explain the recently observed field induced charge density wave phase diagrams in (Per)2M(mnt)2 and alpha-(ET)2KHg(SCN)4 in terms of the super-crystalline phase; (3) Fermi liquid versus non-Fermi liquid behavior with an emphasis on the recently discovered non-Fermi liquid Lebed magic angles in Nernst and Hall effects in (TMTSF)2X materials and non-linear Lebed magic angles phenomena; (4) Explanation of the triplet-singlet controversy in the experimental properties of (TMTSF)2X superconductors; (5) The reentrant superconducting phase and the traditional and novel Larkin- Ovchinnikov-Fulde-Ferell phases, observed in (TMTSF)-, (ET)-, and (BETS)-based superconductors; (6) The singlet-triplet mixing phenomenon in quasi-2D and quasi-1D superconductors. The research will be carried out in close collaboration with experimental groups at the NYU, UCLA, Boston College, Tallahassee and Los-Alamos branches of the National High Magnetic Field Laboratory, Clark University, and investigators in Japan and Germany with an emphasis on physical properties of real materials. This research may have impact more broadly on condensed matter physics, such as in the area of high temperature superconductivity and the search for new superconducting materials with higher transition temperatures. This project provides a research environment to train one full-time graduate student and one part-time undergraduate student in scientifically and technologically vital areas of materials physics such as superconductivity, correlated electrons, and computational physics. NON-TECHNICAL SUMMARY This award supports theoretical research and education to study experimentally observed magnetic phenomena in a class of organic materials where the quantum states of electrons are restricted to one or two dimensions by virtue of the properties of the molecular building blocks from which they are made and the way they assemble themselves to form solid materials. These materials are rich with new phenomena and states of matter that emerge when a magnetic field is applied to them. Among these states of matter that appear in a magnetic field is one where the density of electronic charge varies in a periodic way that is superimposed on the normal distribution of electronic charge in a crystal. The PI will use theoretical methods to predict new and explain experimentally discovered phenomena and states of electronic matter that arise in these materials in an applied magnetic field. The theoretical effort here is directly relevant to ongoing experimental efforts and will aid in the understanding of these very complicated materials. For example, the PI plans to study the possibility that a novel kind of mixed superconductivity proposed by the PI may explain unusual properties of superconducting states observed in particular quasi-one dimensional organic metals. Superconductivity is a cooperative state of electrons which can conduct electricity without the losses that degrade electric currents in, for example a copper wire, causing it to heat up. The PI plans to explore other possible superconducting states that may explain puzzles in these materials. The PI plans to carry out research in 5 additional areas that cut across the richness of phenomena and states of matter that occur from the interplay of an applied magnetic field and the one- or two-dimensional nature of these materials. This research will be carried out in close collaboration with experimental groups at various laboratories and universities in the United States, Europe and Japan with an emphasis on advancing understanding of real materials. This research may have impact more broadly on condensed matter physics, such as in the area of high temperature superconductivity and the search for new superconducting materials with higher transition temperatures. This research contributes to the intellectual foundations of new electronic device and information technologies. This project provides a rich research environment to train one full-time graduate student and one part-time undergraduate student in scientifically and technologically vital areas of materials physics such as superconductivity, correlated electrons, and computational physics.