Many-Electron Effects and Phase Transitions in Materials Made of Carbon

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Much attention is given to graphite and fullerene from both physical and chemical points of view. In this project, we concentrate upon the following two phenomena in which the many-electron effects play an important role : 1. The electronic phase transition in strong magnetic fields in graphite and 2. Superconductivity in alkali-metal doped fullerenes.Experimentally, an anomaly has been observed in the electronic resistivity at low temperatures in strong magnetic fields in the c direction of graphite. Conventionally, this is considered to appear due to the formation of a charge-density wave (CDW) along the c-axis, but such an explanation is made without a proper treatment of the two inequivalent edges, H-K-H and H'-K'-H' in the Brillouin zone. We take full account of the difference of those edges and reconstructed the gap equation for CDW as well as a spin-density wave (SDW) from first principles in the Hartree-Fock approximation. We obtain the transition temperature T_c by solving the gap equation and find that SDW has a higher T_c that CDW,indicating that SDW rather than CDW is likely to occur in graphite.In A_3C_<60>, the conduction electrons have a narrow bandwidth which is comparable to the energy of the intramolecular strongly-coupled phonons. Thus we need a strong-coupling theory of superconductivity withvertexcorrections in order to make a quantitative discussion of the pairing mechanism in the system. As a first step to construct such a theory, we develop the gauge-invariant self-consistent (GISC) method and apply it to the fullerenes. We find that the vertex corrections enhance T_c as a whole in the phonon mechanism. We also derive a fundamental theory based on the Baym-Kadanoff's conserving approximation so as to give a firm theoretical basis for GISC.By employing this new theory to investigate the system with a very narrow bandwidth, we find a divergence in the vertex function, indicating an electron-locking effect by local phonons.