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

从物理和化学的角度对石墨和富勒烯给予了很多关注。在这个项目中，我们集中研究了多电子效应起重要作用的两个现象：1。石墨和2.碱金属掺杂富勒烯的超导电性：实验上，在低温下，在石墨c方向的强磁场中，观察到电子电阻率的异常。传统上，这被认为是由于沿沿着c轴形成电荷密度波（CDW）而出现的，但是这样的解释是在没有适当处理布里渊区中的两个不等效边缘H-K-H和H ′-K ′-H ′的情况下做出的。在Hartree-Fock近似下，我们充分考虑了这些边缘的差异，并从第一性原理出发，重建了CDW和自旋密度波（SDW）的差距方程。通过求解差距方程得到了相变温度T_c，发现SDW比CDW具有更高的T_c，表明石墨中可能发生SDW而不是CDW.在A_3C_中<60>，传导电子具有与分子内强耦合声子能量相当的窄带宽.因此，我们需要一个具有顶点修正的强耦合超导理论，以便对系统中的配对机制进行定量的讨论。作为构建这样一个理论的第一步，我们开发的规范不变的自洽（GISC）方法，并将其应用到富勒烯。我们发现在声子机制中，顶点修正使T_c整体上增强.我们还推导了一个基于Baym-Kadanoff守恒近似的基本理论，从而为GISC提供了坚实的理论基础.用这个新理论研究了具有很窄带宽的系统，发现了顶点函数的发散，表明了局域声子的电子锁定效应.

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.