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大的关注。在这个项目中，我们集中研究以下两种现象，其中多电子效应起着重要的作用：石墨和2.强磁场下的电子相变。碱金属掺杂富勒烯的超导性。实验结果表明，在强磁场作用下，石墨c方向的低温电阻率存在异常。通常，这被认为是由于沿c轴形成电荷密度波（CDW）而出现的，但这种解释没有适当地处理布里渊带中的两个不等价边，H-K-H和H'-K‘-H’。我们充分考虑了这些边的差异，从Hartree-Fock近似的第一性原理出发，重构了CDW和自旋密度波（SDW）的间隙方程。我们通过求解间隙方程得到了转变温度T_c，发现SDW的T_c高于CDW，说明石墨中可能发生SDW而不是CDW。在A_3C_<60>中，传导电子具有与分子内强耦合声子的能量相当的窄带宽。因此，我们需要一个具有顶点修正的超导强耦合理论，以便对系统中的配对机制进行定量讨论。作为构建这一理论的第一步，我们开发了标准不变自洽（GISC）方法，并将其应用于富勒烯。我们发现顶点修正整体上增强了声子机制中的T_c。本文还推导了基于Baym-Kadanoff守恒近似的基本理论，为GISC提供了坚实的理论基础。通过应用这一理论研究窄带系统，我们发现顶点函数存在散度，表明局域声子具有电子锁定效应。

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.