Phase of matter by geometrical phases: application for quantum liquids and graphene

石墨烯是一种典型的量子材料，其中量子干涉起着重要作用。特别是在强磁场中的零能量朗道能级，石墨烯的特征——手性对称性是基本的。然而，到目前为止，大多数理论都没有包括多体效应。在这个项目中，我们构建了一个手性凝聚态理论，它是石墨烯具有相互作用的多体基态。并与实验结果进行了比较。这意味着我们的理论是有效的。我们也阐明了随机性与手性对称性的作用。并进行了法拉第旋转理论实验。然后成功地观察并建立了石墨烯的光量子霍尔效应。

Graphene is a typical quantum material where quantum interference plays an important role. Especially at the zero energy Landau level in a strong magnetic field, the chiral symmetry, which is a characteristic feature of graphene, is fundamental. However most of the theories do not include manybody effects until now. Here in this project, we have constructed a theory of the chiral condensate which is a manybody ground state of graphene with interaction. Then comparison of excitation gap with experiments is performed consistently. It implies validities of our theory. Also we have clarified the role of randomness with chiral symmetry.Also Faraday rotation experiments with theoretical consideration has been performed. Then optical quantum Hall effects of graphene is successfully observed and established.