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，量子干涉在其中起着重要的作用。特别是在强磁场中的零能朗道能级，作为石墨烯特有特征的手征对称性是根本。然而，迄今为止，大多数理论都没有考虑多体效应.在这个项目中，我们构建了一个手性凝聚体的理论，它是石墨烯具有相互作用的多体基态。然后，激发间隙与实验进行了比较一致。这意味着我们的理论的有效性。同时，我们也阐明了随机性与手征对称性的关系，并进行了法拉第旋转实验和理论分析。在此基础上，成功地观察到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.