分数量子霍尔效应拓扑序的研究

项目名称： 分数量子霍尔效应拓扑序的研究

项目编号： No.11274403

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 胡自翔

作者单位： 重庆大学

项目金额： 78万元

中文摘要： 本项目着眼于凝聚态物理的基础理论，主要研究分数量子霍尔效应中新的量子态的拓性质以及其低能激发性质。具体研究内容包括对半导体材料以及石墨烯材料等二维电子气系统中可能实现的分数量子霍尔态的拓扑性质以及拓扑相进行研究，尤其是对非阿贝尔量子霍尔态及其准粒子激发和边缘态激发的性质进行研究，并讨论在真实情况下系统中的杂质，二维电子气的厚度，各向异性以及朗道能级混合的影响。本项目注重理论和实验的结合，关于拓扑量子态的研究属于目前凝聚态物理中的前沿领域，因为它超出了利用对称性，序参量来描述量子态和量子相变的传统方法。主要结合大规模数值计算，模拟以及解析分析的方法来研究分数霍尔效应，并致力于发展密度矩阵重整化群等方法在分数量子霍尔效应研究上的应用。本项目有助于理解目前新的实验结果，而对具有拓扑序的物质，尤其是对具有非阿贝尔拓扑序的量子态的研究对于凝聚态物理理论的发展也具有较大意义。

中文关键词： 霍尔效应；非阿贝尔；准粒子；边缘态；石墨烯

英文摘要： This project focuses on the foundamental theory in condensed matter physics. We try to understand the topological properties and the low-lying excitation properties in the fractional quantum Hall(FQH) states which are shown in new plateaus in semiconductors or new materials experimentally. The research contains searhing for the new FQH states, especially the non-Abelian FQH states in the two-dimensional electron gas(2DEG) system such as the GaAs/GaAlAs heterostructure, quantum well, or graphene system. We will explore the topological properties of the FQH states by studying their edge excitations and the quasiparticle excitations. In realistic situation, we should also consider the effects of disorder, the layer thickness of the 2DEG, anisotropy in system and Landau level mixing et al. Understanding the topological order and topological phase is a very hot and challenging topic in the condensed matter physics since it is out of the description of the Laudau's theory. Some of the FQH states, such as at the filling 5/2 or 12/5, have non-trivial quasiparticle excitation which satisfy non-Abelian statistics. The non-Abelian quasiparticles are crucial in the topological protected quantum computation. In this project, we study the FQH states by the help of large-scale numerical computations, simulations, and analyt

英文关键词： Hall effect；non-Abelian；quasiparticle；edge states；graphene