近年来，拓扑绝缘体中的多体凝聚效应逐渐成为当前国际凝聚态物理研究的一个重要前沿领域。本项目主要研究拓扑(磁)激子和拓扑超导两类多体凝聚系统。前者主要包括：揭示拓扑序参量随激子浓度及电子-空穴浓度失配的变化规律；全面阐述自旋-轨道耦合效应与拓扑(磁)激子凝聚相的关系；系统研究杂质与拓扑缺陷对拓扑(磁)激子凝聚相的影响，揭示拓扑(磁)激子凝聚系统中发生分数化电荷和量子相变的条件与深刻物理内涵；研究拓扑(磁)激子的光吸收谱、有效质量、超流性、轨道磁性等物理性质。后者主要包括：系统研究拓扑超导相的奇异物性，揭示其内禀起源；研究拓扑超导相对杂质与拓扑缺陷的响应，揭示拓扑超导配对的物理机制；研究其它系统与拓扑超导相耦合时所呈现的新奇物理性质等。此外，本项目还拟深入研究多体凝聚效应对拓扑绝缘体量子反常霍尔效应等输运性质的影响。预期这些研究工作将促进我国在拓扑绝缘体领域的研究进展。

The many-body condensation effect in topological insulators has recently been an interesting and important field in condensed matter physics. The main purpose of this program is to study two topological many-body condensed systems, which include the topological (magneto)exciton and the topological superconductor ones. For the topological (magneto)exciton systems, we will study (i) the properties of the topological order parameters as functions of exciton number density, (ii) the spin-orbit coupling effect on the condensed exciton phases, (iii) the effect of impurities and topological defects, (iv) the intrinsic physics of the fractional charge phenomena and quantum phase transitions, and (v) the physical properties of the topological magnetoexcitons, including the optical absorption spectrum, effective mass, superfluidity, and the obital magnetization. For the topological superconductor systems, we will study (i) the Andreev bounded states properties, (ii) the novel physical prooerties of the topological superconductor phases and their intrinsic origin, (iii) the responses to the impurities and topological defects and the physical mechanism of the topological superconducting pairs, and (iv) the novel physical properties of the topological superconductors coupling with other systems. Also, we will investigate the many-body condensation effect on the anomalous quantum transport properties of the topological insulators.