基于非厄米拓扑系统的量子输运性质研究

自量子霍尔效应被发现以来，人们对拓扑理论的研究日益完善. 近来，科学家将电子拓扑性质的研究拓展到了非厄米量子系统. 非厄米拓扑量子系统具有许多不同于传统厄米拓扑量子系统的物理性质，例如：体态-边缘态对称性破坏，分数量子化的拓扑数和非厄米趋肤效应等. 这些奇异的拓扑特性导致了如异常的边界态局域、体态的单方向局域和非局域化的量子输运等新奇的量子输运新现象. 本课题拟对非厄米拓扑量子体系的量子输运性质进一步深入研究，重点研究PT对称及PT对称破缺时，非厄米拓扑绝缘体/拓扑超导体异质结中非局域输运对Andreev反射及交叉Andreev的影响，寻找非厄米拓扑量子系统中的稳定态，并为量子调控稳定态之间的量子跃迁提供理论方案. 本课题研究将增进人们对基于非厄米拓扑体系量子输运的理解，解决当前非厄米哈密顿在量子输运计算中发散等问题，并为非厄米项引入而导致的几率不守恒量子输运结果提供定性的物理解释.

From the discovery of quantum Hall effect, topological theory has also been explored across a broad range of fields. Recently people have extended the research of topological theroy to the fields of non-Hermitian quantum systems. There are lots of completely different topological properties between the non-Hermitian topological systems and the Hermitian topological systems, such as the breakdown of conventional bulk-boundary correspondence, the fractional topological invariant and the non-Hermitian skin effect under open boundary. These characteristics in the non-Hermitian topological systems induce to the novel transports properties: anomalous local boundary states, bulk non-unidirectional localized at the surface of the systems and delocalized quantum transports. In this project, we plan to study deeply the quantum transport properties of non-Hermitian topological systems, focus on the effect of delocalized effect on the Andreev reflection and crossed Anreev reflection in presence of PT symmetry and PT symmetry-broken conditions, and search for the stable states in various non-Hermitian topological structures and provide theoretical solutions for quantum transitions between different stable states. The accompliment of this project will improve the understanding of quantum transport based on non-Hermitian topological systems, and solve the problems of computational divergence caused by non-Hermit terms in current quantum transport methods. It also provides a qualitative physical explanation for the quantum transport results caused by non-conservation of probability.