Protecting a single solid-state spin from a spin bath in diamond for quantum sensing

2018财年，我的研究主要集中在以下两个方面：(1)高温超导体上二维磁性拓扑绝缘体中的Majorana角态。D维二阶拓扑超导体(TSC)的特征是具有通常有隙(d-1)边界的无间隙(d-2)维拓扑保护态。在这项工作中，我们研究了具有2D磁性拓扑绝缘体邻近的二阶TSC与高温超导体的耦合，其中Majorana束缚态(MBS)局域化在具有间隙边缘模的正方形样品的角点处。基于边缘理论的详细分析揭示了在2D样品的拐角处存在MBS的原因，这是由于配对对称性导致在任意两个相邻边缘的交点处出现的狄拉克质量的符号变化所致。(2)非厄米系统的二阶拓扑相。D维二阶拓扑绝缘体(SOTI)可以承载具有拓扑保护的(d-2)维无间隙边界模。在这项工作中，我们证明了二维非厄米SOTI可以容纳仅位于一角的零能模。三维非厄米SOTI支持二阶边界模，它不是沿着铰链定域的，而是反常地位于一角。二阶2D(3D)非厄米系统中通常的体角(铰链)对应被打破。

In FY2018, my research is mainly focused on the following two topics: (1) Majorana corner states in a 2D magnetic topological insulator on a high-temperature superconductor. A d-dimensional second-order topological superconductor (TSC) is characterized by topologically protected gapless (d-2) dimensional states with the usual gapped (d - 1) boundaries. In this work, we studied a second-order TSC with a 2D magnetic topological insulator proximity coupled to a high-temperature superconductor, where Majorana bound states (MBSs) are localized at the corners of a square sample with gapped edge modes. A detailed analysis, based on edge theory, revealed the origin of the existence of MBSs at the corners of the 2D sample, which results from the sign change of the Dirac mass emerging at the intersection of any two adjacent edges due to pairing symmetry. (2) Second-order topological phases in non-Hermitian systems. A d-dimensional second-order topological insulator (SOTI) can host topologically protected (d-2)-dimensional gapless boundary modes. In this work, we showed that a 2D non-Hermitian SOTI can host zero-energy modes localized only at one corner. A 3D non-Hermitian SOTI is shown to support second-order boundary modes localized not along hinges but anomalously at a corner. The usual bulk-corner (hinge) correspondence in the second-order 2D (3D) non-Hermitian system breaks down.