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

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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.