Chiral topological superconductors are expected to appear as intermediate states when a quantum anomalous Hall system is proximity coupled to an $s$-wave superconductor and the magnetization direction is reversed. In this paper, we address the edge state properties of ordinary quantum Hall systems proximity coupled to $s$-wave superconductors, accounting explicitly for Landau quantization. We find that the appearance of topological superconducting phases with an odd number of Majorana edge modes is dependent on the structure of the system's vortex lattice. More precisely, vortex lattices containing odd number of superconducting flux quanta per unit cell, always support an even number of chiral edge channels and are therefore adiabatically connected to normal quantum Hall insulators. We discuss strategies to engineer chiral topological superconductivity in proximity-coupled quantum Hall systems by manipulating vortex-lattice structure.

中文翻译：

---

量子霍尔体系中的涡-格结构和拓扑超导

当量子反常霍尔系统邻近耦合到电子时，手性拓扑超导体有望以中间状态出现。 $s$波超导体和磁化方向相反。在本文中，我们讨论了普通量子霍尔系统的耦合到$s$波超导体，明确说明了Landau量化。我们发现，奇数个Majorana边缘模式的拓扑超导相的出现取决于系统涡旋格的结构。更精确地讲，每单位晶胞包含奇数个超导通量量子的涡流晶格始终支持偶数个手性边缘通道，因此绝热地连接到普通量子霍尔绝缘体。我们讨论了通过操纵涡旋-晶格结构来设计邻近耦合量子霍尔系统中手性拓扑超导性的策略。