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.

• Received 15 April 2019
• Revised 30 December 2019

DOI:https://doi.org/10.1103/PhysRevB.101.024516