Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime

Abstract

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.

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• Interference of chiral Andreev edge states
• Vortex-enabled Andreev processes in quantum Hall-superconductor hybrids
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Phase diagram of superconductivity in the integer quantum Hall regime
• Nonequilibrium edge transport in quantum Hall based Josephson junctions
• Finite field transport response of a dilute magnetic topological insulator based Josephson junction
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
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• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Theory of Hofstadter Superconductors