Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas

Abstract

Motivated by recent experiments demonstrating intricate quantum Hall physics on the surface of elemental bismuth, we consider proximity coupling an $s$-wave superconductor to a two-dimensional electron gas with strong Rashba spin-orbit interactions in the presence of a strong perpendicular magnetic field. We focus on the high-field limit so that the superconductivity can be treated as a perturbation to the low-lying Landau levels. In the clean case, wherein the superconducting order parameter takes the form of an Abrikosov vortex lattice, we show that a lattice of hybridized Majorana modes emerges near the plateau transition of the lowest Landau level. However, unless magnetic-symmetry-violating perturbations are present, the system always has an even number of chiral Majorana edge modes and thus is strictly speaking Abelian in nature, in agreement with previous work on related setups. Interestingly, however, a weak topological superconducting phase can very naturally be stabilized near the plateau transition for the square vortex lattice. The relevance of our findings to potential near-term experiments on proximitized materials such as bismuth will be discussed.

13 pages, 9 figures

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Strong spin-orbit splitting on Bi surfaces
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Epitaxy of Semiconductor-Superconductor nanowires
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• One-dimensional Topological Edge States of Bismuth Bilayers
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
• Strongly interacting Majorana fermions
• Majorana-Hubbard model on the square lattice
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• Phase diagrams of Majorana-Hubbard ladders

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• Phase diagram of superconductivity in the integer quantum Hall regime
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Making s-wave superconductors topological with magnetic field
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor