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.

arXiv comment13 pages, 9 figures

References in corpus (57)

• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Majorana fermions in a tunable semiconductor device
• Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• Higher-Order Topology in Bismuth
• Evidence for Majorana bound state in an iron-based 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
• Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor
• Chiral Topological Superconductor From the Quantum Hall State
• Epitaxy of Semiconductor-Superconductor nanowires
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• One-dimensional Topological Edge States of Bismuth Bilayers
• Observation of half-integer thermal Hall conductance
• Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe
• Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• The Ginzburg-Landau Theory of Type II superconductors in magnetic field
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes
• Deconfined quantum criticality and Neel order via dimer disorder
• Ballistic edge states in Bismuth nanowires revealed by SQUID interferometry
• Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
• Phase Diagram of the Interacting Majorana Chain Model
• Andreev Molecules in Semiconductor Nanowire Double Quantum Dots
• All Majorana Models with Translation Symmetry are Supersymmetric
• Strongly interacting Majorana fermions
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Variational study of the nu=1 quantum Hall ferromagnet in the presence of spin-orbit interaction
• Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state
• Disorder-induced Majorana metal in interacting non-Abelian anyon systems
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Electronic structure of topological superconductors in the presence of a vortex lattice
• Majorana fermions in vortex lattices
• Ising Anyons in Frustration-Free Majorana-Dimer Models
• Majorana-Hubbard model on the square lattice
• Majorana fermions on a disordered triangular lattice
• Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiral p-wave superconductor
• Majorana fermions on the Abrikosov flux lattice in a $p_x+i{p}_y$ superconductor and thermal conductivity in superclean regime
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• Topological superconductivity in Quantum Hall-superconductor hybrid systems
• Phase diagrams of Majorana-Hubbard ladders
• Topological Mid-gap States of px+ipy Topological Superconductor with Vortex superlattice
• Hierarchy of gaps and magnetic minibands in graphene in the presence of the Abrikosov vortex lattice
• How vortex bound states affect the Hall conductivity of a chiral $p\pm ip$ superconductor

Cited by in corpus (8)

• A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene
• Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime
• 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