Topological superconductivity in Landau levels

Abstract

The intense search for topological superconductivity is inspired by the prospect that it hosts Majorana quasiparticles. We explore in this work the optimal design for producing topological superconductivity by combining a quantum Hall state with an ordinary superconductor. To this end, we consider a microscopic model for a topologically trivial two-dimensional p-wave superconductor exposed to a magnetic field, and find that the interplay of superconductivity and Landau level physics yields a rich phase diagram of states as a function of $\mu /t$ and $\Delta /t$, where $\mu$, $t$ and $\Delta$ are the chemical potential, hopping strength, and the amplitude of the superconducting gap. In addition to quantum Hall states and topologically trivial p-wave superconductor, the phase diagram also accommodates regions of topological superconductivity. Most importantly, we find that application of a non-uniform, periodic magnetic field produced by a square or a hexagonal lattice of $h/e$ fluxoids greatly facilitates regions of topological superconductivity in the limit of $\Delta /t\to 0$. In contrast, a uniform magnetic field, a hexagonal Abrikosov lattice of $h/2e$ fluxoids, or a one dimensional lattice of stripes produces topological superconductivity only for sufficiently large $\Delta /t$.

11 pages, 9 figures including supplemental material

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Cited by in corpus (10)

• Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Unconventional Self-Similar Hofstadter Superconductivity from Repulsive Interactions
• Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Pattern-dependent proximity effect and Majorana edge mode in one-dimensional quasicrystals
• Phase diagram of superconductivity in the integer quantum Hall regime
• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Theory of Hofstadter Superconductors
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor