Topological superconductivity in Landau levels

TL;DR

This paper investigates how combining quantum Hall states with superconductors can produce topological superconductivity, highlighting the role of non-uniform magnetic fields in facilitating topological phases at low superconducting gaps.

Contribution

It demonstrates that non-uniform magnetic fields significantly enhance the emergence of topological superconductivity in Landau levels, especially at small superconducting gaps.

Findings

Non-uniform magnetic fields promote topological superconductivity at low Δ/t.

Topological phases appear in a rich phase diagram depending on μ/t and Δ/t.

Uniform magnetic fields require larger Δ/t for topological superconductivity.

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 $\Delta/t\rightarrow 0$. 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 $\Delta/t$.