### 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 μ/t and Δ/t, where μ,t, and Δ 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 nonuniform, 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 Δ/t→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 Δ/t.

Original language | English (US) |
---|---|

Article number | 094509 |

Journal | Physical Review B |

Volume | 99 |

Issue number | 9 |

DOIs | |

State | Published - Mar 12 2019 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*99*(9), [094509]. https://doi.org/10.1103/PhysRevB.99.094509

}

*Physical Review B*, vol. 99, no. 9, 094509. https://doi.org/10.1103/PhysRevB.99.094509

**Topological superconductivity in Landau levels.** / Jeon, Gun Sang; Jain, Jainendra K.; Liu, Chaoxing.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Topological superconductivity in Landau levels

AU - Jeon, Gun Sang

AU - Jain, Jainendra K.

AU - Liu, Chaoxing

PY - 2019/3/12

Y1 - 2019/3/12

N2 - 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 μ/t and Δ/t, where μ,t, and Δ 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 nonuniform, 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 Δ/t→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 Δ/t.

AB - 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 μ/t and Δ/t, where μ,t, and Δ 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 nonuniform, 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 Δ/t→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 Δ/t.

UR - http://www.scopus.com/inward/record.url?scp=85063194224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063194224&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.99.094509

DO - 10.1103/PhysRevB.99.094509

M3 - Article

AN - SCOPUS:85063194224

VL - 99

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 2469-9950

IS - 9

M1 - 094509

ER -