Gapless superconductivity and its real-space topology in quasicrystals

TL;DR

This paper investigates gapless superconductivity in Ammann-Beenker quasicrystals, revealing its origin in broken symmetry and confinement, and demonstrates potential for topological phases with edge states under spin-orbit coupling.

Contribution

It introduces the concept of gapless superconductivity in quasicrystals and explores its topological properties, a novel insight into quasicrystalline superconducting phases.

Findings

Gapless superconductivity occurs at and near half filling in quasicrystals.

Broken translational symmetry and confined states drive gapless behavior.

Presence of Rashba spin-orbit coupling induces topologically nontrivial phases with edge states.

Abstract

We study superconductivity in Ammann-Beenker quasicrystals under magnetic field. By assuming an intrinsic $s$-wave pairing interaction and solving for mean-field equations self-consistently, we find gapless superconductivity in the quasicrystals at and near half filling. We show that gapless superconductivity originates in broken translational symmetry and confined states unique to the quasicrystals. When Rashba spin-orbit coupling is present, the quasicrystalline gapless superconductor can be topologically nontrivial and characterized by a nonzero pseudospectrum invariant given by a spectral localizer. The gapless topological superconducting phase exhibits edge states with near-zero energy. These findings suggest that quasicrystals can be a unique platform for realizing gapless superconductivity with nontrivial topology.