Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials

Hassan Shapourian, Yuxuan Wang, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

We study the intrinsic fully gapped odd-parity superconducting order in doped nodal-loop materials with a torus-shaped Fermi surface. We show that the mirror symmetry, which protects the nodal loop in the normal state, also protects the superconducting state as a topological crystalline superconductor. As a result, the surfaces preserving the mirror symmetry host gapless Majorana cones. Moreover, for a Weyl-loop system (twofold degenerate at the nodal loop), the surfaces that break the mirror symmetry (those parallel to the bulk nodal loop) contribute a Chern (winding) number to the quasi-two-dimensional system in a slab geometry, which leads to a quantized thermal Hall effect and a single Majorana zero mode bound at a vortex line penetrating the system. This Chern number can be viewed as a higher-order topological invariant, which supports hinge modes in a cubic sample when mirror symmetry is broken. For a Dirac-loop system (fourfold degenerate at the nodal loop), the fully gapped odd-parity state can be either time-reversal symmetry-breaking or symmetric, similar to the A and B phases of He3. In a slab geometry, the A phase has a Chern number two, while the B phase carries a nontrivial Z2 invariant. We discuss the experimental relevance of our results to nodal-loop materials such as CaAgAs.

Original languageEnglish (US)
Article number094508
JournalPhysical Review B
Volume97
Issue number9
DOIs
StatePublished - Mar 14 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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