Journal
PHYSICAL REVIEW B
Volume 97, Issue 9, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.97.094508
Keywords
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Funding
- NSF [DMR-1455296]
- Gordon and Betty Moore Foundation's EPiQS Initiative through University of Illinois [GBMF4305]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1455296] Funding Source: National Science Foundation
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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 He-3. In a slab geometry, the A phase has a Chern number two, while the B phase carries a nontrivial Z(2) invariant. We discuss the experimental relevance of our results to nodal-loop materials such as CaAgAs.
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