Topological Crystalline Superconductivity in Locally Non-centrosymmetric Multilayer Superconductors

TL;DR

This paper proposes a topological crystalline superconductivity in multilayer superconductors with local non-centrosymmetry, highlighting the role of mirror symmetry and odd-parity pair-density wave states in realizing Majorana modes.

Contribution

It introduces a novel topological phase in multilayer SCs protected by mirror symmetry, expanding the understanding of topological superconductivity beyond standard classifications.

Findings

PDW state is a topological crystalline superconductor protected by mirror symmetry.

Bilayer PDW reduces to a non-centrosymmetric superconductor, trilayer to a spinless p-wave superconductor.

Chiral Majorana edge modes can exist without spin-triplet pairing or chemical potential tuning.

Abstract

Topological crystalline superconductivity in the locally non-centrosymmetric multilayer superconductors (SCs) is proposed. We study the odd-parity pair-density wave (PDW) state induced by the spin-singlet pairing interaction through the spin-orbit coupling. It is shown that the PDW state is a topological crystalline SC protected by a mirror symmetry, although it is topologically trivial according to the classification based on the standard topological periodic table. The topological property of the mirror subsectors is intuitively explained by adiabatically changing the BdG Hamiltonian. A subsector of the bilayer PDW state reduces to the two-dimensional non-centrosymmetric SC, while a subsector of trilayer PDW state is topologically equivalent to the spinless p-wave SC. Chiral Majorana edge modes in trilayers can be realized without Cooper pairs in the spin-triplet channel and chemical potential tuning.