Topological Crystalline Superconductivity in Locally Noncentrosymmetric Multilayer Superconductors

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.PACS numbers: 74.20. Rp, 74.45.+c, 74.78.Fk Topologically nontrivial phases of superconductors (SCs) have evolved into one of the major research topics of modern condensed matter physics recently [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . A characteristic feature of topological SCs is the fully gapped bulk spectrum accompanied by topologically protected gapless edge states. Many of the topological superconducting states are realized in odd-parity SCs, and one of the most extensively studied examples is the chiral p x ± ip y -wave SC 1,2 . However, only few materials are considered as possible hosts of odd-parity superconductivity, because the conditions for spin-triplet pairing are quite unfavorable in most cases. So far, Sr 2 RuO 4 17 and some uranium-based heavy fermion compounds 18,19 show strong evidence for the spin-triplet odd-parity superconductivity, but unfortunately their superconducting gap might have nodes on the Fermi surface. Recently, oddparity topological superconductivity in a doped topological insulator Cu x Bi 2 Se 3 has been proposed 13,16 , however, experimental results are under debate 20,21 .In a recent study we showed that odd-parity superconductivity occurs naturally in multilayer systems with layer-dependent spin-orbit coupling arising from the local lack of inversion symmetry 22 . We will consider here such locally non-centrosymmetric systems composed of the blocks of superconducting layers, e.g. trilayer systems as depicted in Fig. 1. Here the layer-dependent Rashba spin-orbit coupling is responsible for unusual electronic and superconducting properties 23 . The coupling constant of the Rashba spin-orbit coupling shows the layer-dependence, (α 1 , α 2 , α 3 ) = (α, 0, −α), ensured by the global inversion symmetry. We have shown that in such a system an odd-parity superconducting state can be stabilized by a magnetic field, even if the zerofield phase is the even-parity state (see Fig. 1) 22 . To be precise, the order parameter in the spin-singlet channel changes sign between the outer-most layers in the field-induced superconducting state (see Fig. 1). Considering the ...

Electric Octupole Order in Bilayer Rashba System

“…11) When the multipole moment is appropriately defined, ferroic odd-parity multipole order is accompanied by spontaneous global inversion symmetry breaking. The odd-parity toroidal order was demonstrated in LiCoPO 4 , 12,13) and magnetic quadrupole order has recently been implied in Sr 2 IrO 4 . 14,15) In this paper, we focus on the odd-parity EO state and clarify the thermodynamic stability in the bilayer Rashba system.…”

Odd-parity superconductors with two-component order parameters: Nematic and chiral, full gap, and Majorana node

“…On the other hand, the mechanisms and properties of odd-parity superconductivity in spin-orbit-coupled systems have been less explored until recently. In the last few years, a number of theoretical and numerical studies have shown that in the presence of strong spin-orbit interaction, odd-parity pairing can be realized in a broad range of materials without proximity to magnetic instabilities [6][7][8][9][10][11][12][13].…”

Field-induced topological pair-density wave states in a multilayer optical lattice

“…We stress again that our proposal is very different from those proposed in Refs. [27,29] where a layer-dependent SO coupling produces the PDW superfluid. Our scheme, which utilizes a layer-independent SO coupling, has the advantage of simplicity.…”

“…For example, the PDW state investigated in Ref. [27] is protected by mirror symmetry in a tri-layer system, and a pair of non-trivial chiral edge excitations emerge as long as the protecting symmetries are not broken. Thus the PDW states provide an ideal experimental candidate in the search of symmetry-protected topological phases for interacting fermions.…”

“…Most of the previous theoretical proposals on realizing PDW phases in multi-layer systems are based on a layer-dependent spin-orbit (SO) coupling [26,27,29,40], which results in a layer-dependent order parameter, i.e., the PDW phase. In cold-atom experiments, the SO coupling is induced by Raman coupling between hyperfine ground states of the atom [41,42].…”