Odd-parity multipole fluctuation and unconventional superconductivity in locally noncentrosymmetric crystal

Abstract

A microscopic calculation and symmetry argument reveal superconductivity in the vicinity of parity-violating magnetic order. In a crystal structure lacking local space inversion symmetry, an augmented cluster magnetic multipole order may break global inversion symmetry, and therefore it is classified into an odd-parity multipole order. We investigate unconventional superconductivity induced by an odd-parity magnetic multipole fluctuation in a two-dimensional two-sublattice Hubbard model motivated by Sr2IrO4. We find that even-parity superconductivity is more significantly suppressed by spin-orbit coupling than that in a globally noncentrosymmetric system. Consequently, two odd-parity superconducting states are stabilized by magnetic multipole fluctuations in a large spin-orbit coupling region. Both of them are identified as Z2 topological superconducting states. The obtained gap function of inter-sublattice pairing shows a gapped or nodal structure protected by nonsymmorphic symmetry. Our finding implies a family of odd-parity topological superconductors. Candidate materials are discussed.

Superconductivity induced by fluctuations of momentum-based multipoles

“…It is attributed to the number of components in the magnetic dipole bases taken into account: {x,ŷ,ẑ} for the former and {x,ŷ} for the latter. For a fluctuation of the quadrupoles, the vertex function in Table III (48) which consists of two attractive pairing channels with A 1g and E g symmetry. Solutions of the linearized gap equation (D6) for the interaction vertex are given in Table IV(c).…”

“…For example, an electric quadrupole order may be closely related to superconductivity in PrTr 2 Al 20 (Tr= Ti, V) [29][30][31][32][33][34] and PrIr 2 Zn 20 [39,40]; an electric hexadecapole [35,36] or a magnetic dotriacontapole order [37] in URu 2 Si 2 and various multipoles in PrOs 4 Sb 12 [38] have also been intensively discussed. Another topic is odd-parity multipoles; recent theoretical studies have pointed out that odd-parity multipoles invoke unconventional superconductivity not only in the coexisting state [18,19,41,42] but also in the disordered state due to the multipole fluctuations [43][44][45][46][47][48].…”

“…In a pioneering work by Kozii and Fu [43], they proposed odd-parity superconductivity mediated by fluctuations of momentum-based OE multipoles, which are represented by an electron's spin texture on the Fermi surface in spin-orbitcoupled systems. However, superconductivity induced by the other classes of (EE, EM, and OM) multipole fluctuations, which has been investigated in specific models or materials [38,48], remains to be clarified in generic situations. Furthermore, crystalline electric fields (CEFs) may cause higher anisotropy of superconductivity [47], although Kozii and Fu considered only isotropic systems [43].…”

A $$\phi ^6$$ soliton with a long-range tail

“…However, gradually increasing g from zero supports more and more bound states. Besides the bound states, one can explore the scattering ones considering energies above the threshold in the equation of motion (36). We show the upper and lower components of the fermionic scattering states for the scattering from both directions in Fig.…”

“…They studied the fermion bound spectrum as well as the scattering of fermions from the localized topological structure and found a closed form for the scattering cross-section for small fermion-skyrmion coupling. Parity or inversion symmetry breaking models with topological solutions are of importance in many areas of physics, for example in the context of superconductivity [35][36][37][38][39], fractional quantum Hall effect [40], mesoscopic electron transport [41], current of abnormal parity [42], heavy-ion collisions [43], nonlinear Schrödinger equations [44] and hydrodynamics [45].…”