Classification of multipole superconductivity in multi-orbital systems and its implications

Abstract

Motivated by a growing interest in multi-orbital superconductors with spin-orbit interactions, we perform the group-theoretical classification of various unconventional superconductivity emerging in symmorphic $\mathrm{O}$, ${\mathrm{D}}_4$, and ${\mathrm{D}}_6$ space groups. The generalized Cooper pairs, which we here call "multipole" superconductivity, possess spin-orbital coupled (multipole) degrees of freedom, instead of the conventional spin singlet/triplet in single-orbital systems. From the classification, we obtain the following key consequences, which have been overlooked in the long history of research in this field: (1) A superconducting gap function with ${\Gamma }_9\otimes {\Gamma }_9$ in ${\mathrm{D}}_6$ possesses nontrivial momentum dependence, different from the usual spin 1/2 classification. (2) Unconventional gap structure can be realized in the BCS approximation of purely local (on-site) interactions irrespective of attractive/repulsive. It implies the emergence of an electron-phonon (e-ph) driven unconventional superconductivity. (3) Reflecting symmetry of orbital basis functions, there appear not symmetry-protected but inevitable line nodes/gap minima, and thus, anisotropic $s$-wave superconductivity can be naturally explained without any competitive fluctuations.

arXiv comment18 pages, 4 figures, 7 tables

References in corpus (30)

• Heavy fermion superconductivity and magnetic order in non-centrosymmetric $CeP{t}_{3}Si$
• Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state
• Superconductivty without inversion symmetry: MnSi versus CePt_3Si
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Angular Position of Nodes in the Superconducting Gap of Quasi-2D Heavy-Fermion Superconductor CeCoIn_5
• The Order Parameter for the Superconducting Phases of UPt${}_3$
• Multiple Superconducting Phases in New Heavy Fermion Superconductor PrOs4Sb12
• Minimal electronic models for superconducting BiS${}_2$ layers
• Spin-triplet p-wave pairing in a 3-orbital model for iron pnictide superconductors
• Three orbital model for the iron-based superconductors
• 2D superconductivity with strong spin-orbit interaction
• Heavy Fermion Superconductivity in the Quadrupole Ordered State of PrV2Al20
• Nodal Structure of Unconventional Superconductors Probed by the Angle Resolved Thermal Transport Measurements
• Pairing of j=3/2 fermions in half-Heusler superconductors
• Sign reversal of field-angle resolved heat capacity oscillations in a heavy fermion superconductor CeCoIn${}_5$ and $d_{x^2-y^2}$ pairing symmetry
• Observation of Modulated Quadrupolar Structures in PrPb3
• Order parameter in superconductors with non-degenerate bands
• Crystal Structure, Lattice Vibrations, and Superconductivity of LaO${}_{1-x}$F${}_x$BiS${}_2$
• In-plane Charge Fluctuations in Bismuth Sulfide Superconductors
• $S_4$ Symmetric Microscopic Model for Iron-Based Superconductors
• Odd Parity and Line Nodes in Non-Symmorphic Superconductors
• Pairing symmetry and properties of iron-based high temperature superconductors
• Gap Symmetry and Stability Analysis in the Multi-Orbital Fe-Based Superconductors
• Symmetry of superconducting states with two orbitals on a tetragonal lattice: application to $La{O}_{1-x}{F}_{x}FeAs$
• Symmetry and topology of two-dimensional noncentrosymmetric superconductors
• Theory of anisotropic s-wave superconductivity with point-node like gap minima: analysis of (Y,Lu)Ni_2B_2C
• Verification of Anisotropic s-Wave Superconducting Gap Structure in CeRu2 from Low-Temperature Field-Angle-Resolved Specific Heat Measurements
• TAO pairing: a fully gapped pairing scenario for the Iron-Based Superconductors
• Constrain on possible pairing symmetry in a two-orbital model of FeAs-based superconductors
• On-site Atractive Multiorbital Hamiltonian for $d$-Wave Superconductors

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