Classification of topological crystalline superconducting nodes on high-symmetry lines: Point nodes, line nodes, and Bogoliubov Fermi surfaces

Abstract

Recent development in exact classification of a superconducting gap has elucidated various unconventional gap structures, which have not been predicted by the classification of order parameter based on the point group. One of the important previous results is that all symmetry-protected line nodes are characterized by nontrivial topological numbers. Another intriguing discovery is the gap structures depending on the angular momentum $j_z$ of normal Bloch states on threefold and sixfold rotational-symmetric lines in the Brillouin zone. Stimulated by these findings, we classify irreducible representations of the Bogoliubov-de Gennes Hamiltonian at each $\mathbf{k}$ point on a high-symmetry $n$-fold ($n=2$, $3$, $4$, and $6$) axis for centrosymmetric and paramagnetic superconductors, by using the combination of group theory and $K$ theory. This leads to the classification of all crystal symmetry-protected nodes (including $j_z$-dependent nodes) on the axis that crosses a normal-state Fermi surface. As a result, it is shown that the classification by group theory completely corresponds with the topological classification. Based on the obtained results, we discuss superconducting gap structures in SrPtAs, CeCoIn${}_5$, UPt${}_3$, and UCoGe.

21 pages, 10 figures

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• Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor UPt${}_3$
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Intrinsic ac anomalous Hall effect of nonsymmorphic chiral superconductors with an application to $\mathrm{UP}{\mathrm{t}}_3$
• Quantum Criticality in the Ferromagnetic Superconductor UCoGe under Pressure and Magnetic Field
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Cited by in corpus (35)

• Insulator-metal transition and topological superconductivity in UTe2 from a first-principles calculation
• Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe${}_2$
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Exceeding the Landau superflow speed limit with topological Bogoliubov Fermi surfaces
• Spin-triplet superconductivity in Weyl nodal-line semimetals
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Superconductivity induced by fluctuations of momentum-based multipoles
• Electronic multipoles and multiplet pairs induced from Pomeranchuk and Cooper instabilities of Bogoliubov Fermi surfaces
• Instability of $j=3/2$ Bogoliubov Fermi-surfaces
• Type-II Weyl semimetal vs gravastar
• Time-Reversal Symmetry Breaking Superconductivity in Three-Dimensional Dirac Semimetallic Silicides
• Majorana multipole response: General theory and application to wallpaper groups
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Odd-frequency pairing inherent in Bogoliubov Fermi liquid
• Topological d-wave superconductivity in two dimensions
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Topological Anomalous Skin Effect in Weyl Superconductors
• Nematic Bogoliubov Fermi surfaces from magnetic toroidal order in FeSe${}_{1-x}$S${}_x$
• Topological gapless points in superconductors: From the viewpoint of symmetry
• Linking structures of doubly charged nodal surfaces in centrosymmetric superconductors
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Impurity effect on Bogoliubov Fermi surfaces: Analysis based on iron-based superconductors
• Coexistence of Chiral Majorana Edge States and Bogoliubov Fermi Surfaces in Two-Dimensional Nonsymmorphic Dirac Semimetal/Superconductor Heterostructures
• Supercurrent-Induced Weyl Superconductivity
• Majorana multipole response with magnetic point group symmetry
• Fragile topology in nodal-line semimetal superconductors
• Spin fluctuations in the ultranodal superconducting state of Fe(Se,S)
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture
• Superconducting Gap Structures in Wallpaper Fermion Systems
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction
• Theory of Hofstadter Superconductors
• Evolution and Instability of Bogoliubov Fermi Surfaces under Zeeman Field