Vanishing edge currents in non-$p$-wave topological chiral superconductors

Abstract

The edge currents of two dimensional topological chiral superconductors with nonzero Cooper pair angular momentum---e.g., chiral $p$-, $d$-, and $f$-wave superconductivity---are studied. Bogoliubov-de Gennes and Ginzburg--Landau calculations are used to show that in the continuum limit, \emph{only} chiral $p$-wave states have a nonzero edge current. Outside this limit, when lattice effects become important, edge currents in non-$p$-wave superconductors are comparatively smaller, but can be nonzero. Using Ginzburg--Landau theory, a simple criterion is derived for when edge currents vanish for non-$p$-wave chiral superconductivity on a lattice. The implications of our results for putative chiral superconductors such as Sr2RuO4 and UPt3 are discussed.

9 pages, 5 figures. Published version

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Cited by in corpus (12)

• Topological surface states in nodal superconductors
• Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids
• Non-topological nature of the edge current in a chiral p-wave superconductor
• Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation
• Orbital momentum of chiral superfluids and spectral asymmetry of edge states
• Surface magnetism in a chiral d-wave superconductor with hexagonal symmetry
• Orbital angular momentum in a nonchiral topological superconductor
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects
• Interband interference effects at the edge of a multiband chiral p-wave superconductor
• Even odder after twenty-three years: the superconducting order parameter puzzle of Sr2RuO4
• Laser pulse probe of chirality of Cooper pairs