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 (27)

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• Orbital momentum of chiral superfluids and spectral asymmetry of edge states
• Superconductivity in Correlated Multi-Orbital Systems with Spin-Orbit Coupling: Coexistence of Even- and Odd-Frequency Pairing and the Case of Strontium Ruthenate
• Surface magnetism in a chiral d-wave superconductor with hexagonal symmetry
• Coreless vortices as direct signature of chiral $d$-wave superconductivity
• Hidden anomalous Hall effect in Sr${}_2$RuO${}_4$ with chiral superconductivity dominated by the Ru $d_{xy}$ orbital
• Orbital angular momentum in a nonchiral topological superconductor
• Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors
• Degeneracy between even- and odd-parity superconductivity in the quasi-1D Hubbard model and implications for Sr2RuO4
• A review of some new perspectives on the theory of superconducting Sr${}_2$RuO${}_4$
• Robustness of chiral surface current and subdominant $s$-wave Cooper pairs
• 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
• Strong-coupling approach to temperature dependence of competing orders of superconductivity: Possible time-reversal symmetry breaking and nontrivial topology
• Even odder after twenty-three years: the superconducting order parameter puzzle of Sr2RuO4
• Laser pulse probe of chirality of Cooper pairs
• Examining the possibility of chiral superconductivity in Sr${}_2$RuO${}_4$ and other compounds via applied supercurrent
• Quantum theory for edge current and noise in two-dimensional topological superconductors
• Vortices in Two-Dimensional Chiral Superfluids
• Designing edge currents using mesoscopic patterning in chiral d-wave superconductors
• Chiral Current Inversion Induced by Flat-Band Andreev Bound States
• Exotic Topological Phenomena in Chiral Superconducting States on Doped Quantum Spin Hall Insulators with Honeycomb Lattices
• Chirality reversal at finite magnetic impurity strength and local signatures of a topological phase transition
• Long-range Cooper pair splitting by chiral Majorana edge states