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.

arXiv comment9 pages, 5 figures. Published version

References in corpus (33)

• Time-Reversal Symmetry Breaking Superconductivity in Sr2RuO4
• Chiral superconductivity from repulsive interactions in doped graphene
• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Evaluation of Spin-Triplet Superconductivity in Sr2RuO4
• Fermion zero modes on vortices in chiral superconductors
• The Order Parameter for the Superconducting Phases of UPt${}_3$
• Chiral P-Wave Order in Sr_2RuO_4
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Observation of broken time-reversal symmetry in the heavy fermion superconductor UPt${}_3$
• Upper limit on spontaneous supercurrents in Sr${}_2$RuO${}_4$
• Chiral $d$-wave Superconductivity in SrPtAs
• Pairing State with a time-reversal symmetry breaking in FeAs based superconductors
• Spontaneous Hall effect in chiral p-wave superconductor
• Spin triplet superconductivity with line nodes in Sr2RuO4
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Is Sr2RuO4 a Chiral P-Wave Superconductor?
• Identifying the pairing symmetry in the Sr2RuO4 superconductor
• Edge properties of the chiral d-wave superconducting state in doped graphene
• Anisotropic chiral d+id superconductivity in NaxCoO2 yH2O
• Intrinsic Hall effect in a multiband chiral superconductor in the absence of an external magnetic field
• Impurity Induced Polar Kerr Effect in A Chiral p-wave Superconductor
• d+id'-wave Superconducting States in Graphene
• Possible f-wave superconductivity in Sr${}_2$RuO${}_4$?
• Mass flows and angular momentum density for $p_x+i{p}_y$ paired fermions in a harmonic trap
• Suppression of spontaneous currents in Sr${}_2$RuO${}_4$ by surface disorder
• Intrinsic optical dichroism in the chiral superconducting state of Sr${}_2$RuO${}_4$
• Properties of edge states in spin-triplet two-band superconductor
• Suppression of Spontaneous Supercurrents in a Chiral p-Wave Superconductor
• Superconductors with broken time-reversal symmetry: Spontaneous magnetization and quantum Hall effects
• Abelian Chern-Simons Term in Superfluid 3He-A
• Andreev Bound States, Surfaces and Subdominant Pairing in High Tc Superconductors
• Edge-currents in superconductors with a broken time-reversal symmetry
• Local Time-Reversal Symmetry Breaking in d_(x2-y2) Superconductors

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