Nontopological nature of the edge current in a chiralp-wave superconductor

Abstract

The edges of time reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are non-topological-and therefore sensitive to microscopic details-even if we neglect Meissner screening. We give insight into the non-topological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov-de Gennes equations, the quasiclassical approximation, and the gradient expansion, and describe those special cases where edge currents do have a topological character. While edge currents are not quantized, they are generically large, but can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr2RuO4.

Thermal Hall conductivity and topological transition in a chiralp-wave superconductor forSr2RuO4

“…These current, however, are not a direct feature of topology, in the sense that their magnitude depends strongly on the band structure and the orientation and quality of the surface [15,24,25]. It has been shown that surface currents are essentially insensitive to changes of Chern number, e.g.…”

Evolution of the filamentary 3-Kelvin phase inPb−Ru−Sr2RuO4Josephson junctions

“…For the bulk state of SRO in the zero-magnetic field, multiple studies [1][2][3][4] , in particular, the observation of the polar Kerr effect 13 and intrinsic magnetism in µSR experiments 14 , count as evidence for the realization of a time-reversal symmetry breaking (TRSB) chiral p-wave state [1][2][3][4] . On the other hand, several experimental attempts to observe spontaneous edge currents expected for the chiral p-wave state led to negative results [15][16][17] and have triggered several theoretical studies exploring potential reasons for this conflicting result [18][19][20] . Microscopic calculations concerning the pairing symmetry show a close competition between a chiral and helical p-wave state, the former having inplane-and the latter c-axis equal-spin pairing 21 .…”

Interband interference effects at the edge of a multiband chiralp-wave superconductor

“…II C for a complementary explanation based on the order parameter variations). By contrast, since there is no apparent spectral flow, the current in the [++] model hardly varies at finite mixing 15 . What is most striking is the inverted current flow in the [+−] model in the presence of noticeable interband mixing, given that our model employs rather moderate edge disorder (manifest in the fact that the extension of interband mixing is much narrower than the coherence length and that the ∆ y -components survive at the edge in Fig.2).…”

“…What is most striking is the inverted current flow in the [+−] model in the presence of noticeable interband mixing, given that our model employs rather moderate edge disorder (manifest in the fact that the extension of interband mixing is much narrower than the coherence length and that the ∆ y -components survive at the edge in Fig.2). Previous one-band studies showed that current inversion is possible by varying the gap structure 15 and edge orientation in lattice models 19 . Our study therefore demonstrates an additional mechanism, interband interference, for FIG.…”

“…Recently, there have been numerous theoretical attempts to address this issue. In particular, due to U (1) symmetry breaking the edge current is not expected to be topologically protected 15,16 , hence chiral p-wave models with anisotropic gap structure, be it single band or multiband, may generate substantially smaller current compared with that of a simple isotropic chiral p-wave model 15,[17][18][19][20][21] . Additional strong suppression is possible in the presence of strong surface disorder 20,21 .…”