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The bulk-boundary correspondence guarantees topologically protected edgestates in a two-dimensional topological superconductor. Unlike in topologicalinsulators, these edge states are, however, not connected to a quantized (spin)current as the electron number is not conserved in a Bogolyubov-de GennesHamiltonian. Still, edge currents are in general present. Here, we use thetwo-dimensional Rashba system as an example to systematically analyze theeffect symmetry reductions have on the order-parameter mixing and the edgeproperties in a superconductor of Altland-Zirnbauer class DIII(time-reversal-symmetry preserving) and D (time-reversal-symmetry breaking). Inparticular, we employ both Ginzburg-Landau and microscopic modeling to analyzethe bulk superconducting properties and edge currents appearing in a stripgeometry. We find edge (spin) currents independent of bulk topology andassociated topological edge states which evolve continuously even when goingthrough a phase transition into a topological state. Our findings emphasize theimportance of symmetry over topology for the understanding of the non-quantizededge currents.

Role of Topology and Symmetry for the Edge Currents of a 2D Superconductor