  The bulk-boundary correspondence guarantees topologically protected edge
states in a two-dimensional topological superconductor. Unlike in topological
insulators, these edge states are, however, not connected to a quantized (spin)
current as the electron number is not conserved in a Bogolyubov-de Gennes
Hamiltonian. Still, edge currents are in general present. Here, we use the
two-dimensional Rashba system as an example to systematically analyze the
effect symmetry reductions have on the order-parameter mixing and the edge
properties in a superconductor of Altland-Zirnbauer class DIII
(time-reversal-symmetry preserving) and D (time-reversal-symmetry breaking). In
particular, we employ both Ginzburg-Landau and microscopic modeling to analyze
the bulk superconducting properties and edge currents appearing in a strip
geometry. We find edge (spin) currents independent of bulk topology and
associated topological edge states which evolve continuously even when going
through a phase transition into a topological state. Our findings emphasize the
importance of symmetry over topology for the understanding of the non-quantized
edge currents.
