Large Chern Number and Edge Currents in Sr2RuO4.

We show from a weak-coupling microscopic calculation that the most favored chiral superconducting order parameter in Sr2RuO4 has a Chern number of |C|=7. The two dominant components of this order parameter are given by sin(3k(x))+isin(3k(y)) and sin(k(x))cos(k(y))+isin(k(y))cos(k(x)) and lie in the same irreducible representation E(u) of the tetragonal point group as the usually assumed gap function, sin(k(x))+isin(k(y)). While the latter gap function leads to C=1, the two former lead to C=-7, which is also allowed for an E_{u} gap function since the tetragonal symmetry only fixes C modulo 4. Since it was shown that the edge currents of a |C|>1 superconductor vanish exactly in the continuum limit, and can be strongly reduced on the lattice, this form of order parameter could help resolve the conflict between experimental observation of time-reversal symmetry breaking and yet the absence of observed edge currents in Sr2RuO4.