Large Chern Number and Edge Currents in Sr2RuO4

Using the results of a previously reported microscopic calculation, we show that the most favored chiral superconducting order parameter in Sr$_2$RuO$_4$ has Chern number $|C|=7$ in the weak coupling limit. This order parameter has a momentum dependence of the type $\sin(k_x) \cos(k_y) + i \sin(k_y) \cos(k_x)$ and lies in the same irreducible representation $E_u$ of the tetragonal point group as the usually assumed gap function $\sin(k_x) + i \sin(k_y)$. While the latter gap function leads to $C=1$, the former leads 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 Sr$_2$RuO$_4$.