Impurities and orbital dependent superconductivity in Sr_2RuO_4

There now exists a wealth of experimental evidence that Sr_2RuO_4 is an odd-parity superconductor. Experiments further indicate that among the bands stemming from the Ru {xy,xz,yz} orbitals, the portion of the Fermi surface arising from the xy orbitals exhibits a much larger gap than the portions of the Fermi surface arising from the {xz,yz} orbitals. In this paper the role of impurities on such an orbital dependent superconducting state is examined within the Born approximation. In contrast to expected results for a nodeless p-wave superconductor the unique nature of the superconducting state in Sr_2RuO_4 implies that a low concentration of impurities strongly influences the low temperature behavior.