Orbital dependent superconductivity in Sr₂RuO₄

We show that for superconducting Sr_2RuO_4 any unconventional pairing in the part of the Fermi surface with Ru 4d-xy orbital character is weakly coupled to that with Ru 4d-xz, 4d-yz orbital character. This naturally gives rise to two disparate energy scales in the superconducting state which leads to novel low temperature properties in a variety of thermodynamic and transport properties and which would also account for the large residual density of states seen in specific heat and NQR measurements.