Orbital Dependent Superconductivity inSr2RuO4

We show that for superconducting ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ any unconventional pairing in the part of the Fermi surface with Ru ${4d}_{\mathrm{xy}}$ orbital character is weakly coupled to that with Ru $\{{4d}_{\mathrm{xz}}{,4d}_{\mathrm{yz}}\}$ 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 nuclear quadrapole resonance measurements.