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We establish the existence of bulk odd-frequency superconductivity inSr$_2$RuO$_4$ and show that an intrinsic Kerr effect is a direct evidence ofthis state. We use both general two- and three-orbital models, as well as arealistic tight-binding description of Sr$_2$RuO$_4$ to demonstrate thatodd-frequency pairing arises due to finite hybridization between differentorbitals in the normal state, and is further enhanced by finite inter-orbitalpairing.

Odd-frequency superconductivity in Sr$_2$RuO$_4$ measured by Kerr rotation