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In the light of the recently discussed mechanism for suppression ofsuperconductivity in multi-orbital systems called inter-orbital effect, here weextend our analysis of the upper critical field in Sr$_2$RuO$_4$ now understrain. We show that the presence of the standard orbital effect and the newmechanism can consistently account for the qualitative changes observed in theupper critical field for the strained system, in particular, combining theoverall enhancement of the critical field with the reduction in the anisotropy.The proposed picture holds for a triplet superconducting state, showing that asinglet state is not the only possibility to account for the observations. Wesuggest further experiments in order to clarify our understanding about thesuperconducting phase of Sr$_2$RuO$_4$.

A note on the upper critical field of Sr$_2$RuO$_4$ under strain