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Recent experimental advances in using strain engineering to significantlyalter the band structure of moderately correlated systems offer opportunitiesand challenges to weak-coupling renormalization group (RG) analysis approachesfor predicting superconducting instabilities. On one hand, the RG approach canprovide theoretical guidance. On the other hand, it is now imperative to betterunderstand how the predictions of the RG approach depends on microscopic andnon-universal model details. Here we focus on the effect of band-selectivemass-renormalization often observed in angle resolved photoemissionspectroscopy. Focusing on a specific example of uniaxially strained$\rm{Sr_2RuO_4}$ we carry out the weak-coupling RG analysis from two sets ofband structures as starting points: one is based on density functional theory(DFT) calculations and the other is based on angle-resolved photoemissionspectroscopy (ARPES) measurements. Despite good agreement between the Fermisurfaces of the the two band structures we find the two sets of band structuresto predict qualitatively different trends in the strain dependence of thesuperconducting transition temperature $T_c$ as well as the dominant channel.

Band-structure-dependence of renormalization-group prediction on pairing channels