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We analyze within quasi-particle theory a recent resonant inelastic x-rayscattering (RIXS) experiment on $\mathrm{YBa_2Cu_3O_{6+x}}$ with the incomingphoton energy detuned at several values from the resonance maximum [Minola etal., Phys. Rev. Lett. 114, 217003 (2015)]. Surprisingly, the data shows muchweaker dependence on detuning than expected from recent measurements on adifferent cuprate superconductor, $\mathrm{Bi_2Sr_2CuO_{6+x}}$ [Guarise et al.,Nat. Commun. 5, 5760 (2014)]. We demonstrate here, that this discrepancy,originally attributed to collective magnetic excitations, can be understood interms of the differences between the band structures of these materials. Wefind good agreement between theory and experiment over a large range ofdopings, both in the underdoped and in the overdoped regime. Moreover, wedemonstrate that the RIXS signal depends sensitively on excitations at energieswell above the Fermi surface, that are inaccessible to traditionally used bandstructure probes, such as angle-resolved photemisson spectroscopy. This makesRIXS a powerful probe of band structure, not suffering from surface preparationproblems and small sample sizes, making it potentially applicable to a numberof cuprate materials.

Resonant inelastic x-ray scattering as a probe of band structure effects in cuprates