Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model

We perform an instability analysis of the Emery three-band model at hole doping and weak coupling within a channel-decomposed functional renormalization group flow proposed in Phys. Rev. B 79, 195125 (2009). In our approach, momentum dependences are taken into account with improved precision compared to previous studies of related models. Around a generic parameter set, we find a strong competition of antiferromagnetic and d-wave Cooper instabilities with a smooth behavior under a variation of doping and additional hopping parameters. For increasingly incommensurate ordering tendencies in the magnetic channel, the d-wave pairing gap is deformed at its maxima. Comparing our results for the Emery model to those obtained for the two-dimensional one-band Hubbard model with effective parameters, we find that, despite considerable qualitative agreement, multi-orbital effects have a significant impact on a quantitative level.