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We perform a two-loop renormalization group (RG) analysis of a 2D effectivemultiband model, which is relevant for describing the low-energy properties ofsome iron-chalcogenide superconducting materials. Crucial ingredients in thisanalysis are the calculation of higher-order contributions in the RG schemethat go beyond the widely-used parquet approximation and the consequentinclusion of nontrivial self-energy effects of the model that yield ananisotropic renormalization of the quasiparticle weight in the system. Themotivation of our work is the experimental discovery by Sprau et al. (2017)that orbitally-selective renormalization of the quasiparticle weight in theHund's metal phase at moderate temperatures underpins the highly unusual gap inthe superconducting phase of the FeSe compound at lower temperatures. Oneprediction we arrive here is that the underlying origin of nematicity in thesesystems may indeed come from orbital-selectivity, instead of a Pomeranchukinstability in the $d_{\pm}$ channel. This orbital selectivity is driven by thepresence of stripe-type antiferromagnetic fluctuations in the model. Therefore,we argue that the present RG results may provide a scenario from aweak-to-moderate coupling perspective, in which the role of orbital selectivityto describe the physical properties of some iron-chalcogenide superconductorsis emphasized.

Orbital selectivity versus Pomeranchuk instability in the iron-chalcogenide superconductors: A two-loop renormalization group study