  We perform a two-loop renormalization group (RG) analysis of a 2D effective
multiband model, which is relevant for describing the low-energy properties of
some iron-chalcogenide superconducting materials. Crucial ingredients in this
analysis are the calculation of higher-order contributions in the RG scheme
that go beyond the widely-used parquet approximation and the consequent
inclusion of nontrivial self-energy effects of the model that yield an
anisotropic renormalization of the quasiparticle weight in the system. The
motivation of our work is the experimental discovery by Sprau et al. (2017)
that orbitally-selective renormalization of the quasiparticle weight in the
Hund's metal phase at moderate temperatures underpins the highly unusual gap in
the superconducting phase of the FeSe compound at lower temperatures. One
prediction we arrive here is that the underlying origin of nematicity in these
systems may indeed come from orbital-selectivity, instead of a Pomeranchuk
instability in the $d_{\pm}$ channel. This orbital selectivity is driven by the
presence of stripe-type antiferromagnetic fluctuations in the model. Therefore,
we argue that the present RG results may provide a scenario from a
weak-to-moderate coupling perspective, in which the role of orbital selectivity
to describe the physical properties of some iron-chalcogenide superconductors
is emphasized.
