Abstract
I present the results of first principles calculations of the electronic structure and magnetic interactions for the recently discovered superconductor YFe${}_{2}$Ge${}_{2}$ and use them to identify the possible nature of superconductivity and quantum criticality in this compound. I find that the Fe $3d$ derived states near the Fermi level show a rich structure with the presence of both linearly dispersive and heavy bands. The Fermi surface exhibits nesting between hole and electron sheets that manifests as a peak in the susceptibility at $(1/2,1/2)$. The antiferromagnetic spin fluctuations associated with this peak may be responsible for mediating the superconductivity in this compound resulting in a ${s}_{\ifmmode\pm\else\textpm\fi{}}$ state similar to that of the previously discovered iron-based superconductors. I also find that various magnetic orderings are almost degenerate in energy, which indicates that the proximity to quantum criticality is due to competing magnetic interactions.
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