Excitonic instability and unconventional pairing in the nodal-line materials ZrSiS and ZrSiSe

We use a functional renormalization group (fRG) approach to investigate potential interaction-induced instabilities in a two-dimensional model for the Dirac nodal-line materials ZrSiS and ZrSiSe employing model parameters derived from ab initio calculations. Our results characterize the excitonic instability recently found in random-phase approximation for ZrSiS as an on-site spin-charge-degenerate exciton. Beyond this, we show that the fRG analysis produces an energy scale for the onset of the instability, in good agreement with the experimentally observed mass enhancement. Additionally, by exploring the parameter space of the model, we find that reducing the band splitting increases the instability scale and gives the chance to drive the system into an unconventional superconducting pairing state. The model parameters for the case of the structurally similar material ZrSiSe suggest the d-wave superconducting state as the leading instability with a very small critical scale.