Electronic interactions in a vacancy-engineered honeycomb lattice: Transition from a nodal-line semimetal to a magnetic insulator

Nodal-line semimetals (NLSMs) harbor a variety of novel physical properties owing to the particularities of the band degeneracies that characterize the spectrum of these materials. In symmetry-enforced NLSMs, band degeneracies, being imposed by symmetries, are robust to arbitrarily strong perturbations that preserve the symmetries. We investigate the effects of electron-electron interactions on a recently proposed vacancy-engineered NLSM known as holey graphene. Using mean-field calculations and quantum Monte Carlo simulation, we show that the Hubbard model on the depleted holey-graphene lattice at half filling exhibits a transition from a NLSM to an insulating antiferromagnetic phase for an arbitrarily weak repulsive interaction $U$. In contrast to the semimetal-insulator transition in the pristine honeycomb lattice, which occurs at a finite critical value of $U$, in the depleted lattice, the transition at $U=0$ is associated with a van Hove singularity arising from the crossing of accidental nodal lines and those enforced by symmetry. We also employ linear spin wave theory (LSWT) to the effective Heisenberg model in the strong-coupling limit and obtain the global antiferromagnetic order parameter ${m}_{\mathrm{AFM}}\ensuremath{\approx}0.146$. The order parameters from both QMC and LSWT agree quantitatively. Our findings indicate that vacancy engineering offers an effective way to tailor the magnetic properties of quantum materials.