Superconductivity near ordinary and higher order Van Hove singularities: A determinant quantum Monte Carlo study

2D materials are highly tunable systems, naturally providing a fruitful platform to explore various electronic phenomena. When a 2D metal is tuned through a van Hove singularity in the density of states, BCS theory predicts a significant enhancement of the superconducting transition temperature Tc (absent competing instabilities). When the interaction strength increases, however, the picture becomes less clear. We report determinant quantum Monte Carlo results for Tc in the 2D attractive Hubbard model across both the ordinary and higher-order Van Hove singularity; we observe a mild enhancement of Tc, significantly less than that expected on the basis of weak-coupling BCS theory. These results suggest that achieving a divergent density of states is not sufficient to find high Tc-superconductivity.