Superconductivity near two-dimensional Van Hove singularities: a determinant quantum Monte Carlo study

The superconducting transition temperature T c of the two-dimensional attractive Hubbard model is computed in the vicinity of both ordinary (logarithmic) and higher-order (power-law) Van Hove singularities using determinant quantum Monte Carlo simulations. For interaction strengths U W/3, where W is the electronic bandwidth, T c is enhanced in the neighborhood of the Van Hove point, albeit more weakly than expected from weak-coupling BCS theory. Enhancing the Van Hove singularity from logarithmic to power-law yields only a minor additional enhancement of T c. For U W/3, the maximum T c shifts away from the Van Hove point and instead occurs at a density unrelated to any features in the non-interacting density of states, consistent with a strong-coupling interpretation. We find that the maximal T c in the model is achieved at intermediate U and at a density away from the Van Hove point.