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

TL;DR

This study uses determinant quantum Monte Carlo to analyze how Van Hove singularities affect the superconducting transition temperature in a two-dimensional attractive Hubbard model, revealing nuanced behavior across interaction strengths.

Contribution

It provides the first detailed quantum Monte Carlo analysis of the impact of both logarithmic and power-law Van Hove singularities on $T_c$ in this model.

Findings

$T_c$ is modestly enhanced near Van Hove points for weak interactions.

Enhancing Van Hove singularity from logarithmic to power-law yields minor $T_c$ increase.

Maximum $T_c$ occurs at intermediate interaction strength and away from Van Hove points.

Abstract

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 $|U| \lesssim W/3$, 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 $|U| \gtrsim W/3$, 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.