Gustav Romare and colleagues at the University of Wisconsin-Madison have discovered the peak superconducting transition temperature in a two-dimensional model does not occur where expected. Their determinant quantum Monte Carlo simulations reveal the maximum T_c shifts away from the Van Hove point, appearing instead at a density unrelated to features in the non-interacting density of states. This finding challenges predictions from weak-coupling BCS theory and suggests a strong-coupling interpretation of superconductivity in this system. The work demonstrates maximal T_c is achieved at intermediate interaction strengths, not at the strongest or weakest points.

Van Hove Singularities Influence on 2D Superconductivity

This finding challenges expectations from weak-coupling BCS theory, which predicts peak superconductivity precisely at these points of enhanced electronic density. The simulations computed $T_{c}$ in the vicinity of both standard logarithmic and higher-order power-law Van Hove singularities, probing the influence of singularity strength on superconducting behavior. While enhancing the Van Hove singularity from a logarithmic to a power-law form does increase $T_{c}$ , the improvement is surprisingly minor.

This suggests that simply amplifying the strength of the Van Hove singularity is not the primary route to maximizing superconductivity within this model. This result supports a strong-coupling interpretation of the superconductivity observed, moving beyond the limitations of simpler, weak-coupling theories. The simulations also explored the relationship between interaction strength and $T_{c}$ , revealing a detailed dependence. The maximal $T_{c}$ was not found at either very weak or very strong interactions, but rather at intermediate values of U, indicating an optimal balance is required for achieving the highest superconducting temperature.

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. This finding is significant because it suggests that an optimal balance of interactions is important for maximizing superconductivity.

Weak-Coupling BCS Theory vs. Observed T_c Enhancement

Enhancing the strength of a Van Hove singularity, a point where the density of states diverges, from logarithmic to a power-law form yields only a minor additional enhancement of $T_{c}$ , according to new simulations. Maximizing superconductivity isn’t simply about amplifying the singularity itself, consistent with a strong-coupling interpretation of superconductivity.

The simulations focused on the two-dimensional attractive Hubbard model, a standard framework for understanding superconductivity, and explored how interaction strength affects $T_{c}$ near these singularities. 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, 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.

Power-Law vs. Logarithmic Van Hove Singularity Effects

The simulations pinpoint a surprising shift in the conditions for achieving maximal superconductivity; the peak $T_{c}$ does not occur at the Van Hove point itself. The team’s findings indicate that the system’s behavior deviates from the predictions of perturbation theory, and that the interplay between interaction strength and electronic structure is complex. The maximal $T_{c}$ within the model is achieved at intermediate values of U, a parameter representing the strength of electron-electron interactions.

The simulations reveal that the highest temperatures are attained when interactions are balanced, indicating a sweet spot where electron pairing and coherence are maximized. The simulations were performed on square lattices, allowing for accurate calculations at larger system sizes. The research team extracted the electronic DOS in the interacting system using a proxy based on the imaginary-time Green’s function directly sampled in the DQMC simulation.

Shifted Maximum T_c with Stronger Interaction Strength

This finding challenges the assumption that stronger singularities automatically lead to higher transition temperatures, a cornerstone of some theoretical predictions. Beyond a critical interaction strength of approximately U = W/3, where W represents the electronic bandwidth, the influence of the Van Hove singularity on $T_{c}$ diminishes rapidly, causing the peak temperature to shift away from the expected density. This movement is observed with increasing interaction strength, indicating that the conditions for achieving maximal superconductivity become increasingly detached from the features of the non-interacting density of states.

2D Material Relevance & Parameter Optimization for T_c

Simulations reveal the highest superconducting transition temperature (T_c) in the two-dimensional attractive Hubbard model occurs not at the predicted Van Hove point, but at a density where the non-interacting electronic structure shows no particular feature. “For, there is a maximum in $T_{c}$ near the VHS fillings, which is broadened with increasing |U|,” the authors note.

👉 More information
🗞 Superconductivity near two-dimensional Van Hove singularities: A determinant quantum Monte Carlo study
✍️ Gustav Romare, Daniel Shaffer, Alex Levchenko, Edwin Huang and Ilya Esterlis
🧠 DOI: http://link.aps.org/doi/10.1103/s8kf-crkv

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