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

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Superconductivity near two-dimensional Van Hove singularities".

Mira: Here's the gist of the paper. The gist The superconducting transition temperature Tc 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.

Kai: Model and Methods The study utilizes the attractive Hubbard model, defined by the Hamiltonian H = X kσ ϵkc†kσckσ + U X i ni↑ni↓, where U = −U < 0.

Mira: For the ordinary VHS case, t′′ = 0 and a second neighbor hopping t′ is needed to move the logarithmic VHS away from perfect nesting of the Fermi surface.

Kai: The non-interacting bandwidth is defined as W = 8t in both cases.

Paper summary: Kai: To summarize the paper "Superconductivity near two-dimensional Van Hove singularities: a determinant quantum Monte Carlo study," they use determinant quantum Monte Carlo simulations to compute Tc of the two-dimensional attractive Hubbard model near both ordinary logarithmic and higher-order power-law Van Hove singularities.

Mira: The core thesis is that for interaction strengths U less than or equal to W over three, Tc gets enhanced near the Van Hove point, but this enhancement is weaker than predicted by standard weak-coupling BCS theory.

Lev: They also find that moving from a logarithmic singularity to a power-law one only gives them a minor extra boost in Tc.

Kai: Then they look at stronger coupling, U greater than W over three, and they see that the maximum Tc moves away from the Van Hove point and appears at a density unrelated to any non-interacting features.

Mira: This shift supports a strong-coupling interpretation where physics changes fundamentally beyond that interaction strength.

Lev: The model itself is free from the notorious fermion minus-sign problem for any electron density, which lets them simulate it efficiently by determinant quantum Monte Carlo for large system sizes and low temperatures over a range of densities around the Van Hove point (ref: <ref:2604.13161#pg2>).

Kai: They extract Tc from the superfluid density rho s using the BKT criterion, where rho s over T minus c equals two pi Tc, and they get this directly from DQMC data using a formula involving an expectation value of the diamagnetic term Kxx and a current-current correlation function Λxx at zero momentum (ref: <ref:2604.13161#pg3>).

Mira: The perturbative analysis shows that the treatment including both self-energy effects and corrections to the pairing vertex is in satisfactory agreement with the DQMC calculations for coupling strengths less than or equal to one over four (ref: <ref:2604.13161#pg2>).

Lev: But they also note that both self-energy and vertex corrections tend to reduce Tc by smearing the density of states and decreasing the effective interaction strength.

Kai: So for weak to intermediate coupling, near the Van Hove point enhances Tc, but those same corrections smear things out and bring it back down a bit.

Mira: And when they look beyond that critical coupling strength of order U ∼ W over three, they see that the effects of the Van Hove singularities are rapidly washed out.

Lev: The paper flags this crossover as being quite sudden, moving from Fermi-surface pairing to local pairing (ref: <ref:2604.13161#pg2>).

Kai: So what this means for us is that the enhancement of superconductivity by a Van Hove singularity appears to be a weak-coupling phenomenon, and interactions quickly limit its effectiveness.

Mira: It suggests that relying solely on engineering density of states singularities might not be enough to achieve high Tc in these strongly correlated systems.

Conclusion: Kai: So wrapping up this paper "Superconductivity near two-dimensional Van Hove singularities: a determinant quantum Monte Carlo study," the main point is that proximity to a Van Hove singularity enhances Tc only for interaction strengths less than or equal to W over three.

Mira: Beyond that critical coupling, the influence of the Van Hove singularities rapidly disappears, and the maximal Tc shifts away from those features.

Lev: The authors conclude that for stronger coupling, the maximal Tc is found at intermediate U and a density far from any band structure features, which is consistent with strong-coupling theory.

Kai: This implies that for these parameters, you don't get the optimal result by tuning your system to hit a Van Hove point in the non-interacting density of states.

Mira: The paper suggests that the enhancement of superconductivity by a Van Hove singularity seems to be essentially a weak-coupling phenomenon, and interactions rapidly limit its effectiveness as you move into stronger coupling regimes.

Lev: If we want higher Tc in strongly correlated systems, we need to account for the interplay between interactions and band structure rather than just focusing on DOS singularities.

Kai: They also emphasize that finding a sharp Van Hove singularity in the density of states is needed to really prove this connection exists at all.

Mira: It’s a caution that the findings might be general, as they note that only modest enhancement was found even in Migdal-Eliashberg theory for electron-phonon systems (ref: <ref:2604.13161#pg1>).

Lev: So, the main implication is that we shouldn't just engineer DOS singularities to get high Tc; we have to consider how interactions play with the band structure.

Kai: The paper uses the attractive Hubbard model, which they admit is at best a crude approximation of real materials, so we should keep that in mind when applying these findings.

Mira: That's right, it’s a reminder that these results are derived from a simplified model, and we need to be careful about extrapolating them to the real world.