Magnetic correlations and superconducting pairing near higher-order Van Hove singularities

Higher-order Van Hove singularities in strongly correlated electron systems provide a fertile ground for emergent electronic orders and superconductivity. This study investigates the interplay between magnetic fluctuations and superconducting pairing near higher-order Van Hove singularities on the honeycomb lattice, a paradigmatic platform relevant to graphene. By incorporating third-nearest-neighbor hopping (t’’), we uncover a universal crossover: ferromagnetic fluctuations dominate below the higher-order Van Hove filling, while antiferromagnetic fluctuations take over toward half filling. A key finding is that the already dominant (f_n)-wave pairing is enhanced in the critical region of this magnetic crossover by the higher-order Van Hove. This enhancement is driven by the synergistic effect of the higher-order Van Hove singularities-induced divergent density of states and the competing magnetic fluctuations. Although increased hopping parameters generally suppress superconducting correlation, we identify a critical (t’’) that anomalously enhances pairing via the higher-order Van Hove renormalization. Furthermore, the nearest-neighbor Coulomb interaction suppresses the pairing correlation function in a sign-independent manner. Our results clarify the competitive mechanisms between magnetic fluctuations and unconventional superconductivity in higher-order Van Hove singularities systems, offering a theoretical basis for tailoring quantum phases in graphene-based materials via band engineering.

💡 Research Summary

In this work the authors investigate how higher‑order Van Hove singularities (HOVH) affect magnetic fluctuations and unconventional superconductivity on the honeycomb lattice, a model directly relevant to graphene and its engineered derivatives. Starting from a Hubbard Hamiltonian that includes nearest‑neighbor (t), next‑nearest‑neighbor (t′) and third‑nearest‑neighbor (t″) hoppings, they derive an analytical condition for the emergence of a HOVH: t″ = t − 2t′/4. When this relation is satisfied the saddle point at the M point becomes flattened, turning the usual logarithmic Van Hove divergence of the density of states (DOS) into a power‑law divergence. This dramatically amplifies electronic correlations.

Using determinant quantum Monte Carlo (DQMC) at finite temperature (β = 6) and constrained‑path Monte Carlo (CPMC) for ground‑state properties, the authors explore a range of electron fillings ⟨n⟩ from 0.5 to 1.0, a moderate on‑site interaction U = 3|t|, and several values of t′ (fixed at 0.10|t|) and t″. The spin susceptibility χ_s(q) reveals a universal crossover: for fillings below the HOVH (e.g., ⟨n⟩ = 0.50) the susceptibility peaks at the Γ point, indicating dominant ferromagnetic (FM) fluctuations that grow with increasing t″. Near the HOVH filling (⟨n⟩ ≈ 0.75) FM and antiferromagnetic (AFM) fluctuations compete; increasing t″ suppresses the Γ‑point FM response while enhancing the M‑point AFM response. For fillings above the HOVH (⟨n⟩ ≥ 0.81) the system is dominated by AFM correlations, which are gradually weakened as t″ is raised. Real‑space spin‑spin correlations corroborate these momentum‑space trends.

Superconducting pairing is examined through the long‑range pairing correlation functions C_α(r) for several symmetries: nearest‑neighbor d + id, next‑nearest‑neighbor p + ip, and next‑next‑nearest‑neighbor f_n. With t′ = 0.10|t|, t″ = 0.20|t| and filling ⟨n⟩ ≈ 0.88 (close to the HOVH), the f_n‑wave channel displays the slowest decay with distance, overtaking the d‑ and p‑wave channels. This dominance is attributed to a synergistic effect: the power‑law divergent DOS supplied by the HOVH amplifies the pairing susceptibility, while the competing FM/AFM fluctuations provide additional attractive channels for the f_n symmetry. Remarkably, when t″ is tuned to the critical value t″_c ≈ 0.15|t| (the point where the HOVH condition is exactly met), the f_n pairing correlation is anomalously enhanced, indicating that the HOVH renormalization can boost superconductivity beyond the simple DOS effect. Conversely, further increase of t″ beyond this optimal point suppresses all pairing correlations, showing that excessive band‑flattening can be detrimental.

The authors also study the effect of a nearest‑neighbor Coulomb repulsion V. Their calculations reveal that V reduces the magnitude of all pairing correlations irrespective of its sign, confirming that direct intersite repulsion generally disfavors Cooper pair formation.

Overall, the paper delivers several key insights: (i) HOVH dramatically strengthens both magnetic fluctuations and unconventional pairing by providing a power‑law divergent DOS; (ii) the third‑nearest‑neighbor hopping t″ serves as a tuning knob that controls a FM ↔ AFM crossover and simultaneously optimizes the f_n‑wave superconducting channel; (iii) the f_n‑wave symmetry emerges as the most robust pairing near the HOVH, suggesting it as a promising candidate for high‑temperature superconductivity in graphene‑based systems; and (iv) intersite Coulomb repulsion V uniformly suppresses pairing. These findings offer a concrete theoretical framework for experimental strategies—such as strain, twist angle engineering, or chemical functionalization—to manipulate t′ and t″, thereby realizing HOVH and tailoring magnetic and superconducting phases in two‑dimensional materials.