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

TL;DR

This work addresses how higher-order Van Hove singularities on a honeycomb lattice influence magnetic fluctuations and unconventional superconductivity in a Hubbard model relevant to graphene. Using determinant Quantum Monte Carlo (DQMC) for spin responses and constrained-path Monte Carlo (CPMC) for pairing, the study locates the HOVH via $t''=(t-2t')/4$ and analyzes spin and pairing channels across fillings. A key finding is a ferromagnetic-to-antiferromagnetic crossover near the HOVH, with the $f_n$-wave pairing channel enhanced by the HOVH DOS divergence and magnetic fluctuations, including a notable anomalous boost at a critical $t'' \approx 0.15$. The results show that the pairing is sensitive to $t'$, $t''$, and the NN interaction $V$, offering a theoretical framework for engineering correlated phases in graphene-based materials through band structure tuning and strain.

Abstract

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.

Figures (11)

• Figure 1: (a) Sketch of the honeycomb lattice with double-27 sites of $N=2\times3L^2$ with $L=3$. (b) The first Brillouin zone and high symmetry points. (c) The form of NN $d+id$ pairing symmetry. (d) The form of NNN $f_n$ pairing symmetry.
• Figure 2: (a) The DOS as functions of energy with $t = 1.00$, $t' = 0$, $t" = 0$ (black solid line) and $t = 1.00$, $t' = 0.10$, $t" = 0.20$ (red solid line). The red dotted line shows fillings $\langle n \rangle$ as a function of energy with $t = 1.00$, $t' = 0.10$, and $t" = 0.20$. (b) Noninteracting band dispersions for different $t"$ values at fixed $t=1.0, t'=0.20$
• Figure 3: The relationship between the spin susceptibility and $\mathbf{q}$ for different TNN hopping integrals $t"$ at fixed $U = 3.0|t|$ and $\beta = 6$ when $L=4$. (a) $\langle n \rangle = 0.50$. (b) $\langle n \rangle = 0.75$. (c) $\langle n \rangle = 0.81$. (d) $\langle n \rangle = 1.00$.
• Figure 4: The pairing correlation as a function of distance for different pairing symmetries with (a) $\langle n \rangle = 0.733$; (b) $\langle n \rangle = 0.813$; (c) $\langle n \rangle = 0.893$; (d) $\langle n \rangle = 0.973$.
• Figure 5: Pairing correlation functions for different pairing symmetries with (a) $t' = 0$, (b) $t' = 0.10$, (c) $t' = 0.20$, and (d) $t' = 0.30$.