Kekulé order from diffuse nesting near higher-order Van Hove points

Abstract

Translation symmetry-breaking order is assumed to be suppressed by the lack of Fermi surface nesting near certain higher-order Van Hove singularities (HOVHS). We show the anisotropic band-flattening inherent to such HOVHS, combined with broadening of the Fermi surface due to elevated critical temperatures, results in the Fermi surface becoming approximately nested at a wavevector unrelated to the precise shape of the Fermi surface - leading to a $\sqrt{3}\times\sqrt{3}$ Kekulé density wave formation. The effect is demonstrated using unbiased renormalization group calculations for a model of the breathing kagome lattice. Our mechanism - termed diffuse nesting - represents an entirely new notion in the study of Fermi surface instabilities.

Figures (15)

• Figure 1: Breathing kagome model. (a) Breathing kagome lattice configuration with hoppings up to fourth nearest neighbor. (b) Corresponding band structure with density of states, characterized by an algebraic divergence at the Fermi level. The inset displays the broadened Fermi surface at $T=0.01\,t$.
• Figure 2: Leading eigenvalues and order parameter. (a) Leading eigenvalues of the effective scattering vertex in the particle-hole channel on a transfer momentum $\boldsymbol{q}$-mesh in the Brillouin zone. The dominant eigenvalues are situated at the two inequivalent $K$-points. (b) Order parameter obtained by combining functional renormalization group calculations with Landau-Ginzburg and mean-field analysis.
• Figure 3: Susceptibility and Fermi surface nesting in the kinetic breathing kagome model with FS broadening modeled by temperature. (a) Maximal eigenvalue of the particle-hole susceptibility \ref{['eqn:bare_susc']} for three different temperatures $T$. At higher $T$, the peak at momentum $K$ surpasses the $\Gamma$ peak. (b) Overlap (black) of initial (gray) and $K$-shifted (purple) Fermi surface for $T=10^{-2}\,t$. Circular nesting features drive $K$-order at finite $T$.
• Figure 4: Generalized model. (a) Taylor expanded higher-order Van Hove dispersion situated at the $M$-points of the hexagonal Brillouin zone. (b) Corresponding bandstructure and Fermi surface at higher-order Van Hove filling.
• Figure SM 1: Kinetic model for the breathing kagome lattice. The hopping processes $t_{1,2,3,4}$ from sublattice $A$ to the neighbouring unit cells are shown with circles illustrating the hopping distance. The hopping $t_4$ vanishes along a line perpendicular to the residual mirror symmetry at each sublattice (purple). In Co$_3$Sn$_2$S$_2$, the blue sites correspond to Co atoms and the yellow sites to S atoms which hybridise with the kagome lattice of Co, driving the breathing distortion.