Figure 3: Definition of couplings and band geometry for the kagomé lattice model.

(a) Lattice and chirality conventions for hopping terms in the kagomé lattice model Hamiltonian. Basis vectors a₁, a₂ are shown in red; basis elements are shown by differently coloured/numbered sites. Hopping elements are shown with black and blue edges; arrowheads indicate the chirality convention for complex hoppings. (b) Band geometry over the reciprocal lattice unit cell spanned by b₁, b₂, for parameter values minimizing σ_B and maximizing gaps, respectively. Axes of ellipses are proportional to the eigenvectors of the quantum metric g^α(k). Ellipse color is given by the relative deviation of Berry curvature B_α(k) from its Brillouin zone-averaged value.