Fig. 3: Loop current patterns and Brillouin zone.

The 5 LC pattern possibilities that we study a–e and a sketch of the Brillouin zone (f). Each pattern comes in a set of 3, with ordering wave vectors M_{ℓ = 1, 2, 3}. Only the representative with the ordering wave vector M₃ is shown. The other two may be obtained via C_6z rotations. The red, blue, and teal sites are V, and they form a kagome lattice. The orange sites are the planar Sb, and they form a triangular lattice and live in the centers of the hexagons formed by the kagome lattice. This reflects the same color scheme as in Fig. 1. The greyed-out region is the extended 2 × 2 unit cell that our LC patterns live in. The red and blue shadings denote whether the flux of a given plaquette is out-of-page or in-page, respectively. a–c LC patterns belong to the (even-parity) \(m{M}_{2}^{+}\) irrep, while d–e belong to the (odd-parity) \(m{M}_{3}^{-}\) irrep; see Supplementary, Section 1. a, b, d have only V-V currents, while c, e have in addition V-Sb currents. Note that the ordering wave vectors Q_ℓ, which connect different M-points, are themselves M-points (e.g., Q₃ = M₂ − M₁ = M₃ = − M₃ up to a reciprocal lattice vector). The color scheme for these three M-vectors (red, blue, teal) is chosen to coincide with the sublattice weight of the kagome sites (also red, blue, teal) at different M-points in the Brillouin zone.