Figure 1

(a) We choose a six-site unit cell for the Kagomé lattice. The sites are labeled $0,\dots ,5$ as shown. Only those bonds depicted as bold solid lines (positive hopping) and bold dashed lines (negative hopping) are contained within the unit cell. (b) The Brillouin zone for the doubled unit cell (gray area), with reciprocal lattice basis vectors ${\mathit{b}}_i$ shown. The outer hexagon is the Brillouin zone for the 3-site unit cell of a single up-pointing triangle. The positions of the Dirac nodes are denoted by the black circles. (c) Plot of the band structure of the $U(1)$-Dirac state on the line from $\mathit{k}=0$ to $\mathit{k}={\mathit{b}}_2$ with energy in units of $\chi J$ (see text). The flat band is doubly degenerate; all others are nondegenerate. The Fermi level corresponding to one spinon per site is indicated by the dashed line.Reuse & Permissions