Antiferromagnetism,f-wave, and chiralp-wave superconductivity in a kagome lattice with possible application tosd2graphenes

We investigate the electronic instabilities in a kagome lattice with Rashba spin-orbital coupling by the unbiased singular-mode functional renormalization group. At the parent $1/3$ filling, the normal state is a quantum spin Hall system. Since the bottom of the conduction band is near the van Hove singularity, the electron-doped system is highly susceptible to competing orders upon electron interactions. The topological nature of the parent system enriches the complexity and novelty of such orders. We find ${120}^{\ensuremath{\circ}}$-type intra-unit-cell antiferromagnetic order, $f$-wave superconductivity, and chiral $p$-wave superconductivity with increasing electron doping above the van Hove point. In both types of superconducting phases, there is a mixture of comparable spin singlet and triplet components because of the Rashba coupling. The chiral $p$-wave superconducting state is characterized by a Chern number $Z=1$, supporting a branch of Weyl fermion states on each edge. The model bares close relevance to the so-called $s{d}²$ graphenes proposed recently.