Doping quantum spin liquids on the Kagome lattice

We review recent density-matrix renormalization group (DMRG) studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high-temperature superconductivity, have been theoretically anticipated we find instead a tendency toward fractionalized insulating charge-density-wave (CDW) states. In agreement with earlier work (Jiang, Devereaux, and Kivelson, Phys. Rev. Lett. ${\bf 119}$, 067002 (2017)), results for the $t$-$J$ model reveal that starting from a fully gapped QSL, light doping leads to CDW long-range order with a pattern that depends on lattice geometry and doping concentration such that there is one doped-hole per CDW unit cell, while the spin-spin correlations remain short-ranged. Alternatively, this state can be viewed as a stripe crystal or Wigner crystal of spinless holons, rather than doped holes. From here, by studying generalized versions of the $t$-$J$ model, we extend these results to light doping of other types of QSLs, including critical and chiral QSLs. Our results suggest that doping these QSLs also leads to insulating states with long-range CDW orders. While the superconducting correlations are short-ranged, they can be significantly enhanced by second-neighbor electron hopping. The relevance of our numerical results to Kagome materials is also discussed.