  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.
