  Herbertsmithite and Zn-doped barlowite are two compounds for experimental
realization of twodimensional gapped kagome spin liquid. Theoretically, it has
been proposed that charge doping a quantum spin liquid gives rise to exotic
metallic states, such as high-temperature superconductivity. However, one
recent experiment about herbertsmithite with successful Li-doping shows
surprisingly the insulating state even under the heavy doped scenario, which
can hardly be explained by many-body physics. Using first-principles
calculation, we performed a comprehensive study about the Li intercalated
doping effect of these two compounds. For the Li-doped herbertsmithite, we
identified the optimized Li position at the Cl-(OH)$_3$-Cl pentahedron site
instead of previously speculated Cl-(OH)$_3$ tetrahedral site. With the
increase of Li doping concentration, the saturation magnetization decreases
linearly due to the charge transfer from Li to Cu ions. Moreover, we found that
Li forms chemical bonds with the nearby (OH)$^-$ and Cl$^-$ ions, which lowers
the surrounding chemical potential and traps the electron, as evidenced by the
localized charge distribution, explaining the insulating behavior measured
experimentally. Though with different structure from herbertsmithite, Zn-doped
Barlowite shows the same features upon Li doping. We conclude that Li doping
this family of kagome spin liquid cannot realize exotic metallic states, other
methods should be further explored, such as element substitution with different
valence electrons.
