  Doped band insulators, HfNCl, WO$_3$, diamond, Bi$_2$Se$_3$, \bis2 families,
STO/LAO interface, gate doped SrTiO$_3$ and MoS$_2$ etc. are unusual
superconductors. With an aim to build a general theory for superconductivity in
doped band insulators we focuss on \bis2 family, discovered by Mizuguchi et al.
in 2012. While maximum Tc is only $\sim$ 11 K in \laofx, a number of
experimental results are puzzling and anomalous; they resemble high Tc and
unconventional superconductors. Using a two orbital model of Usui, Suzuki and
Kuroki we show that the uniform low density free fermi sea in \laofh is
\textit{unstable towards formation of next nearest neighbor Bi-S-Bi diagonal
valence bond} (charge -2e Cooper pair) and their \textit{Wigner
crystallization}. Instability to this novel state of matter is caused by
unscreened nearest neighbor coulomb repulsions (V $\sim$ 1 eV) and a hopping
pattern with sulfur mediated diagonal next nearest neighbor Bi-S-Bi hopping t'
$\sim$ 0.88 eV, larger than nearest neighbor Bi-Bi hopping, t $\sim$ 0.16 eV.
Wigner crystal of Cooper pairs quantum melt for doping around x = 0.5 and
stabilize certain resonating valence bond states and superconductivity. We
study few variational RVB states and suggest that \bis2 family members are
latent high Tc superconductors, but challenged by competing orders and fragile
nature of manybody states sustained by unscreened Coulomb forces. One of our
superconducting state has d$_{xy}$ symmetry and a gap. We also predict 2d
\textit{Bose metal or vortex liquid} normal state, as charge -2e valence bonds
survive in the normal state.
