  Motivated by recent experiments on twisted van der Waals materials, we
perform an analytical and numerical study of the effects of strong on-site and
short-range interactions in fractionally filled ideal Chern bands. We uncover
an extensive non-trivial ground state manifold within the band filling range $0
< \nu < 1$ and introduce a general principle, the ''three-rule'', for combining
flatband wave functions, which governs their zero-energy property on the torus
geometry. Based on the structure of these wave functions, we develop a
variational approach that reveals distinct phases under different
perturbations: metallic behavior emerges from a finite dispersion, and
superconductivity is induced by attractive Cooper channel interactions. Our
approach, not reliant on the commonly applied mean-field approximations,
provides an analytical expression for the macroscopic wave function of the
off-diagonal long-range order correlator, attributing pairing susceptibility to
the set of non-trivial zero-energy ground state wave functions. Extending to
finite screening lengths and beyond the ideal limit using exact diagonalization
simulations, we demonstrate the peculiar structure in the many-body wave
function's coefficients to be imprinted in the low-energy spectrum of the
topologically ordered Halperin spin-singlet state. Our findings also make
connections to frustration-free models of non-commuting projector Hamiltonians,
potentially aiding the future construction of exact ground states for various
fractional fillings.
