  Superconductivity (SC) is observed in rhombohedral trilayer graphene (RTG)
with an extremely low charge carrier densities, between the normal metal state
and a probable inter-valley coherent (IVC) state. The measured coherence length
in RTG is roughly two orders of magnitude shorter than the value predicted by a
conventional BCS theory. To resolve these discrepancies, we propose that the
RTG SC phase arises from the pairing of quasiparticles within the IVC phase. We
illustrate the SC behavior using gapped Dirac cones with the chemical potential
close to the conduction band's bottom and establish the Ginzburg-Landau theory.
Our findings indicate that the mean-field transition temperature,
$T_\mathrm{MF}$, is primarily determined by the density of states of
quasiparticles within the IVC phase, and is more suppressed in comparison with
the BCS relation. Interestingly, we discover that the coherence length behaves
according to $\xi\sim 1/\sqrt{T_\mathrm{MF}}$. When the chemical potential lies
within the band gap, the conventional coherence length becomes small, while the
quantum metric contribution can diverge. Applying our approach to a microscopic
model for RTG, our predictions align well with experimental data and
effectively capture key measurable features of quantities such as the
mean-field transition temperature $T_\mathrm{MF}$ and the coherence length
$\xi$. Furthermore, we reveal that the quantum metric contribution, stemming
from the multi-band properties of the IVC quasiparticles, plays a significant
role in determining the coherence length around the transition regime from
superconductivity to IVC. Lastly, experimental predictions are discussed on
bebaviors of the upper critical field and coherence length at low temperatures.
