  We report the observation of superconductivity in rhombohedral trilayer
graphene electrostatically doped with holes. Superconductivity occurs in two
distinct regions within the space of gate-tuned charge carrier density and
applied electric displacement field, which we denote SC1 and SC2. The high
sample quality allows for detailed mapping of the normal state Fermi surfaces
by quantum oscillations, which reveal that in both cases superconductivity
arises from a normal state described by an annular Fermi sea that is proximal
to an isospin symmetry breaking transition where the Fermi surface degeneracy
changes. The upper out-of-plane critical field $B_{C\perp}\approx 10
\mathrm{mT}$ for SC1 and $1\mathrm{mT}$ for SC2, implying coherence lengths
$\xi$ of 200nm and 600nm, respectively. The simultaneous observation of
transverse magnetic electron focusing implies a mean free path
$\ell\gtrsim3.5\mathrm{\mu m}$. Superconductivity is thus deep in the clean
limit, with the disorder parameter $d=\xi/\ell<0.1$. SC1 emerge from a
paramagnetic normal state and is suppressed with in-plane magnetic fields in
agreement with the Pauli paramagnetic limit. In contrast, SC2 emerges from a
spin-polarized, valley-unpolarized half-metal. Measurements of the in-plane
critical field show that this superconductor exceeds the Pauli limit by at
least one order of magnitude. We discuss our results in light of several
mechanisms including conventional phonon-mediated pairing, pairing due to
fluctuations of the proximal isospin order, and intrinsic instabilities of the
annular Fermi liquid. Our observation of superconductivity in a clean and
structurally simple two-dimensional metal hosting a variety of gate tuned
magnetic states may enable a new class of field-effect controlled mesoscopic
electronic devices combining correlated electron phenomena.
