  Due to their unique electron dispersion and lack of a Fermi surface, Coulomb
interactions in undoped two-dimensional Dirac systems, such as single, bi- and
tri-layer graphene, can be marginal or relevant. Relevant interactions can
result in spontaneous symmetry breaking, which is responsible for a large class
of physical phenomena ranging from mass generation in high energy physics to
correlated states such as superconductivity and magnetism in condensed matter.
Here, using transport measurements, we show that rhombohedral-stacked trilayer
graphene (r-TLG) offers a simple, yet novel and tunable, platform for study of
various phases with spontaneous or field-induced broken symmetries. Here, we
show that, contrary to predictions by tight-binding calculations,
rhombohedral-stacked trilayer graphene (r-TLG) is an intrinsic insulator, with
a giant interaction-induced gap {\Delta}~42meV. This insulating state is a
spontaneous layer antiferromagnetic with broken time reversal symmetry, and can
be suppressed by increasing charge density n, an interlayer potential, a
parallel magnetic field, or a critical temperature Tc~38K. This gapped
collective state can be explored for switches with low input power and high
on/off ratio.
