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

Giant Interaction-Induced Gap and Electronic Phases in Rhombohedral Trilayer Graphene