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Intrinsic Hall conductivity, emerging when chiral symmetry is broken, is atthe heart of future low energy consumption devices because it can generatenon-dissipative charge neutral current. A symmetry breaking state is alsoinduced by electronic correlation even for the centro-symmetric crystallinematerials. However, generation of non-dissipative charge neutral current byintrinsic Hall conductivity induced by such spontaneous symmetry breaking isexperimentally elusive. Here we report intrinsic Hall conductivity andgeneration of a non-dissipative charge neutral current in a spontaneousantiferromagnetic state of zero Landau level of bilayer graphene, where spinand valley contrasting Hall conductivity has been theoretically predicted. Weperformed nonlocal transport experiment and found cubic scaling relationshipbetween the local and nonlocal resistance, as a striking evidence of theintrinsic Hall effect. Observation of such spontaneous Hall transport is amilestone toward understanding the electronic correlation effect on thenon-dissipative transport. Our result also paves a way toward electricalgeneration of a spin current in non-magnetic graphene via coupling of spin andvalley in this symmetry breaking state combined with the valley Hall effect.

Spin-valley Hall transport induced by spontaneous symmetry breaking in half-filled zero Landau level of bilayer graphene