Intrinsic Hall conductivity, emerging when chiral symmetry is broken, is at the heart of future low energy consumption devices because it can generate non-dissipative charge neutral current. A symmetry breaking state is also induced by electronic correlation even for the centro-symmetric crystalline materials. However, generation of non-dissipative charge neutral current by intrinsic Hall conductivity induced by such spontaneous symmetry breaking is experimentally elusive. Here we report intrinsic Hall conductivity and generation of a non-dissipative charge neutral current in a spontaneous antiferromagnetic state of zero Landau level of bilayer graphene, where spin and valley contrasting Hall conductivity has been theoretically predicted. We performed nonlocal transport experiment and found cubic scaling relationship between the local and nonlocal resistance, as a striking evidence of the intrinsic Hall effect. Observation of such spontaneous Hall transport is a milestone toward understanding the electronic correlation effect on the non-dissipative transport. Our result also paves a way toward electrical generation of a spin current in non-magnetic graphene via coupling of spin and valley in this symmetry breaking state combined with the valley Hall effect.
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