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We show a dramatic deviation from ergodicity for the conductance fluctuationsin graphene. In marked contrast to the ergodicity of dirty metals, fluctuationsgenerated by varying magnetic field are shown to be much smaller than thoseobtained when sweeping Fermi energy. They also exhibit a strongly anisotropicresponse to the symmetry-breaking effects of a magnetic field, when appliedperpendicular or parallel to the graphene plane. These results reveal a complexpicture of quantum interference in graphene, whose description appears morechallenging than for conventional mesoscopic systems.

Non-Ergodicity & Microscopic Symmetry Breaking of the Conductance Fluctuations in Disordered Mesoscopic Graphene