Observation of Hofstadter butterfly and valley Hall effect in hBN/graphene/hBN heterostructures

Recently, heterostructures of 2-D materials have attracted great interests because they form superlattices which allow band engineering as well as use of multiple degenerate degrees of freedom. We have fabricated hexag- onal boron nitride (hBN)/graphene/hBN superlattices with one-dimensional edge contacts as well as a Hall-bar geometry. Clear conductance oscillations in magnetic fields have been observed, originating from the Hofstadter's butterfly which indicates the good alignment of graphene and hBN crystal orientation. In addition, giant non-local resistance near secondary Dirac point originated by the valley Hall effect has been observed in zero magnetic field. Our experimental results indicate the high quality samples of graphene superlattices with quasi-ballistic transport regime are realized.