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Zero-energy modes and gate-tunable gap in graphene on hexagonal boron nitride



Markus Kindermann, Bruno Uchoa, David L. Miller


In this article, we derive an effective theory of graphene on a hexagonal boron nitride (h-BN) substrate. We show that the h-BN substrate generically opens a spectral gap in graphene despite the lattice mismatch. The origin of that gap is particularly intuitive in the regime of strong coupling between graphene and its substrate, when the low-energy physics is determined by the topology of a network of zero-energy modes. For twisted graphene bilayers, where inversion symmetry is present, this network percolates through the system and the spectrum is gapless. The breaking of that symmetry by h-BN causes the zero-energy modes to close into rings. The eigenstates of these rings hybridize into flat bands with gaps in between. The size of this band gap can be tuned by a gate voltage and it can reach the order of magnitude needed to confine electrons at room temperature.
Physical Review B


graphene, boron nitride, band gap


Kindermann, M. , Uchoa, B. and Miller, D. (2012), Zero-energy modes and gate-tunable gap in graphene on hexagonal boron nitride, Physical Review B, [online], (Accessed April 14, 2024)
Created September 12, 2012, Updated October 12, 2021