Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride

Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride

February 15, 2012 | Matthew Yankowitz, Jiamin Xue, Daniel Cormode, Javier D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, Pablo Jarillo-Herrero, Philippe Jacquod, Brian J. LeRoy
This study reports the emergence of superlattice Dirac points in graphene on hexagonal boron nitride (hBN). Graphene on hBN exhibits a rotation-dependent Moiré pattern, which acts as a weak periodic potential. This potential leads to the formation of new Dirac points at energies determined by the wavelength of the Moiré pattern. The new massless Dirac fermions generated at these points have a significantly reduced Fermi velocity. The local density of states near these Dirac cones shows hexagonal modulations, indicating anisotropic Fermi velocity. Graphene's electronic properties are governed by the massless Dirac equation, leading to phenomena like Klein tunneling. However, periodic potentials can create new Dirac points without opening gaps, due to the chirality of Dirac fermions. STM experiments show that hBN generates effective periodic potentials, leading to Moiré patterns with high mobility and suppressed charge inhomogeneities. The rotation between graphene and hBN lattices, along with the longer lattice constant of hBN, leads to Moiré patterns. The Moiré wavelength depends on the lattice mismatch and rotation angle. Theoretical calculations show that the energy of the new Dirac points is determined by the reciprocal superlattice vectors. Experimental dI/dV measurements confirm the presence of these new Dirac points, with dips in the density of states at energies corresponding to the superlattice potential. Theoretical models show that the periodic potential induces a new Dirac point with a reduced Fermi velocity. The Fermi velocity at the new Dirac points is found to be 0.64 ± 0.03 × 10⁶ m/s for electrons and 0.78 ± 0.03 × 10⁶ m/s for holes. The presence of the superlattice Dirac point is also evident in the global conductivity as a function of gate voltage. The study demonstrates that the periodic potential from hBN leads to new Dirac points, which can be used to control electron transport in graphene. Future work aims to exploit this periodic potential for novel graphene devices. The results highlight the importance of hBN in enhancing graphene's electronic properties and provide insights into the behavior of Dirac fermions in periodic potentials.This study reports the emergence of superlattice Dirac points in graphene on hexagonal boron nitride (hBN). Graphene on hBN exhibits a rotation-dependent Moiré pattern, which acts as a weak periodic potential. This potential leads to the formation of new Dirac points at energies determined by the wavelength of the Moiré pattern. The new massless Dirac fermions generated at these points have a significantly reduced Fermi velocity. The local density of states near these Dirac cones shows hexagonal modulations, indicating anisotropic Fermi velocity. Graphene's electronic properties are governed by the massless Dirac equation, leading to phenomena like Klein tunneling. However, periodic potentials can create new Dirac points without opening gaps, due to the chirality of Dirac fermions. STM experiments show that hBN generates effective periodic potentials, leading to Moiré patterns with high mobility and suppressed charge inhomogeneities. The rotation between graphene and hBN lattices, along with the longer lattice constant of hBN, leads to Moiré patterns. The Moiré wavelength depends on the lattice mismatch and rotation angle. Theoretical calculations show that the energy of the new Dirac points is determined by the reciprocal superlattice vectors. Experimental dI/dV measurements confirm the presence of these new Dirac points, with dips in the density of states at energies corresponding to the superlattice potential. Theoretical models show that the periodic potential induces a new Dirac point with a reduced Fermi velocity. The Fermi velocity at the new Dirac points is found to be 0.64 ± 0.03 × 10⁶ m/s for electrons and 0.78 ± 0.03 × 10⁶ m/s for holes. The presence of the superlattice Dirac point is also evident in the global conductivity as a function of gate voltage. The study demonstrates that the periodic potential from hBN leads to new Dirac points, which can be used to control electron transport in graphene. Future work aims to exploit this periodic potential for novel graphene devices. The results highlight the importance of hBN in enhancing graphene's electronic properties and provide insights into the behavior of Dirac fermions in periodic potentials.
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Understanding Emergence of superlattice Dirac points in graphene on hexagonal boron nitride