Insulating Behavior at the Neutrality Point in Single-Layer Graphene

Amet, François; Williams, James R.; Watanabe, Kenji; Taniguchi, Takashi; Goldhaber‐Gordon, David

doi:10.1103/physrevlett.110.216601

Cited by 138 publications

(140 citation statements)

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“…The inversionasymmetric perturbation potential can strongly affect the gap opening at the Dirac point. The gap opening in graphene/h-BN is a highly debated issue, with some theoretical and experimental studies arguing for its existence 4,12,14,19,21,[23][24][25] whereas others rule it out 2,[6][7][8]11 . Such knowledge gaps in understanding the fundamental electronic structure of graphene/h-BN call for a careful examination of the electronic structure by angle-resolved photoemission spectroscopy (ARPES), which can map out the dispersions of the original Dirac cone and the SDCs with both energy-and momentum-resolution and detect the gap opening directly if there is any.…”

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confidence: 99%

Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride

et al. 2016

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Graphene/hexagonal boron nitride (h-BN) has emerged as a model van der Waals heterostructure 1 as the superlattice potential, which is induced by lattice mismatch and crystal orientation, gives rise to various novel quantum phenomena, such as the self-similar Hofstadter butterfly states 2-5 . Although the newly generated second-generation Dirac cones (SDCs) are believed to be crucial for understanding such intriguing phenomena, fundamental knowledge of SDCs, such as locations and dispersion, and the e ect of inversion symmetry breaking on the gap opening, still remains highly debated due to the lack of direct experimental results. Here we report direct experimental results on the dispersion of SDCs in 0 • -aligned graphene/h-BN heterostructures using angle-resolved photoemission spectroscopy. Our data unambiguously reveal SDCs at the corners of the superlattice Brillouin zone, and at only one of the two superlattice valleys. Moreover, gaps of approximately 100 meV and approximately 160 meV are observed at the SDCs and the original graphene Dirac cone, respectively. Our work highlights the important role of a strong inversion-symmetry-breaking perturbation potential in the physics of graphene/h-BN, and fills critical knowledge gaps in the band structure engineering of Dirac fermions by a superlattice potential.Hexagonal boron nitride (h-BN) shares a similar honeycomb lattice structure to graphene, yet its lattice is stretched by 1.8%. Moreover, the breaking of the inversion symmetry by distinct boron and nitrogen sublattices leads to a large bandgap (5.97 eV) in the π band, which is in sharp contrast to the gapless Dirac cones in graphene. By stacking graphene atop h-BN to form a van der Waals heterostructure 1 , graphene/h-BN not only exhibits greatly improved properties for device applications, such as reduced ripples, suppressed charge inhomogeneities and higher mobility 6,7 , but also provides unique opportunities for band structure engineering of Dirac fermions by a periodic potential 8,9 . The superlattice potential induced by the lattice mismatch and crystal orientation can significantly modify the electronic properties of graphene and lead to various novel quantum phenomena, for example, the emergence of second-generation Dirac cones (SDCs), which are crucial for the realization of Hofstadter butterfly states under an applied magnetic field 2-5 , renormalization of the Fermi velocity 8,[10][11][12] , gap opening at the Dirac point 4,13-16 , topological currents 15 and gate-dependent pseudospin mixing 17 . Hence, understanding the effects of the superlattice potential on the band structure of graphene is crucial for advancing its device applications, and for gaining new knowledge about the fundamental physics of Dirac fermions in a periodic potential.Previously, the existence of SDCs has been deduced from scanning tunnelling spectroscopy, resistivity and capacitance measurements 2,5,18,19 . However, such measurements are not capable of mapping out the electronic dispersion with momentum-resolved informatio...

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Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride

et al. 2016

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“…For an external magnetic field, by varying the gate voltage, we consider the lifting of the spin and valley degeneracies at the zeroth Landau level and the magnetic oscillations of the capacitance associated with the quantized Landau levels. The quantum capacitance is advantageous over traditional transport measurements 20,[36][37][38][39] because it allows us to directly probe the DOS at the zeroth Landau level and is less sensitive to scattering details. We provide a quantitative description of the DOS at E F and insight into the spin and valley splittings.…”

Section: Introductionmentioning

confidence: 99%

“…34,35 On the other hand, degeneracy lifting is difficult to probe by transport experiments due to scattering details. 20,[36][37][38][39] In the following, we will address this issue by considering the quantum capacitance. In fact, recent quantum capacitance measurements have confirmed both the gap opening and lifting of the spin and valley degeneracies due to many body interactions in terms of the density of states (DOS).…”

Section: Introductionmentioning

confidence: 99%

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Theory of substrate, Zeeman, and electron-phonon interaction effects on the quantum capacitance in graphene

Tahir

Sabeeh

Shaukat

et al. 2013

Journal of Applied Physics

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“…By changing the occupation of the midgap states, the valley ferromagnetic order can be controlled with a gate voltage. This exotic state has clear experimental signatures and can lead to the experimental realization of valley order in graphene at low temperature and weak applied magnetic fields 34 .…”

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Valley order and loop currents in graphene on hexagonal boron nitride

2015

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In this letter, we examine the role of Coulomb interactions in the emergence of macroscopically ordered states in graphene supported on hexagonal boron nitride substrates. Due to incommensuration effects with the substrate and interactions, graphene can develop gapped low energy modes that spatially conform into a triangular superlattice of quantum rings. In the presence of these modes, we show that Coulomb interactions lead to spontaneous formation of chiral loop currents in bulk and to macroscopic spin-valley order at zero temperature. We show that this exotic state breaks time reversal symmetry and can be detected with interferometry and polar Kerr measurements.PACS numbers: 71.21. Cd,73.21.La,73.22.Gk Introduction. In spite of the presence of quasiparticles with Dirac cone spectrum 1 , the emergence of topological order in graphene is hindered by the fermionic doubling problem, where electrons have a four-fold degeneracy in valleys and spins 2 . Due to the vanishingly small density of states (DOS) at the Dirac points, many-body instabilities in general are quantum critical and require strong coupling regimes 3 . We argue that one promising possibility to generate many body states that lift the fermionic degeneracy and break time reversal symmetry (TRS) is to use substrates to reconstruct the DOS of graphene near the Dirac points into nearly flat bands.In incommensurate two-layer crystals with honeycomb structure, the Dirac points are protected by a combination of parity and TRS 4 . On top of hexagonal boron nitride (BN), where inversion symmetry is broken, graphene can open a gap in the spectrum of the order of ∼ 20 − 50meV 5-8 , as recently observed in transport measurements 9 . Due to the 1.8% lattice mismatch between graphene and its substrate 10-12 and possible twisted configurations between the two 10-14 , BN creates local potentials in graphene which modulate with the same periodicity of the Moire pattern created by the two incommensurate structures (Fig.1a) 15 . In the continuum limit, the Hamiltonian of graphene in the presence of the BN substrate can be generically written as

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Insulating Behavior at the Neutrality Point in Single-Layer Graphene

Cited by 138 publications

References 34 publications

Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride

Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride

Theory of substrate, Zeeman, and electron-phonon interaction effects on the quantum capacitance in graphene

Valley order and loop currents in graphene on hexagonal boron nitride

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