Electrostatically Induced Quantum Point Contacts in Bilayer Graphene

Overweg, Hiske; Eggimann, Hannah J.; Chen, Xi; Slizovskiy, Sergey; Eich, Marius; Pisoni, Riccardo; Lee, Yongjin; Rickhaus, Peter; Watanabe, Kenji; Taniguchi, Takashi; Fal’ko, Vladimir I.; Ihn, Thomas; Ensslin, Klaus

doi:10.1021/acs.nanolett.7b04666

Cited by 116 publications

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“…The device was fabricated as described in Ref. [7]. Mechanically exfoliated bilayer graphene flakes are encapsulated in hexagonal boron nitride (hBN) and an additional few layer graphite flake serves as back gate.…”

Section: Device Fabricationmentioning

confidence: 99%

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts

et al. 2020

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We experimentally determine the energy spectrum of a quantum point contact realized by a suitable gate geometry in bilayer graphene. Using finite bias spectroscopy we measure the energy scales arising from the lateral confinement as well as the Zeeman splitting and find a spin g-factor gs ∼ 2. The valley g-factor is highly tunable by vertical electric fields, gv ∼ 40 − 120. The results are quantitatively explained by a calculation considering topological magnetic moment and its dependence on confinement and the vertical displacement field. arXiv:1911.05968v1 [cond-mat.mes-hall]

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Section: Device Fabricationmentioning

confidence: 99%

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts

et al. 2020

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“…In experiments, this single-particle gap is induced and tuned using dual-gated geometries. This has been exploited to define electrostatic nanostructures such as quantum point contacts [11,12] and quantum dots [13,14]. With its four layers, TDBG is thin enough that crystal fields matter.…”

Section: Introductionmentioning

confidence: 99%

Gap Opening in Twisted Double Bilayer Graphene by Crystal Fields

et al. 2019

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Crystal fields occur due to a potential difference between chemically different atomic species. In Van-der-Waals heterostructures such fields are naturally present perpendicular to the planes. It has been realized recently that twisted graphene multilayers provide powerful playgrounds to engineer electronic properties by the number of layers, the twist angle, applied electric biases, electronic interactions and elastic relaxations, but crystal fields have not received the attention they deserve.Here we show that the bandstructure of large-angle twisted double bilayer graphene is strongly modified by crystal fields. In particular, we experimentally demonstrate that twisted double bilayer graphene, encapsulated between hBN layers, exhibits an intrinsic bandgap. By the application of an external field, the gaps in the individual bilayers can be closed, allowing to determine the crystal fields. We find that crystal fields point from the outer to the inner layers with strengths in the bottom/top bilayer E b = 0.13 V/nm ≈ −Et = 0.12 V/nm. We show both by means of first principles calculations and low energy models that crystal fields open a band gap in the groundstate. Our results put forward a physical scenario in which a crystal field effect in carbon substantially impacts the low energy properties of twisted double bilayer graphene, suggesting that such contributions must be taken into account in other regimes to faithfully predict the electronic properties of twisted graphene multilayers. arXiv:1910.10524v2 [cond-mat.mes-hall] 4 Nov 2019 a c FIG. 1. a) Two twisted, AB-stacked bilayer graphene (BG) sheets. The electrostatic potential of the outer layers is different from the potential in the inner layers. This leads to crystal fields Et = −E b pointing in opposite direction in the top and bottom BG. In the experiment, the two bilayer systems are encapsulated in hBN which reduces the strength of the crystal fields compared to vacuum. b) The TDBG band structure consists of Brillouin-zones of the top and bottom BG rotated with respect to each other. For large twist angles θ, the bands of the top and bottom layer intersect at energies large compared to the Fermi energies of the individual layers. Therefore, at typical Fermi energies, the individual BG band structures remain intact.The crystal fields open a single-particle gap in both layers. c) In such a structure we observe a gap at zero density and zero external field in a resistance versus density trace R(ntot). We show traces for two devices, device 1 is further discussed in the main text and further measurements of device 2 and device 3 are shown in the Supplemental Material.

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“…We model the observed interference pattern using tight-binding calculations assuming completely decoupled layers. This second experiment confirms the assumed electronic decoupling and, for arbitrary gate voltages, the electrostatic model that considers thick graphene.Methods In order to achieve ballistic transport, we encapsulate[17] either twisted bilayer graphene (sample B) or graphene-(3.5 nm hBN)-graphene between hBN layers (sample A) and use a graphite bottom gate [18,19]. The 3 a b −6 −4 −2 0 2 4 6 V tg (V) −10 −5 0 5 10 V bg (V) Sample B dG/dV tg −10 −5 0 5 10 −8 −4 0 4 8ε=6.9 c d e 8 10 12 14 16 18 ∆ρ (a.u.)…”

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“…Methods In order to achieve ballistic transport, we encapsulate[17] either twisted bilayer graphene (sample B) or graphene-(3.5 nm hBN)-graphene between hBN layers (sample A) and use a graphite bottom gate [18,19]. The 3 a b −6 −4 −2 0 2 4 6 V tg (V) −10 −5 0 5 10 V bg (V) Sample B dG/dV tg −10 −5 0 5 10 −8 −4 0 4 8…”

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confidence: 99%

The electronic thickness of graphene

et al. 2020

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The van-der-Waals stacking technique enables the fabrication of heterostructures, where two conducting layers are atomically close. In this case, the finite layer thickness matters for the interlayer electrostatic coupling. Here we investigate the electrostatic coupling of two graphene layers, twisted by θ = 22 • such that the layers are decoupled by the huge momentum mismatch between the K and K' points of the two layers. We observe a splitting of the zero-density lines of the two layers with increasing interlayer energy difference. This splitting is given by the ratio of single-layer quantum capacitance over interlayer capacitance Cm and is therefore suited to extract Cm. We explain the large observed value of Cm by considering the finite dielectric thickness dg of each graphene layer and determine dg ≈ 2.6Å. In a second experiment we map out the entire density range with a Fabry-Pérot resonator. We can precisely measure the Fermi-wavelength λ in each layer, showing that the layers are decoupled. We find that λ exceeds 600 nm at the lowest densities and can differ by an order of magnitude between the upper and lower layer. These findings are reproduced using tight-binding calculations. arXiv:1907.00582v1 [cond-mat.mes-hall] 1 Jul 2019 2 a b c d C hBN hBN 2xGraphene Graphite topgate C 2. 2μ m 2 . 3 μ m 3.5nm K b K' b θ K t K' t Sample A Sample B FIG. 1. a) Top-view and side-view of two aligned layers of graphene that are decoupled in the middle (blue part) by a thin intermediate layer of hBN. A graphite back gate and a local top gate allow to control the density and thereby the carrier wavelength in the upper-and lower layer individually. b) Using atomic force microscopy we measured the encapsulated hBN layer to be 3.5nm thick (sample A). c) Alternatively, the decoupling wavefunctions can be achieved by twisting two graphene layers (sample B). d) For large twist angles, the valleys in the upper/lower layer (Kt, K b ) are separated by a large momentum, leading to an effective electronic decoupling of the layers.The van-der-Waals stacking technique allows scientists to bring two conductive crystalline layers into atomically close proximity [1]. This has been exploited in a variety of experiments, including the formation of layer polarized, counter-propagating Landau levels [2] and experiments that build on strong capacitive coupling such as Coulomb-drag measurements [3] or interlayer exciton condensation [4,5].There are two main approaches of how to bring two conductive layers in close proximity, while suppressing an overlap of the layer wavefunctions: One approach introduces a thin layer of hexagonal Boron-Nitride (hBN) (see e.g. [3,4,6]) as depicted in Fig. 1a,b, and the other twists the layers by a large angle (θ > 5 • ) [2, 7-9]; see Fig. 1c,d. In the former case, decoupling is achieved by spatial separation. In the latter case, the layers are ultimately close, but they remain decoupled due to a large momentum mismatch (K t − K b ) between the upper and lower layer ( Fig. 1d). Experimental signatures of decoup...

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Electrostatically Induced Quantum Point Contacts in Bilayer Graphene

Cited by 116 publications

References 33 publications

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts

Gap Opening in Twisted Double Bilayer Graphene by Crystal Fields

The electronic thickness of graphene

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