Limitations to Carrier Mobility and Phase-Coherent Transport in Bilayer Graphene

Engels, Stephan; Terrés, Bernat; Epping, Alexander; Khodkov, Tymofiy; Watanabe, Kenji; Taniguchi, Takashi; Beschoten, Bernd; Stampfer, Christoph

doi:10.1103/physrevlett.113.126801

Cited by 64 publications

(79 citation statements)

References 43 publications

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“…3e) preventing a more precise estimation. Such a large length scale agrees reasonably well with recent study on inter-valley scattering 21,22 , and is also consistent with the areal density of atomic defects (12.05 m -2 ) found in Kish graphite 23 , which is the same type of specimen used in this study.The observation of a giant nonlocal response in the middle of the energy gap in insulating BLG was unexpected. Although midgap helical edge sates in 2D quantum spin Hall systems can support long-range nonlocal conduction [24][25][26] , such spin helical edge states did not exist in our study because BLG is topologically trivial.…”

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confidence: 79%

“…The valley current in BLG decreases through intervalley scattering, which requires a large momentum transfer (e.g., by atomic scale disorders). Such disorders are found to be Page 8 of 16 extremely rare in cleaved BLG crystals 19,20 , implying a large valley diffusion length 21,22 . In the present study, an appreciable nonlocal signal was observed in samples up to 10 m long.…”

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confidence: 99%

“…extremely rare in cleaved BLG crystals 19,20 , implying a large valley diffusion length 21,22 . In the present study, an appreciable nonlocal signal was observed in samples up to 10 m long.…”

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Gate-tunable topological valley transport in bilayer graphene

et al. 2015

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Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands 1 , is a distinct feature of two-dimensional Dirac materials [1][2][3][4][5] . Similar to spin, the valley pseudospin is spanned by a time reversal pair of states, though the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interests [2][3][4][5] . Bilayer graphene (BLG) is a unique system whose intrinsic inversion symmetry can be controllably broken by a perpendicular electric field, offering a rare possibility for continuously tunable valley-topological transport. Here, we used a perpendicular gate electric field to break the inversion symmetry in BLG, and a giant nonlocal response was observed as a result of the topological transport of the valley pseudospin. We further showed that the valley transport is fully tunable by external gates, and that the nonlocal signal persists up to room temperature and over long distances. These observations challenge contemporary understanding of topological transport in a gapped system, and the robust topological transport may lead to future valleytronic applications.In crystalline solids, a topological current can be induced by the Berry phase of the electronic wave function 6 . Examples include the quantum Hall current in a magnetic field, and the spin Hall current arising from spin-orbit coupling. Such topological transport is robust against impurities and defects in materials -a feature that is much sought after in potential electronic applications. In such applications, the ability to switch and to continuously tune the topological transport is crucial. The topological current is in principle dictated by the crystal symmetry, which is difficult to change in Page 3 of 16 bulk materials. Bilayer graphene, however, offer new opportunities in which inversion symmetry can be controllably broken by an external electric field in the perpendicular direction.The topological current controlled by the inversion symmetry breaking is associated with carriers' valley pseudospin, which characterises the two-fold degenerate band-edges located at the corners of the hexagonal Brillouin zone. The topological Hall current, odd under time-reversal but even under inversion, is strictly zero in pristine mono-and bi-layer graphene which respect both symmetries. When the inversion symmetry is broken, however, time-reversal symmetry requires the Hall currents to have opposite signs and equal magnitudes in the two valleys (i.e., a valley The nonlocal transport persists up to room temperature and over long distances (up to 10 m). Our results represent major progress in the quest for a robust, tunable valley pseudospin system among various alternatives [3][4][5]11,12 , and indicate the possibility of using the nonlocal topological transport in practical applications under ambient conditio...

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Gate-tunable topological valley transport in bilayer graphene

et al. 2015

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“…In general, Rj of the kink states ranges from 40 to 100 kΩ, which corresponds to a mean free path (MFP) of k = 70-200 nm using the Landauer-Büttiker formula = 0 (1 + / k ) (1), where R0 = h/4e 2 = 6.5 kΩ is the ballistic resistance limit of the 4-fold degenerate kink states and L = 1 m is the junction length in device 1 24 . Although a small contact resistance (several kΩ) may originate from the electrode/kink interface (see Supplementary Section 5), the large value of Rj indicates significant backscattering, i.e.…”

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Gate-controlled topological conducting channels in bilayer graphene

et al. 2016

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The existence of inequivalent valleys K and K′ in the momentum space of two-dimensional hexagonal lattices provides a new electronic degree of freedom, the manipulation of which can potentially lead to new types of electronics, in analogy to the role played by electron spin 1-3 . In materials with broken inversion symmetry, such as an electrically gated bilayer graphene 4,5 , the momentum-space Berry curvature  carries opposite sign in the K and K′ valleys. A sign reversal of  along an internal boundary of the sheet gives rise to counterpropagating one-dimensional conducting modes encoded with opposite valley indices. These metallic states are topologically protected against backscattering in the absence of valley-mixing scattering, and thus can carry current ballistically 1,6-11 . In bilayer graphene, the reversal of  can occur at the domain wall of AB and BA stacked domains 12-14 , or at the line junction of two oppositely gated regions 6 . The latter approach can provide a scalable platform to implement valleytronic operations such as valves and waveguides 9,15 , but is technically challenging to realize. Here we fabricate a dual-split-gate structure in bilayer graphene and demonstrate transport evidence of the predicted metallic states. They possess a mean free path of up to a few hundred nanometers in the absence of a magnet field. The application of perpendicular magnetic field suppresses backscattering significantly and enables a 400-nanometer-long junction to exhibit conductance close to the ballistic limit of 4 e 2 /h at 8 Tesla. Our experiment paves the path to the realization of gate-controlled ballistic valley transport and the development of valleytronic applications in atomically thin materials.Exploiting the valley degree of freedom in hexagonal lattices may offer an alternative pathway to achieving low-power-consumption electronics. Experiments have shown that a net valley polarization in the material can be induced by the use of circularly polarized light 2,16,17 or a net bulk current [18][19][20] . However the use of light is not always desirable in electronics and device proposals using bulk valley polarization often put stringent requirements on the size and edge orientation of the active area 3 . Alternatively, electrically created, valley-polarized topological conducting channels in high-mobility bilayer graphene may offer a robust, scalable platform to realize valleytronic operations 1,6,[8][9][10][11][12][13][14][15] . Figure 1a illustrates the dual-split-gating scheme proposed by Martin et al 6 , where an AB-stacked bilayer graphene (BLG) sheet is controlled by two pairs of top and bottom gates separated by a line junction. The device operates in the regime where both the left and the right regions of the BLG sheet are insulating due to a bulk band gap induced by the independently applied displacement fields DL and DR. In the "odd" field configuration, where DLDR < 0, theory predicts the existence of eight conducting modes (referred to as the "kink" states) propagating along the line ...

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“…The phase coherence length at T = 1.7 K is estimated to be on the order of the device size, but it falls off with 1/T . 16 The above discussed oscillations can be reproduced by transport calculations for an ideal SLG p-n junction at an intermediate magnetic field B, based on the scalable tight-binding model 17 . The ideal junction is modeled by connecting two semi-infinite graphene ribbons (oriented along armchair) with their carrier densities given by n L in the far left and n R in the far right.…”

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Oscillating Magnetoresistance in Graphene p–n Junctions at Intermediate Magnetic Fields

et al. 2017

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We report on the observation of magnetoresistance oscillations in graphene p-n junctions. The oscillations have been observed for six samples, consisting of single-layer and bilayer graphene, and persist up to temperatures of 30 K, where standard Shubnikov-de Haas oscillations are no longer discernible. The oscillatory magnetoresistance can be reproduced by tight-binding simulations. We attribute this phenomenon to the modulated densities of states in the n-and p-regions.p-n junctions are among the basic building blocks of any electronic circuit. The ambipolar nature of graphene provides a flexible way to induce p-n junctions by electrostatic gating. This offers the opportunity to tune the charge carrier densities in the n-and p-doped regions independently. The potential gradient across a p-n interface depends on the thickness of the involved insulators and can also be modified by appropriate gate voltages. Due to the high electronic quality of present day graphene devices a number of transport phenomena in pnp or npn junctions have been reported, such as ballistic Fabry-Pérot oscillations 1-3 and so-called snake states 4,5 , both of which depend on characteristic length scales of the sample.Here we report on the discovery of yet another kind of oscillation, which does not depend on any such length scale. The oscillations occur in the bipolar regime, in the magnetic field range where Shubnikov-de Haas oscillations are observed in the unipolar regime. These novel oscillations in the bipolar regime are governed by the unique condition that the distance between two resistance minima (or maxima) in gate voltage space is given by a constant filling factor difference of ∆ν = 8. The features are remarkably robust: they occur in samples with one and two p-n interfaces; in single and bilayer graphene; up to temperatures of 30 K (where Shubnikovde Haas oscillations have long disappeared); over a large density range; for interface lengths ranging from 1 µm to 3 µm and in both pnp and npn regimes. match the periodicity of the aforementioned snake states. In this paper we address this phenomenon and suggest a model which can qualitatively explain the oscillations. Measurements were performed on six samples in total, which all consist of a graphene flake encapsulated between two hexagonal boron nitride (h-BN) flakes on a Si/SiO 2 substrate. They all show similar behavior. This paper focuses on measurements performed on one sample (sample A), with the device geometry sketched in Fig. 1a. Specifications of the other five samples are summarized in table I. The bilayer graphene (BLG) flake was encapsulated with the dry transfer technique described in Ref. 6. A top gate was evaporated on the middle part of the sample, which divides the device into two outer regions, only gated by the back gate (single-gated regions), and the dual-gated middle region. The other five samples were made with the more recent van der Waals pick-up technique. 7 Unless stated otherwise, the measurements were performed at 1.7 K. An AC voltage bias of 50 µ...

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Limitations to Carrier Mobility and Phase-Coherent Transport in Bilayer Graphene

Cited by 64 publications

References 43 publications

Gate-tunable topological valley transport in bilayer graphene

Gate-tunable topological valley transport in bilayer graphene

Gate-controlled topological conducting channels in bilayer graphene

Oscillating Magnetoresistance in Graphene p–n Junctions at Intermediate Magnetic Fields

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