Mobilities and scattering times in decoupled graphene monolayers

Schmidt, Hennrik; Lüdtke, T.; Barthold, P.; Haug, Rolf J.

doi:10.1103/physrevb.81.121403

Cited by 46 publications

(56 citation statements)

References 21 publications

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“…In fact, if planar regions in our tubes exist, the interlayer coupling is strongly decreased probably due to incommensurate stacking. This reduction in the interlayer coupling was also observed in twisted graphene [114].…”

Section: Chapter 5 Results Obtained At Room Temperaturesupporting

confidence: 48%

Conductivity of multiwall carbon nanotubes: Role of multiple shells and defects

2010

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Section: Chapter 5 Results Obtained At Room Temperaturesupporting

confidence: 48%

Conductivity of multiwall carbon nanotubes: Role of multiple shells and defects

2010

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Section: Introductionmentioning

confidence: 99%

“…The sequence demonstrates that interlayer coupling is too weak to split the layer degeneracy. We conclude that the twist angle is large enough to model the system as two monolayer graphene sheets conducting in parallel (26,27).In low-disorder samples, electron exchange interactions can break the graphene spin-valley degeneracy, leading to quantum Hall ferromagnetism (28-30). We indeed observe such degeneracy breaking at higher field as a sequence of plateaus at all integer multiples of e 2 /h from -4 to 4 (B = 4 T, Figure 1E).…”

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Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

et al. 2016

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†These authors contributed equally to this work. AbstractA quantum Hall edge state provides a rich foundation to study electrons in 1-dimension (1d) but is limited to chiral propagation along a single direction. Here, we demonstrate a versatile platform to realize new 1d systems made by combining quantum Hall edge states of opposite chiralities in a graphene electron-hole bilayer. Using this approach, we engineer helical 1d edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong nonlocal transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Moreover, we investigate these electron-hole bilayers in the fractional quantum Hall regime, where we observe conduction through fractional and integer edge states of opposite chiralities, paving the way towards the realization of 1d helical systems with fractional quantum statistics.A helical 1d conductor is an unusual electronic system where forward and backward moving electrons have opposite spin polarizations. Theoretically, a helical state can be realized by combining two quantum Hall edge states with opposite chiralities and opposite spin polarizations (1,2). Most experimental efforts though have focused on materials with strong spin-orbit coupling(3-5), which avoids the need for magnetic fields. However, an approach based on quantum Hall edge states offers greater flexibility in system design with less dependence on material parameters. Moreover, a quantum Hall platform could harness the unique statistics of fractional quantum Hall states. Recent proposals have predicted that such a system, in the form of a fractional quantum spin Hall state(6-8), could host fractional generalizations of Majorana bound states.To simultaneously realize two quantum Hall states with opposite chiralities, it is necessary to have coexisting electron-like and hole-like bands. Such electron-hole quantum Hall states are observed in semi-metals but suffer from low hole-mobilities (9, 10). In this respect, graphene is an attractive system because it has high carrier mobilities and is electron-hole symmetric. In fact, the graphene electron and hole bands can be inverted by the Zeeman effect to realize helical states (11,12), but requires very large magnetic fields (13,14). A similar outcome could be realized more easily in a bilayer system, where an electric field can dope one layer into the electron band and the other into the hole band. In a moderate magnetic field, this electronhole bilayer will develop quantum Hall edge states with opposite chiralities in each layer. Here, we demonstrate a graphene electron-hole bilayer, which we use to realize a helical 1-dimensional conductor made from quantum Hall edge states.All studied devices consist of two monolayer graphene flakes stacked together using a dry transfer process (15,16). The stacking results in a rotational misalignment, or twist, between the layers. The domin...

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“…By engineering the substrate underlying exfoliated samples [3][4][5], identifying exfoliated fragments with folds [6], or controlling epitaxial growth conditions [7,8], the size and shape of the honeycomb lattice arrays [9,10] and the number of graphene layers and their orientations can all be varied. This structural diversity nourishes hopes for a future carbon-based electronics [11] with band-structure and transport characteristics that can be tailored for different types of applications.…”

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confidence: 99%

Transport between twisted graphene layers

2010

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Commensurate-incommensurate transitions are ubiquitous in physics and are often accompanied by intriguing phenomena. In few-layer graphene (FLG) systems, commensurability between honeycomb lattices on adjacent layers is regulated by their relative orientation angle θ, which is in turn dependent on sample preparation procedures. Because incommensurability suppresses inter-layer hybridization, it is often claimed that graphene layers can be electrically isolated by a relative twist, even though they are vertically separated by a fraction of a nanometer. We present a theory of interlayer transport in FLG systems which reveals a richer picture in which the specific conductance depends sensitively on θ, single-layer Bloch state lifetime, in-plane magnetic field, and bias voltage. We find that linear and differential conductances are generally large and negative near commensurate values of θ, and small and positive otherwise.Experimental advances in the fabrication of graphenebased structures [1,2] have now provided researchers with a multitude of systems that have strikingly distinct electronic properties. By engineering the substrate underlying exfoliated samples [3][4][5], identifying exfoliated fragments with folds[6], or controlling epitaxial growth conditions [7,8], the size and shape of the honeycomb lattice arrays [9,10] and the number of graphene layers and their orientations can all be varied. This structural diversity nourishes hopes for a future carbon-based electronics[11] with band-structure and transport characteristics that can be tailored for different types of applications.FLG has advantages over single-layer-graphene because it has a larger current-carrying capacity and because its electronic properties are sensitive to more engineerable system parameters [12]. In nature it appears in a variety of stacking arrangements, the most common being Bernal and rhombohedral sequences which can form three dimensional lattices. It has been understood for some time [13] [16]. The present work is motivated primarily by the need to achieve a more complete understanding of transport in these graphitic nanostructures, which currently appear to provide the most promising platform for applications.In a bilayer system, the relative rotation angle θ can be classified as either commensurate or incommensurate [17]. In the former case the misaligned bilayer system still forms a crystal, albeit one with larger lattice vectors and more than four atoms per unit cell. Commensurability occurs at a countably infinite set of orientations; but the probability that a randomly selected orientation angle is commensurate vanishes. The energy bands of commensurate twisted multilayers disperse approximately linearly with momentum [18][19][20], except at energies very close to the Dirac point. However, the Dirac velocity is reduced FIG. 1: Interlayer (RC) equilibration rate as a function of twist angle θ. These results were calculated for two layers with equal carrier densities (n = 5 × 10 12 cm −2 ) and ǫFτ = 3, where ǫF is the Fermi e...

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Mobilities and scattering times in decoupled graphene monolayers

Cited by 46 publications

References 21 publications

Conductivity of multiwall carbon nanotubes: Role of multiple shells and defects

Conductivity of multiwall carbon nanotubes: Role of multiple shells and defects

Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

Transport between twisted graphene layers

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