Dependence of quantum-Hall conductance on the edge-state equilibration position in a bipolar graphene sheet (original) (raw)

Quantum Hall conductance of two-terminal graphene devices

Physical Review B, 2009

Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including N-shaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.

Quantum Hall Effect in a Gate-Controlled p-n Junction of Graphene

Science, 2007

The unique band structure of graphene allows reconfigurable electric-field control of carrier type and density, making graphene an ideal candidate for bipolar nanoelectronics. We report the realization of a single-layer graphene p-n junction in which carrier type and density in two adjacent regions are locally controlled by electrostatic gating. Transport measurements in the quantum Hall regime reveal new plateaus of two-terminal conductance across the junction at 1 and 3 /2 times the quantum of conductance, e 2 /h, consistent with recent theory. Beyond enabling investigations in condensed-matter physics, the demonstrated local-gating technique sets the foundation for a future graphene-based bipolar technology.

Quantum Hall resistances of a multiterminal top-gated graphene device

Physical Review B, 2009

Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams et al., Science 317, 638 (2007); B.Özyilmaz et al., Phys. Rev. Lett. 99, 166804 (2007)], asymmetric QH resistances are observed, which provide information on reflection as well as transmission of the QH edge states. Most quantized values of resistances are well analyzed by the assumption that all edge states are equally populated. Contrary to the expectation, however, a 5/2 transmission of the edge states is also found, which may be caused by incomplete mode mixing and/or by the presence of counter-propagating edge states. This four-terminal scheme can be conveniently used to study the edge-state equilibration in locally gated graphene devices as well as mono-and multi-layer graphene hybrid structures.

Emergence of helical edge conduction in graphene at the ν = 0 quantum Hall state

Physical Review B, 2016

The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt-angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) ν = 0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field theoretical description of the low-energy excitations, associated with quantum fluctuations of the spin-valley domain wall ground-state configuration which characterizes the two-dimensional (2D) system with an edge. This analysis yields a model describing a onedimensional charged edge mode coupled to charge-neutral spin-wave excitations in the 2D bulk. Focusing particularly on the FM phase, naively expected to exhibit perfect conductance, we study a mechanism whereby the coupling to these bulk excitations assists in generating back-scattering. Our theory yields the conductance as a function of temperature and the Zeeman energy-the parameter that tunes the transition between the FM and CAF phases-with behavior in qualitative agreement with experiment.

Observation of chiral quantum-Hall edge states in graphene

Applied Physics Letters, 2009

In this study, we determined the chiral direction of the quantum-Hall (QH) edge states in graphene by adopting simple two-terminal conductance measurements while grounding different edge positions of the sample. The edge state with a smaller filling factor is found to more strongly interact with the electric contacts. This simple method can be conveniently used to investigate the chirality of the QH edge state with zero filling factor in graphene, which is important to understand the symmetry breaking sequence in high magnetic fields ( 25 T).

Valley-isospin dependence of the quantum Hall effect in a graphene p-n junction

Physical Review B, 2007

We calculate the conductance G of a bipolar junction in a graphene nanoribbon, in the highmagnetic field regime where the Hall conductance in the p-doped and n-doped regions is 2e 2 /h. In the absence of intervalley scattering, the result G = (e 2 /h)(1 − cos Φ) depends only on the angle Φ between the valley isospins (= Bloch vectors representing the spinor of the valley polarization) at the two opposite edges. This plateau in the conductance versus Fermi energy is insensitive to electrostatic disorder, while it is destabilized by the dispersionless edge state which may exist at a zigzag boundary. A strain-induced vector potential shifts the conductance plateau up or down by rotating the valley isospin.

Theory of the quantum Hall effect in graphene

We study the quantum Hall effect (QHE) in graphene based on the current injection model. In our model, the presence of disorder, the edge-state picture, extended states and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics.

Theory of the quantum Hall effect in finite graphene devices

Physical Review B, 2010

Bilayer-induced asymmetric quantum Hall effect in epitaxial graphene

The transport properties of epitaxial graphene on SiC(0001) at quantizing magnetic fields are investigated. Devices patterned perpendicularly to SiC terraces clearly exhibit bilayer inclusions distributed along the substrate step edges. We show that the transport properties in the quantum Hall regime are heavily affected by the presence of bilayer inclusions, and observe a significant departure from the conventional quantum Hall characteristics. A quantitative model involving enhanced inter-channel scattering mediated by the presence of bilayer inclusions is presented that successfully explains the observed symmetry properties.

Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene

Nature Physics, 2006

T here are two known distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems 1,2 , and the other is its relativistic counterpart observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase π, which results in shifted positions of the Hall plateaus 3-9 . Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and show Berry's phase 2π affecting their quantum dynamics. The Landau quantization of these fermions results in plateaus in Hall conductivity at standard integer positions, but the last (zero-level) plateau is missing. The zero-level anomaly is accompanied by metallic conductivity in the limit of low concentrations and high magnetic fields, in stark contrast to the conventional, insulating behaviour in this regime. The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies. provides a schematic overview of the quantum Hall effect (QHE) behaviour observed in bilayer graphene by comparing it with the conventional integer QHE. In the standard theory, each filled single-degenerate Landau level contributes one conductance quantum e 2 /h towards the observable Hall conductivity (here e is the electron charge and h is Planck's constant). The conventional QHE is shown in , where plateaus in Hall conductivity σ xy make up an uninterrupted ladder of equidistant steps. In bilayer graphene, QHE plateaus follow the same ladder but the plateau at zero σ xy is markedly absent . Instead, the Hall conductivity undergoes a double-sized step across this region. In addition, longitudinal conductivity σ xx in bilayer graphene remains of the order of e 2 /h, even at zero σ xy . The origin of the unconventional QHE behaviour lies in the coupling between two graphene layers, which transforms massless Dirac fermions, characteristic of single-layer graphene 3-9 , into a new type of chiral quasiparticle. Such quasiparticles have an ordinary parabolic spectrum ε(p) = p 2 /2m with effective mass m, but

Dependence of quantum-Hall conductance on the edge-state equilibration position in a bipolar graphene sheet (original) (raw)

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