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Register a new userQuantum Hall Effect in Bilayer Graphene: Disorder Effect and Quantum Phase Transition
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We numerically study the quantum Hall effect (QHE) in bilayer graphene based on tight-binding model in the presence of disorder. Two distinct QHE regimes are identified in the full energy band separated by a critical region with non-quantized Hall Effect. The Hall conductivity around the band center (Dirac point) shows an anomalous quantization proportional to the valley degeneracy, but the $ u=0$ plateau is markedly absent, which is in agreement with experimental observation. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and higher plateaus disappear first. The central two plateaus around the band center are most robust against disorder scattering, which is separated by a small critical region in between near the Dirac point. The longitudinal conductance around the Dirac point is shown to be nearly a constant in a range of disorder strength, till the last two QHE plateaus completely collapse.
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We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two emph{distinct} quantum Hall effect (QHE) regimes exist in the energy band with the unconventional half-integer QHE appearing near the band center, consistent with the experimental observation. The latter is more robust against disorder scattering than the conventional QHE states near the band edges. The phase diagram for the unconventional QHE is obtained where the destruction of the Hall plateaus at strong disorder is through the float-up of extended levels toward band center and higher plateaus always disappear first. We further predict a new insulating phase between $ u =pm 2$ QHE states at the band center, which may explain the experimentally observed resistance discontinuity near zero gate voltage.
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.
We study an epitaxial graphene monolayer with bilayer inclusions via magnetotransport measurements and scanning gate microscopy at low temperatures. We find that bilayer inclusions can be metallic or insulating depending on the initial and gated carrier density. The metallic bilayers act as equipotential shorts for edge currents, while closely spaced insulating bilayers guide the flow of electrons in the monolayer constriction, which was locally gated using a scanning gate probe.
We measured the magnetoresistance of bilayer quantum Hall (QH) effects at the fractional filling factor $ u =2/3$ by changing the total electron density and the density difference between two layers. Three different QH states were separated by two types of phase transition: One is the spin transition and the other is the pseudospin transition. In addition, two different hystereses were detected, one of which is specific to bilayer systems. The phase transitions and the hystereses are described well by a composite fermion model extended to a bilayer system.
When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is an ideal realization of such a 2D system. Here, we report an experimental investigation of magneto transport in a high mobility single layer of graphene. Adjusting the chemical potential using the electric field effect, we observe an unusual half integer QHE for both electron and hole carriers in graphene. Vanishing effective carrier masses is observed at Dirac point in the temperature dependent Shubnikov de Haas oscillations, which probe the relativistic Dirac particle-like dispersion. The relevance of Berrys phase to these experiments is confirmed by the phase shift of magneto-oscillations, related to the exceptional topology of the graphene band structure.
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