Conformal Invariance and Shape-Dependent Conductance of Graphene Samples
arXiv:0804.4043 · doi:10.1103/PhysRevB.78.035416
Abstract
For a sample of an arbitrary shape, the dependence of its conductance on the longitudinal and Hall conductivity is identical to that of a rectangle. We use analytic results for a conducting rectangle, combined with the semicircle model for transport coefficients, to study properties of the monolayer and bilayer graphene. A conductance plateau centered at the neutrality point, predicted for square geometry, is in agreement with recent experiments. For rectangular geometry, the conductance exhibits maxima at the densities of compressible quantum Hall states for wide samples, and minima for narrow samples. The positions and relative sizes of these features are different in the monolayer and bilayer cases, indicating that the conductance can be used as a tool for sample diagnostic.
9 pages, 6 figures
References in corpus (14)
- Two-Dimensional Gas of Massless Dirac Fermions in Graphene
- The Raman Fingerprint of Graphene
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Energy Band Gap Engineering of Graphene Nanoribbons
- Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
- Graphene Nano-Ribbon Electronics
- Bipolar supercurrent in graphene
- Transport measurements across a tunable potential barrier in graphene
- Electronic transport and quantum Hall effect in bipolar graphene p-n-p junction
- Quantized Transport in Graphene p-n Junctions in Magnetic Field
- Dissipative Quantum Hall Effect in Graphene near the Dirac Point
- Charge and Spin Transport at the Quantum Hall Edge of Graphene
- Universal flow diagram for the magnetoconductance in disordered GaAs layers
- The Quantum Hall Effect in Graphene: Emergent Modular Symmetry and the Semi-circle Law
Cited by in corpus (44)
- Electronic transport in two dimensional graphene
- Observation of the Fractional Quantum Hall Effect in Graphene
- Electronic Properties of Graphene in a Strong Magnetic Field
- Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
- Stacking-Dependent Band Gap and Quantum Transport in Trilayer Graphene
- Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
- Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
- Transport and elastic scattering times as probes of the nature of impurity scattering in single and bilayer graphene
- Quantum Hall effect in graphene with superconducting electrodes
- Measurement of the ν= 1/3 fractional quantum Hall energy gap in suspended graphene
- Tunable quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene
- Observation of Supercurrent in PbIn-Graphene-PbIn Josephson Junction
- Magnetoconductance Oscillations in High-Mobility Suspended Bilayer and Trilayer Graphene
- Hall Effect Gyrators and Circulators
- Unveiling the Landau Levels Structure of Graphene Nanoribbons
- Limitations to Carrier Mobility and Phase-Coherent Transport in Bilayer Graphene
- Electrical Transport in High Quality Graphene pnp Junctions
- Reactive-Ion-Etched Graphene Nanoribbons on a Hexagonal Boron Nitride Substrate
- Transport through evanescent waves in ballistic graphene quantum dots
- Fractional Quantum Hall Effect in Suspended Graphene: Transport Coefficients and Electron Interaction Strength
- Quantum Hall resistances of multiterminal top-gated graphene device
- Integer and Fractional Quantum Hall Effect in Two-Terminal Measurements on Suspended Graphene
- Signatures of van Hove singularities probed by the supercurrent in a graphene - hBN superlattice
- Enhanced transport length of spin-helical Dirac fermions in disordered 3D topological insulators
- Aharonov-Bohm oscillations and magnetic focusing in ballistic graphene rings
- Field induced quantum-Hall ferromagnetism in suspended bilayer graphene
- Interface states and anomalous quantum oscillations in graphene hybrid structures
- Quantum Hall transport as a probe of capacitance profile at graphene edges
- Signatures of long-range-correlated disorder in the magnetotransport of ultrathin topological insulators
- Tailoring supercurrent confinement in graphene bilayer weak links
- Voltage Scaling of Graphene Device on SrTiO3 Epitaxial Thin Film
- Giant Hall photoconductivity in narrow-gapped Dirac materials
- Interplay between topological protected valley and quantum Hall edge transport
- Quantum oscillations observed in graphene at microwave frequencies
- Theoretical Aspects of the Fractional Quantum Hall Effect in Graphene
- Observation of chiral quantum-Hall edge states in graphene
- Signature of multilayer graphene strain-controlled domain walls in quantum Hall effect
- Dual top gated graphene transistor in the quantum Hall regime
- An RG potential for the quantum Hall effects
- Quantized multi-terminal resistances in ferromagnetic graphene p-n junctions
- Magnetoconductance Oscillations in Electron-hole Hybridization Gaps and Valley Splittings in Tetralayer Graphene
- Quasi--periodic supercurrent at quantum Hall transitions
- Fractional Quantum Hall plateaus in mosaic-like conductors
- Quantum Hall conductance of two-terminal graphene devices