Graphene quantum dots: Beyond a Dirac billiard

Abstract

We present realistic simulations of quantum confinement effects in ballistic graphene quantum dots with linear dimensions of 10 to 40 nm. We determine wavefunctions and energy level statistics in the presence of disorder resulting from edge roughness, charge impurities, or short-ranged scatterers. Marked deviations from a simple Dirac billiard for massless fermions are found. We find a remarkably stable dependence of the nearest-neighbor level spacing on edge roughness suggesting that the roughness of fabricated devices can be potentially characterized by the distribution of measured Coulomb blockade peaks.

5 figures, higher resolution available upon request

References in corpus (26)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Energy Band Gap Engineering of Graphene Nanoribbons
• Energy Gaps in Graphene Nanoribbons
• Chiral tunneling and the Klein paradox in graphene
• Electronic spin transport and spin precession in single graphene layers at room temperature
• Chaotic Dirac billiard in graphene quantum dots
• Graphene Nano-Ribbon Electronics
• Charged Impurity Scattering in Graphene
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin qubits in graphene quantum dots
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Phase Coherent Transport of Charges in Graphene Quantum Billiard
• Tunable Graphene Single Electron Transistor
• Conductance quantization in mesoscopic graphene
• Edge disorder induced Anderson localization and conduction gap in graphene nanoribbons
• Tunable Coulomb blockade in nanostructured graphene
• Conductance Quantization in Graphene Nanoribbons
• Quantum dot behavior in graphene nanoconstrictions
• Bound states and magnetic field-induced valley splitting in gate-tunable graphene quantum dots
• Symmetry Classes in Graphene Quantum Dots: Universal Spectral Statistics, Weak Localization, and Conductance Fluctuations
• Observation of excited states in a graphene quantum dot
• Analytic Model for the Energy Spectrum of a Graphene Quantum Dot in a Perpendicular Magnetic Field
• Transport gap in side-gated graphene constrictions
• Random Matrix Theory of a Chaotic Andreev Quantum Dot
• Electronic Structure of gated graphene and graphene ribbons

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• Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
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• Characterizing wave functions in graphene nanodevices: electronic transport through ultrashort graphene constrictions on a boron nitride substrate
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• Random matrices and quantum chaos in weakly-disordered graphene nanoflakes
• Graphene quantum dots in perpendicular magnetic fields
• Spectral properties of Dirac billiards at the van Hove singularities
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• Strain-induced transitions to quantum chaos and effective time-reversal symmetry breaking in triangular graphene nanoflakes
• Confined states in quantum dots defined within finite flakes of bilayer graphene: Coupling to the edge, ionization threshold, and valley degeneracy
• Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport
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• Graphene quantum dots probed by scanning tunneling spectroscopy and transport spectroscopy after local anodic oxidation
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