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      Etched graphene quantum dots on hexagonal boron nitride

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          Abstract

          We report on the fabrication and characterization of etched graphene quantum dots (QDs) on hexagonal boron nitride (hBN) and SiO2 with different island diameters. We perform a statistical analysis of Coulomb peak spacings over a wide energy range. For graphene QDs on hBN, the standard deviation of the normalized peak spacing distribution decreases with increasing QD diameter, whereas for QDs on SiO2 no diameter dependency is observed. In addition, QDs on hBN are more stable under the influence of perpendicular magnetic fields up to 9T. Both results indicate a substantially reduced substrate induced disorder potential in graphene QDs on hBN.

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          Chaotic Dirac billiard in graphene quantum dots

          We report on transport characteristics of quantum dot devices etched entirely in graphene. At large sizes, they behave as conventional single-electron transistors, exhibiting periodic Coulomb blockade peaks. For quantum dots smaller than 100 nm, the peaks become strongly non-periodic indicating a major contribution of quantum confinement. Random peak spacing and its statistics are well described by the theory of chaotic neutrino (Dirac) billiards. Short constrictions of only a few nm in width remain conductive and reveal a confinement gap of up to 0.5eV, which demonstrates the in-principle possibility of molecular-scale electronics based on graphene.
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            Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps

            A continuum model for the effective spin orbit interaction in graphene is derived from a tight-binding model which includes the \(\pi\) and \(\sigma\) bands. We analyze the combined effects of the intra-atomic spin-orbit coupling, curvature, and applied electric field, using perturbation theory. We recover the effective spin-orbit Hamiltonian derived recently from group theoretical arguments by Kane and Mele. We find, for flat graphene, that the intrinsic spin-orbit coupling \(\Hi \propto \Delta^ 2\) and the Rashba coupling due to a perpendicular electric field \({\cal E}\), \(\Delta_{\cal E} \propto \Delta\), where \(\Delta\) is the intra-atomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term \(\Delta_{\rm curv} \propto \Delta\). For the values of \(\cal E\) and curvature profile reported in actual samples of graphene, we find that \(\Hi < \Delta_{\cal E} \lesssim \Delta_{\rm curv}\). The effect of spin-orbit coupling on derived materials of graphene, like fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only \(\Hi\) is important. Both for nanotubes and nanotube caps \(\Delta_{\rm curv}\) is in the order of a few Kelvins. We reproduce the known appearance of a gap and spin-splitting in the energy spectrum of nanotubes due to the spin-orbit coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the localized states at the cap, which could allow spin-dependent field-effect emission.
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              Transport gap in side-gated graphene constrictions

              We present measurements on side gated graphene constrictions of different geometries. We characterize the transport gap by its width in back gate voltage and compare this to an analysis based on Coulomb blockade measurements of localized states. We study the effect of an applied side gate voltage on the transport gap and show that high side gate voltages lift the suppression of the conductance. Finally we study the effect of an applied magnetic field and demonstrate the presence of edge states in the constriction.
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                Author and article information

                Journal
                09 August 2013
                Article
                10.1063/1.4818627
                1308.2161
                88785249-f099-4c23-bd3e-13dbf6ff29b2

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Appl. Phys. Lett. 103, 073113 (2013)
                cond-mat.mes-hall

                Nanophysics
                Nanophysics

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