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Power-Law Correlated Disorder in Graphene and Square Nanoribbons

Power-Law Correlated Disorder in Graphene and Square Nanoribbons. Greg M. Petersen Nancy Sandler Ohio University Department of Physics and Astronomy. Disorder in Graphene. Real Disordered Materials Have Correlations. Scattering Mechanisms:. Neutral Absorbents. Neutral Absorbents.

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Power-Law Correlated Disorder in Graphene and Square Nanoribbons

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  1. Power-Law Correlated Disorder in Graphene and Square Nanoribbons Greg M. Petersen Nancy Sandler Ohio University Department of Physics and Astronomy

  2. Disorder in Graphene Real Disordered Materials Have Correlations Scattering Mechanisms: Neutral Absorbents Neutral Absorbents Lijie Ci et al. Nature Mat. (2010) Ripples Strain/Shear Vacancies Topological defects Coulomb Impurities Greg M. Petersen

  3. 1D Anderson Transition? Evidence For Evidence Against Dunlap, Wu, and Phillips, PRL (1990) Abrahams et al. PRL (1979) Johnston and Kramer Z Phys. B (1986) Kotani and Simon, Commun. Math. Phys (1987) García-García and Cuevas, PRB (2009) Cain et al. EPL (2011) Shameless Advertisement:Section: Z16 Moura and Lyra, PRL (1998) Petersen and Sandler (To be submitted) Greg M. Petersen

  4. Introducing Long-Range Disorder α=.1 uncorrelated α=.5 Generation Method: 1. Find spectral density 2. Generate { V(k) } from gaussian with variance S(k) 3. Apply conditions V(k) = V*(-k) 4. Take inverse FT to get { Єi } α=1 Greg M. Petersen

  5. Recursive Green's Function Method Lead Conductor Lead Also get DOS Klimeck http://nanohub.org/resources/165 (2004) Greg M. Petersen

  6. Square Ribbon W/t = 0.5 L = 27-211 All Localized Greg M. Petersen Greg M. Petersen

  7. Zig-Zag Nanoribbons E~0 Zettl, et al. Science (2009) E~0 What role do long range-spatial correlations play?How are the edge states affected? Nakada, Fujita, PRB (1996) Mucciolo et al. PRB (2009) Greg M. Petersen

  8. Zig-Zag Ribbon: Conductance W/t = 0.1 L = 26-212 Black: UC E/t = 0 E/t = 1 E/t = 2 Greg M. Petersen

  9. Zig-Zag Ribbon W/t = 0.1 L = 212 ~14% change Black: UC /t /t Zarea and Sandler PRB (2009) ~50% change /t Greg M. Petersen

  10. Conclusions - We confirm single parameter scaling of the beta function for square ribbons and zig-zag ribbons - The density of states at E=0 is dependent on geometry and disorder Cain et al. EPL (2011) – no transition Petersen, Sandler (2012) - no transition Moura and Lyra, PRL (1998) - transition - Long Range Correlations are Not Sufficient for Anderson Transition in 1D Thank you for your attention! Greg M. Petersen

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