Power-Law Correlated Disorder in Graphene and Square Nanoribbons
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Power-Law Correlated Disorder in Graphene and
Square Nanoribbons
Greg M. PetersenNancy Sandler
Ohio UniversityDepartment of Physics and Astronomy
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Disorder in Graphene
Greg M. Petersen
Neutral Absorbents
Scattering Mechanisms:
Ripples
Strain/Shear
Vacancies
Topological defects
Coulomb Impurities
Neutral Absorbents
Real Disordered Materials Have Correlations
Lijie Ci et al. Nature Mat. (2010)
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1D Anderson Transition?
Greg M. Petersen
Evidence For
Dunlap, Wu, and Phillips, PRL (1990)
Moura and Lyra, PRL (1998)
Evidence Against
Kotani and Simon, Commun. Math. Phys (1987)
García-García and Cuevas, PRB (2009)
Petersen and Sandler (To be submitted)
Shameless Advertisement:
Section: Z16
Cain et al. EPL (2011)
Abrahams et al. PRL (1979)Johnston and Kramer Z Phys. B (1986)
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Introducing Long-Range Disorder
α=.1
α=.5
α=1
uncorrelated
Greg M. Petersen
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 { Є
i }
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Recursive Green's Function Method
Greg M. Petersen
Also get DOSKlimeck http://nanohub.org/resources/165 (2004)
Lead LeadConductor
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Square Ribbon
Greg M. PetersenGreg M. PetersenAll Localized
W/t = 0.5
L = 27-211
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Zig-Zag Nanoribbons
Greg M. Petersen
E~0
E~0
Nakada, Fujita, PRB (1996)
What role do long range-
spatial correlations
play?
How are the edge states affected?
Zettl, et al. Science (2009)
Mucciolo et al. PRB (2009)
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Zig-Zag Ribbon: Conductance
Greg M. Petersen
E/t = 1
E/t = 2
E/t = 0
Black: UC
W/t = 0.1
L = 26-212
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Zig-Zag Ribbon
Greg M. Petersen
/t
/t
/t
~14% change
~50% changeZarea and Sandler PRB (2009)
Black: UC
W/t = 0.1
L = 212
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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
Thank you for your attention!
Greg M. Petersen
- Long Range Correlations are Not Sufficient for Anderson Transition in 1D
Cain et al. EPL (2011) – no transition
Petersen, Sandler (2012)- no transition
Moura and Lyra, PRL (1998)- transition