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

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

3. Shameless Advertisement: Section: Z16
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)
Moura and Lyra, PRL (1998)
Shameless Advertisement: Section: Z16
Petersen and Sandler (To be submitted)
Greg M. Petersen

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

5. Recursive Green's Function Method
Lead
Conductor
Lead
Also get DOS
Klimeck (2004)
Greg M. Petersen

6. Square Ribbon All Localized Greg M. Petersen Greg M. Petersen
W/t = 0.5
L =
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 =
Black: UC
E/t = 0
E/t = 1
E/t = 2
Greg M. Petersen

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

10. Thank you for your attention!
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