Power-Law Correlated Disorder in Graphene and

Square Nanoribbons

Greg M. PetersenNancy Sandler

Ohio UniversityDepartment of Physics and Astronomy

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)

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)

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Section: Z16

Cain et al. EPL (2011)

Abrahams et al. PRL (1979)Johnston and Kramer Z Phys. B (1986)

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 }

Recursive Green's Function Method

Greg M. Petersen

Also get DOSKlimeck http://nanohub.org/resources/165 (2004)

Lead LeadConductor

Square Ribbon

Greg M. PetersenGreg M. PetersenAll Localized

W/t = 0.5

L = 27-211

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)

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

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

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