power-law correlated disorder in graphene and square nanoribbons
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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)
Shameless Advertisement:
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