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Revisiting the Anderson Model with Power-Law Correlated Disorder in 1D

Revisiting the Anderson Model with Power-Law Correlated Disorder in 1D. Greg M. Petersen Nancy Sandler Ohio University Department of Physics and Astronomy. Motivation: New Low-D Materials. Hexagonal Sp2 hybridized A = .250 nm Eg ~ 5.9 eV Mob = 200 cm 2 /Vs. =. +. Graphene.

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Revisiting the Anderson Model with Power-Law Correlated Disorder in 1D

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  1. Revisiting the Anderson Model with Power-Law Correlated Disorder in 1D Greg M. Petersen Nancy Sandler Ohio University Department of Physics and Astronomy

  2. Motivation: New Low-D Materials Hexagonal Sp2 hybridized A = .250 nm Eg ~ 5.9 eV Mob = 200 cm2/Vs = + Graphene Boron-Nitride Hexagonal Sp2 hybridized A = .246 nm Eg = 0 Mob ~ 15,000 cm2/Vs Lijie Ci et al. Nature Mat. (2010) What role do spatial correlations play in this system? Geim, Novoselov, PNAS (2005) Greg M. Petersen

  3. The Model α=.1 uncorrelated α=.5 α=1 De Moura and Lyra, PRL (1998) Numerically obtain eigenvalues AND eigenstates. Greg M. Petersen

  4. Participation Ratio Thouless, Phys. Rep. (1970) Greg M. Petersen

  5. Participation Ratio Mobility Edge Transition at α = 1 Greg M. Petersen

  6. Wavepacket Diffusion and Critical Exponents Sandler et. al., PRB (2003) Plateaus in the data are related to the critical exponent. Greg M. Petersen

  7. Wavepacket Diffusion and Critical Exponents N = 1000 α = 1 ?? Greg M. Petersen

  8. Wavepacket Diffusion and Critical Exponents Extended Harris Criterion Weinrib and Halperin, PRB (1983) Some localization All localized Results qualitatively agree Greg M. Petersen

  9. Conclusions - We confirm theoretical predictions that a transition occurs at α = 1 for 1D spatially correlated systems. - For α < 1, we find a mobility edge. - For α > 1, all states are localized. - We find partial agreement with the extended Harris criterion. Thank you for your attention! Greg M. Petersen

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